{
  "sdk_version": "1.0.8a",
  "program": {
    "blocks": [
      {
        "block_id": "block.0000.prepare",
        "declaration_node_id": "declaration.block.0000.prepare",
        "invocation_node_id": "block.0000.prepare",
        "block_name": "prepare",
        "block_kind": "digital",
        "arguments": [],
        "logical_resources": [
          {
            "node_id": "resource.block.0000.prepare.q0",
            "syntax_node_id": "resource.block.0000.prepare.q0",
            "logical_id": "q0",
            "resource_kind": "qubit",
            "source_span": null,
            "schema_version": "cascaqit.syntax.v1"
          },
          {
            "node_id": "resource.block.0000.prepare.q1",
            "syntax_node_id": "resource.block.0000.prepare.q1",
            "logical_id": "q1",
            "resource_kind": "qubit",
            "source_span": null,
            "schema_version": "cascaqit.syntax.v1"
          }
        ],
        "mapping": {
          "q0": "q0",
          "q1": "q1"
        },
        "required_capabilities": [],
        "source_span": null,
        "metadata": {
          "payload_hash": "ca95b220535a1b46799444e30e2fd11020b92f47c29d468e415f18f8296abaa9",
          "payload_owned": true,
          "payload_parameter_names": []
        },
        "schema_version": "cascaqit.orchestration.v1"
      },
      {
        "block_id": "block.0001.evolve",
        "declaration_node_id": "declaration.block.0001.evolve",
        "invocation_node_id": "block.0001.evolve",
        "block_name": "evolve",
        "block_kind": "analog",
        "arguments": [],
        "logical_resources": [
          {
            "node_id": "resource.block.0001.evolve.q0",
            "syntax_node_id": "resource.block.0001.evolve.q0",
            "logical_id": "q0",
            "resource_kind": "atom",
            "source_span": null,
            "schema_version": "cascaqit.syntax.v1"
          },
          {
            "node_id": "resource.block.0001.evolve.q1",
            "syntax_node_id": "resource.block.0001.evolve.q1",
            "logical_id": "q1",
            "resource_kind": "atom",
            "source_span": null,
            "schema_version": "cascaqit.syntax.v1"
          }
        ],
        "mapping": {
          "q0": "q0",
          "q1": "q1"
        },
        "required_capabilities": [],
        "source_span": null,
        "metadata": {
          "payload_hash": "441c906c64da5ca9ebfc4eeb5571bbb391d00362cd9b653d8d870d3dcf579d28",
          "payload_owned": true,
          "payload_parameter_names": []
        },
        "schema_version": "cascaqit.orchestration.v1"
      },
      {
        "block_id": "block.0002.readout_rotation",
        "declaration_node_id": "declaration.block.0002.readout_rotation",
        "invocation_node_id": "block.0002.readout_rotation",
        "block_name": "readout_rotation",
        "block_kind": "digital",
        "arguments": [],
        "logical_resources": [
          {
            "node_id": "resource.block.0002.readout_rotation.q0",
            "syntax_node_id": "resource.block.0002.readout_rotation.q0",
            "logical_id": "q0",
            "resource_kind": "qubit",
            "source_span": null,
            "schema_version": "cascaqit.syntax.v1"
          },
          {
            "node_id": "resource.block.0002.readout_rotation.q1",
            "syntax_node_id": "resource.block.0002.readout_rotation.q1",
            "logical_id": "q1",
            "resource_kind": "qubit",
            "source_span": null,
            "schema_version": "cascaqit.syntax.v1"
          }
        ],
        "mapping": {
          "q0": "q0",
          "q1": "q1"
        },
        "required_capabilities": [],
        "source_span": null,
        "metadata": {
          "payload_hash": "26745c8ba0f9351c6bed8064ca2534bdbb662d997ec0cfbdc0f25c9bbaa861d8",
          "payload_owned": true,
          "payload_parameter_names": []
        },
        "schema_version": "cascaqit.orchestration.v1"
      },
      {
        "block_id": "block.0003.measure",
        "declaration_node_id": "declaration.block.0003.measure",
        "invocation_node_id": "block.0003.measure",
        "block_name": "measure",
        "block_kind": "measurement",
        "arguments": [],
        "logical_resources": [
          {
            "node_id": "resource.block.0003.measure.q0",
            "syntax_node_id": "resource.block.0003.measure.q0",
            "logical_id": "q0",
            "resource_kind": "qubit",
            "source_span": null,
            "schema_version": "cascaqit.syntax.v1"
          },
          {
            "node_id": "resource.block.0003.measure.q1",
            "syntax_node_id": "resource.block.0003.measure.q1",
            "logical_id": "q1",
            "resource_kind": "qubit",
            "source_span": null,
            "schema_version": "cascaqit.syntax.v1"
          }
        ],
        "mapping": {
          "q0": "q0",
          "q1": "q1"
        },
        "required_capabilities": [],
        "source_span": null,
        "metadata": {
          "measurement_key": "result",
          "payload_owned": true
        },
        "schema_version": "cascaqit.orchestration.v1"
      }
    ],
    "dependencies": [],
    "metadata": {},
    "program_id": "project.noisy.hybrid",
    "schema_version": "cascaqit.orchestration.v1",
    "source_map": {
      "entries": [],
      "schema_version": "cascaqit.syntax.v1"
    },
    "syntax_hash": "0000000000000000000000000000000000000000000000000000000000000000"
  },
  "program_hash": "3ae12596e75deff789e526006cd6fad95bd8363cc46c441de4e19eaecd54aa05",
  "duration_us": 0.6,
  "omega_rad_per_us": 1.1,
  "local_detuning_rad_per_us": [
    0.7,
    0.175
  ],
  "dephasing_rate_per_us": 0.8,
  "readout_p01": 0.08,
  "readout_p10": 0.12,
  "shots_per_run": 128,
  "total_shots": 1152,
  "time_steps": 32,
  "rows": [
    {
      "case": "ideal",
      "seed": 4881,
      "counts": {
        "00": 72,
        "10": 7,
        "01": 48,
        "11": 1
      },
      "probabilities_before_readout": {
        "00": 0.5754896316901827,
        "01": 0.36395656142510147,
        "10": 0.05808150545784879,
        "11": 0.002472301426867029
      },
      "expected_recorded_probabilities": {
        "00": 0.5754896316901827,
        "01": 0.36395656142510147,
        "10": 0.05808150545784879,
        "11": 0.002472301426867029
      },
      "frequency_00": 0.5625,
      "observables": {
        "observable_set_hash": "dbdcda5c7aa312b23da7566b6bc7da5ac7b572b561161122735a2aeef6c5bbcc",
        "items": [
          {
            "observable": {
              "name": "Z(q0)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.8788923862305684,
            "variance": 0.22754817342593736,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "state_vector",
            "source_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
            "estimator_kind": "exact_state",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q1)",
              "terms": [
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.26714227429606296,
            "variance": 0.9286350052839271,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "state_vector",
            "source_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
            "estimator_kind": "exact_state",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q0)*Z(q1)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                },
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.15592386623409932,
            "variance": 0.9756877479386107,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "state_vector",
            "source_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
            "estimator_kind": "exact_state",
            "schema_version": "cascaqit.observables.v1"
          }
        ],
        "schema_version": "cascaqit.observables.v1"
      },
      "state_chain": [
        {
          "transition_id": "transition.0.block.0000.prepare",
          "order_index": 0,
          "block_id": "block.0000.prepare",
          "program_kind": "digital",
          "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
          "kernel": "NumpyDigitalStateVectorKernel",
          "input_state_hash": "a366dfecabfa70e226fc32395f74a800800f0dca5826459ff2c84dfbe7be5254",
          "output_state_hash": "6261624855ea775f2dda16925a5a04fd7e40ee305d577ef8d5cb9f75186a89fe",
          "input_logical_time": 0.0,
          "output_logical_time": 0.0,
          "time_unit": "us",
          "solver_evidence_hash": "e0aba1b5f620a1abc613f7065f8405f71f6e9b5d10ec348db9b3a2435fab8ff3",
          "metadata": {
            "logical_order": [
              "q0",
              "q1"
            ],
            "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
            "payload_id": "payload.0.block.0000.prepare.digital",
            "producer": "NumpyDigitalStateVectorKernel",
            "solver_evidence": {
              "absolute_tolerance": null,
              "accepted_steps": 0,
              "final_time": 0.0,
              "function_evaluations": null,
              "initial_time": 0.0,
              "integrator_requested": "fixed_step_krylov",
              "integrator_selected": "not_applicable",
              "max_step_size": null,
              "metadata": {
                "consumer": "NumpyDigitalStateVectorKernel"
              },
              "min_step_size": null,
              "rejected_steps": null,
              "rejected_steps_available": false,
              "relative_tolerance": null,
              "schema_version": "0.1",
              "segment_count": 0,
              "termination_reason": "not_applicable",
              "time_unit": "us",
              "tolerance_applied": false
            }
          },
          "schema_version": "0.1"
        },
        {
          "transition_id": "transition.1.block.0001.evolve",
          "order_index": 1,
          "block_id": "block.0001.evolve",
          "program_kind": "analog",
          "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
          "kernel": "MatrixFreeAnalogStateVectorKernel",
          "input_state_hash": "6261624855ea775f2dda16925a5a04fd7e40ee305d577ef8d5cb9f75186a89fe",
          "output_state_hash": "f57ede75fd1a1e60a8f4b07000fddb6029e3bc52921c5de0a3168cbcec976aec",
          "input_logical_time": 0.0,
          "output_logical_time": 0.6,
          "time_unit": "us",
          "solver_evidence_hash": "5a1200248280ce6c2f930a38df841189cc608e6ad109338d0a27c18b25706de3",
          "metadata": {
            "logical_order": [
              "q0",
              "q1"
            ],
            "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
            "payload_id": "payload.1.block.0001.evolve.analog",
            "producer": "MatrixFreeAnalogStateVectorKernel",
            "solver_evidence": {
              "absolute_tolerance": null,
              "accepted_steps": 32,
              "final_time": 0.6,
              "function_evaluations": null,
              "initial_time": 0.0,
              "integrator_requested": "fixed_step_krylov",
              "integrator_selected": "fixed_step_krylov",
              "max_step_size": 0.01875,
              "metadata": {
                "interaction_geometry_hash": "c8f7036b5efa5324fc28833aee66676e2832be11e92fc1375477e3da34d401b3",
                "interaction_geometry_source": "nominal_register",
                "interaction_maximum_abs_strength": 0.0,
                "interaction_minimum_distance": 5.0,
                "interaction_pair_count": 0,
                "interaction_pair_table_hash": "4f53cda18c2baa0c0354bb5f9a3ecbe5ed12ab4d8e11ba873c2f11161202b945",
                "interaction_plan_hash": "af6e015cdee51a687043495b129b6fc3d09f4c3455ebe536dd7c4daa8e5f54a2",
                "norm_before_normalization": 0.9999999999999981,
                "normalization_correction": 1.887379141862766e-15,
                "output_dtype": "complex128",
                "output_dtype_epsilon": 2.220446049250313e-16,
                "requested_tolerance_below_output_precision": false,
                "solver": "scipy.sparse.linalg.expm_multiply"
              },
              "min_step_size": 0.01875,
              "rejected_steps": null,
              "rejected_steps_available": false,
              "relative_tolerance": null,
              "schema_version": "0.1",
              "segment_count": 32,
              "termination_reason": "completed",
              "time_unit": "us",
              "tolerance_applied": false
            }
          },
          "schema_version": "0.1"
        },
        {
          "transition_id": "transition.2.block.0002.readout_rotation",
          "order_index": 2,
          "block_id": "block.0002.readout_rotation",
          "program_kind": "digital",
          "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
          "kernel": "NumpyDigitalStateVectorKernel",
          "input_state_hash": "f57ede75fd1a1e60a8f4b07000fddb6029e3bc52921c5de0a3168cbcec976aec",
          "output_state_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
          "input_logical_time": 0.6,
          "output_logical_time": 0.6,
          "time_unit": "us",
          "solver_evidence_hash": "19ce6d439071212a621eef9e16197494ef72777812369c752e8c2da41f550822",
          "metadata": {
            "logical_order": [
              "q0",
              "q1"
            ],
            "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
            "payload_id": "payload.2.block.0002.readout_rotation.digital",
            "producer": "NumpyDigitalStateVectorKernel",
            "solver_evidence": {
              "absolute_tolerance": null,
              "accepted_steps": 0,
              "final_time": 0.6,
              "function_evaluations": null,
              "initial_time": 0.6,
              "integrator_requested": "fixed_step_krylov",
              "integrator_selected": "not_applicable",
              "max_step_size": null,
              "metadata": {
                "consumer": "NumpyDigitalStateVectorKernel"
              },
              "min_step_size": null,
              "rejected_steps": null,
              "rejected_steps_available": false,
              "relative_tolerance": null,
              "schema_version": "0.1",
              "segment_count": 0,
              "termination_reason": "not_applicable",
              "time_unit": "us",
              "tolerance_applied": false
            }
          },
          "schema_version": "0.1"
        }
      ],
      "method": "state_vector",
      "resource_estimate": {
        "method": "state_vector",
        "logical_sites": 2,
        "hilbert_dimension": 4,
        "state_dimension": 4,
        "dtype": "complex128",
        "itemsize_bytes": 16,
        "trajectories": 1,
        "workers": 1,
        "state_bytes": 64,
        "operator_bytes": 128,
        "workspace_bytes": 1408,
        "worker_copy_bytes": 0,
        "sampling_bytes": 4096,
        "result_buffer_bytes": 4096,
        "estimated_peak_bytes": 9792,
        "schema_version": "cascaqit.simulation.planning.v1"
      },
      "options": {
        "method": "state_vector",
        "integrator": "fixed_step_krylov",
        "device": "auto",
        "dtype": "complex128",
        "max_memory_bytes": null,
        "memory_fraction": 0.8,
        "max_wall_time_seconds": null,
        "workers": "auto",
        "trajectories": 256,
        "target_statistical_error": null,
        "rtol": 1e-09,
        "atol": 1e-11,
        "max_steps": 32,
        "blockade_mode": "auto",
        "seed": 0,
        "metadata": {},
        "schema_version": "cascaqit.simulation.planning.v1"
      },
      "noise_model": null
    },
    {
      "case": "ideal",
      "seed": 4882,
      "counts": {
        "01": 45,
        "00": 72,
        "10": 10,
        "11": 1
      },
      "probabilities_before_readout": {
        "00": 0.5754896316901827,
        "01": 0.36395656142510147,
        "10": 0.05808150545784879,
        "11": 0.002472301426867029
      },
      "expected_recorded_probabilities": {
        "00": 0.5754896316901827,
        "01": 0.36395656142510147,
        "10": 0.05808150545784879,
        "11": 0.002472301426867029
      },
      "frequency_00": 0.5625,
      "observables": {
        "observable_set_hash": "dbdcda5c7aa312b23da7566b6bc7da5ac7b572b561161122735a2aeef6c5bbcc",
        "items": [
          {
            "observable": {
              "name": "Z(q0)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.8788923862305684,
            "variance": 0.22754817342593736,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "state_vector",
            "source_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
            "estimator_kind": "exact_state",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q1)",
              "terms": [
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.26714227429606296,
            "variance": 0.9286350052839271,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "state_vector",
            "source_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
            "estimator_kind": "exact_state",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q0)*Z(q1)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                },
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.15592386623409932,
            "variance": 0.9756877479386107,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "state_vector",
            "source_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
            "estimator_kind": "exact_state",
            "schema_version": "cascaqit.observables.v1"
          }
        ],
        "schema_version": "cascaqit.observables.v1"
      },
      "state_chain": [
        {
          "transition_id": "transition.0.block.0000.prepare",
          "order_index": 0,
          "block_id": "block.0000.prepare",
          "program_kind": "digital",
          "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
          "kernel": "NumpyDigitalStateVectorKernel",
          "input_state_hash": "a366dfecabfa70e226fc32395f74a800800f0dca5826459ff2c84dfbe7be5254",
          "output_state_hash": "6261624855ea775f2dda16925a5a04fd7e40ee305d577ef8d5cb9f75186a89fe",
          "input_logical_time": 0.0,
          "output_logical_time": 0.0,
          "time_unit": "us",
          "solver_evidence_hash": "e0aba1b5f620a1abc613f7065f8405f71f6e9b5d10ec348db9b3a2435fab8ff3",
          "metadata": {
            "logical_order": [
              "q0",
              "q1"
            ],
            "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
            "payload_id": "payload.0.block.0000.prepare.digital",
            "producer": "NumpyDigitalStateVectorKernel",
            "solver_evidence": {
              "absolute_tolerance": null,
              "accepted_steps": 0,
              "final_time": 0.0,
              "function_evaluations": null,
              "initial_time": 0.0,
              "integrator_requested": "fixed_step_krylov",
              "integrator_selected": "not_applicable",
              "max_step_size": null,
              "metadata": {
                "consumer": "NumpyDigitalStateVectorKernel"
              },
              "min_step_size": null,
              "rejected_steps": null,
              "rejected_steps_available": false,
              "relative_tolerance": null,
              "schema_version": "0.1",
              "segment_count": 0,
              "termination_reason": "not_applicable",
              "time_unit": "us",
              "tolerance_applied": false
            }
          },
          "schema_version": "0.1"
        },
        {
          "transition_id": "transition.1.block.0001.evolve",
          "order_index": 1,
          "block_id": "block.0001.evolve",
          "program_kind": "analog",
          "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
          "kernel": "MatrixFreeAnalogStateVectorKernel",
          "input_state_hash": "6261624855ea775f2dda16925a5a04fd7e40ee305d577ef8d5cb9f75186a89fe",
          "output_state_hash": "f57ede75fd1a1e60a8f4b07000fddb6029e3bc52921c5de0a3168cbcec976aec",
          "input_logical_time": 0.0,
          "output_logical_time": 0.6,
          "time_unit": "us",
          "solver_evidence_hash": "5a1200248280ce6c2f930a38df841189cc608e6ad109338d0a27c18b25706de3",
          "metadata": {
            "logical_order": [
              "q0",
              "q1"
            ],
            "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
            "payload_id": "payload.1.block.0001.evolve.analog",
            "producer": "MatrixFreeAnalogStateVectorKernel",
            "solver_evidence": {
              "absolute_tolerance": null,
              "accepted_steps": 32,
              "final_time": 0.6,
              "function_evaluations": null,
              "initial_time": 0.0,
              "integrator_requested": "fixed_step_krylov",
              "integrator_selected": "fixed_step_krylov",
              "max_step_size": 0.01875,
              "metadata": {
                "interaction_geometry_hash": "c8f7036b5efa5324fc28833aee66676e2832be11e92fc1375477e3da34d401b3",
                "interaction_geometry_source": "nominal_register",
                "interaction_maximum_abs_strength": 0.0,
                "interaction_minimum_distance": 5.0,
                "interaction_pair_count": 0,
                "interaction_pair_table_hash": "4f53cda18c2baa0c0354bb5f9a3ecbe5ed12ab4d8e11ba873c2f11161202b945",
                "interaction_plan_hash": "af6e015cdee51a687043495b129b6fc3d09f4c3455ebe536dd7c4daa8e5f54a2",
                "norm_before_normalization": 0.9999999999999981,
                "normalization_correction": 1.887379141862766e-15,
                "output_dtype": "complex128",
                "output_dtype_epsilon": 2.220446049250313e-16,
                "requested_tolerance_below_output_precision": false,
                "solver": "scipy.sparse.linalg.expm_multiply"
              },
              "min_step_size": 0.01875,
              "rejected_steps": null,
              "rejected_steps_available": false,
              "relative_tolerance": null,
              "schema_version": "0.1",
              "segment_count": 32,
              "termination_reason": "completed",
              "time_unit": "us",
              "tolerance_applied": false
            }
          },
          "schema_version": "0.1"
        },
        {
          "transition_id": "transition.2.block.0002.readout_rotation",
          "order_index": 2,
          "block_id": "block.0002.readout_rotation",
          "program_kind": "digital",
          "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
          "kernel": "NumpyDigitalStateVectorKernel",
          "input_state_hash": "f57ede75fd1a1e60a8f4b07000fddb6029e3bc52921c5de0a3168cbcec976aec",
          "output_state_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
          "input_logical_time": 0.6,
          "output_logical_time": 0.6,
          "time_unit": "us",
          "solver_evidence_hash": "19ce6d439071212a621eef9e16197494ef72777812369c752e8c2da41f550822",
          "metadata": {
            "logical_order": [
              "q0",
              "q1"
            ],
            "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
            "payload_id": "payload.2.block.0002.readout_rotation.digital",
            "producer": "NumpyDigitalStateVectorKernel",
            "solver_evidence": {
              "absolute_tolerance": null,
              "accepted_steps": 0,
              "final_time": 0.6,
              "function_evaluations": null,
              "initial_time": 0.6,
              "integrator_requested": "fixed_step_krylov",
              "integrator_selected": "not_applicable",
              "max_step_size": null,
              "metadata": {
                "consumer": "NumpyDigitalStateVectorKernel"
              },
              "min_step_size": null,
              "rejected_steps": null,
              "rejected_steps_available": false,
              "relative_tolerance": null,
              "schema_version": "0.1",
              "segment_count": 0,
              "termination_reason": "not_applicable",
              "time_unit": "us",
              "tolerance_applied": false
            }
          },
          "schema_version": "0.1"
        }
      ],
      "method": "state_vector",
      "resource_estimate": {
        "method": "state_vector",
        "logical_sites": 2,
        "hilbert_dimension": 4,
        "state_dimension": 4,
        "dtype": "complex128",
        "itemsize_bytes": 16,
        "trajectories": 1,
        "workers": 1,
        "state_bytes": 64,
        "operator_bytes": 128,
        "workspace_bytes": 1408,
        "worker_copy_bytes": 0,
        "sampling_bytes": 4096,
        "result_buffer_bytes": 4096,
        "estimated_peak_bytes": 9792,
        "schema_version": "cascaqit.simulation.planning.v1"
      },
      "options": {
        "method": "state_vector",
        "integrator": "fixed_step_krylov",
        "device": "auto",
        "dtype": "complex128",
        "max_memory_bytes": null,
        "memory_fraction": 0.8,
        "max_wall_time_seconds": null,
        "workers": "auto",
        "trajectories": 256,
        "target_statistical_error": null,
        "rtol": 1e-09,
        "atol": 1e-11,
        "max_steps": 32,
        "blockade_mode": "auto",
        "seed": 0,
        "metadata": {},
        "schema_version": "cascaqit.simulation.planning.v1"
      },
      "noise_model": null
    },
    {
      "case": "ideal",
      "seed": 4883,
      "counts": {
        "01": 38,
        "00": 75,
        "10": 14,
        "11": 1
      },
      "probabilities_before_readout": {
        "00": 0.5754896316901827,
        "01": 0.36395656142510147,
        "10": 0.05808150545784879,
        "11": 0.002472301426867029
      },
      "expected_recorded_probabilities": {
        "00": 0.5754896316901827,
        "01": 0.36395656142510147,
        "10": 0.05808150545784879,
        "11": 0.002472301426867029
      },
      "frequency_00": 0.5859375,
      "observables": {
        "observable_set_hash": "dbdcda5c7aa312b23da7566b6bc7da5ac7b572b561161122735a2aeef6c5bbcc",
        "items": [
          {
            "observable": {
              "name": "Z(q0)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.8788923862305684,
            "variance": 0.22754817342593736,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "state_vector",
            "source_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
            "estimator_kind": "exact_state",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q1)",
              "terms": [
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.26714227429606296,
            "variance": 0.9286350052839271,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "state_vector",
            "source_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
            "estimator_kind": "exact_state",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q0)*Z(q1)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                },
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.15592386623409932,
            "variance": 0.9756877479386107,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "state_vector",
            "source_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
            "estimator_kind": "exact_state",
            "schema_version": "cascaqit.observables.v1"
          }
        ],
        "schema_version": "cascaqit.observables.v1"
      },
      "state_chain": [
        {
          "transition_id": "transition.0.block.0000.prepare",
          "order_index": 0,
          "block_id": "block.0000.prepare",
          "program_kind": "digital",
          "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
          "kernel": "NumpyDigitalStateVectorKernel",
          "input_state_hash": "a366dfecabfa70e226fc32395f74a800800f0dca5826459ff2c84dfbe7be5254",
          "output_state_hash": "6261624855ea775f2dda16925a5a04fd7e40ee305d577ef8d5cb9f75186a89fe",
          "input_logical_time": 0.0,
          "output_logical_time": 0.0,
          "time_unit": "us",
          "solver_evidence_hash": "e0aba1b5f620a1abc613f7065f8405f71f6e9b5d10ec348db9b3a2435fab8ff3",
          "metadata": {
            "logical_order": [
              "q0",
              "q1"
            ],
            "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
            "payload_id": "payload.0.block.0000.prepare.digital",
            "producer": "NumpyDigitalStateVectorKernel",
            "solver_evidence": {
              "absolute_tolerance": null,
              "accepted_steps": 0,
              "final_time": 0.0,
              "function_evaluations": null,
              "initial_time": 0.0,
              "integrator_requested": "fixed_step_krylov",
              "integrator_selected": "not_applicable",
              "max_step_size": null,
              "metadata": {
                "consumer": "NumpyDigitalStateVectorKernel"
              },
              "min_step_size": null,
              "rejected_steps": null,
              "rejected_steps_available": false,
              "relative_tolerance": null,
              "schema_version": "0.1",
              "segment_count": 0,
              "termination_reason": "not_applicable",
              "time_unit": "us",
              "tolerance_applied": false
            }
          },
          "schema_version": "0.1"
        },
        {
          "transition_id": "transition.1.block.0001.evolve",
          "order_index": 1,
          "block_id": "block.0001.evolve",
          "program_kind": "analog",
          "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
          "kernel": "MatrixFreeAnalogStateVectorKernel",
          "input_state_hash": "6261624855ea775f2dda16925a5a04fd7e40ee305d577ef8d5cb9f75186a89fe",
          "output_state_hash": "f57ede75fd1a1e60a8f4b07000fddb6029e3bc52921c5de0a3168cbcec976aec",
          "input_logical_time": 0.0,
          "output_logical_time": 0.6,
          "time_unit": "us",
          "solver_evidence_hash": "5a1200248280ce6c2f930a38df841189cc608e6ad109338d0a27c18b25706de3",
          "metadata": {
            "logical_order": [
              "q0",
              "q1"
            ],
            "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
            "payload_id": "payload.1.block.0001.evolve.analog",
            "producer": "MatrixFreeAnalogStateVectorKernel",
            "solver_evidence": {
              "absolute_tolerance": null,
              "accepted_steps": 32,
              "final_time": 0.6,
              "function_evaluations": null,
              "initial_time": 0.0,
              "integrator_requested": "fixed_step_krylov",
              "integrator_selected": "fixed_step_krylov",
              "max_step_size": 0.01875,
              "metadata": {
                "interaction_geometry_hash": "c8f7036b5efa5324fc28833aee66676e2832be11e92fc1375477e3da34d401b3",
                "interaction_geometry_source": "nominal_register",
                "interaction_maximum_abs_strength": 0.0,
                "interaction_minimum_distance": 5.0,
                "interaction_pair_count": 0,
                "interaction_pair_table_hash": "4f53cda18c2baa0c0354bb5f9a3ecbe5ed12ab4d8e11ba873c2f11161202b945",
                "interaction_plan_hash": "af6e015cdee51a687043495b129b6fc3d09f4c3455ebe536dd7c4daa8e5f54a2",
                "norm_before_normalization": 0.9999999999999981,
                "normalization_correction": 1.887379141862766e-15,
                "output_dtype": "complex128",
                "output_dtype_epsilon": 2.220446049250313e-16,
                "requested_tolerance_below_output_precision": false,
                "solver": "scipy.sparse.linalg.expm_multiply"
              },
              "min_step_size": 0.01875,
              "rejected_steps": null,
              "rejected_steps_available": false,
              "relative_tolerance": null,
              "schema_version": "0.1",
              "segment_count": 32,
              "termination_reason": "completed",
              "time_unit": "us",
              "tolerance_applied": false
            }
          },
          "schema_version": "0.1"
        },
        {
          "transition_id": "transition.2.block.0002.readout_rotation",
          "order_index": 2,
          "block_id": "block.0002.readout_rotation",
          "program_kind": "digital",
          "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
          "kernel": "NumpyDigitalStateVectorKernel",
          "input_state_hash": "f57ede75fd1a1e60a8f4b07000fddb6029e3bc52921c5de0a3168cbcec976aec",
          "output_state_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
          "input_logical_time": 0.6,
          "output_logical_time": 0.6,
          "time_unit": "us",
          "solver_evidence_hash": "19ce6d439071212a621eef9e16197494ef72777812369c752e8c2da41f550822",
          "metadata": {
            "logical_order": [
              "q0",
              "q1"
            ],
            "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
            "payload_id": "payload.2.block.0002.readout_rotation.digital",
            "producer": "NumpyDigitalStateVectorKernel",
            "solver_evidence": {
              "absolute_tolerance": null,
              "accepted_steps": 0,
              "final_time": 0.6,
              "function_evaluations": null,
              "initial_time": 0.6,
              "integrator_requested": "fixed_step_krylov",
              "integrator_selected": "not_applicable",
              "max_step_size": null,
              "metadata": {
                "consumer": "NumpyDigitalStateVectorKernel"
              },
              "min_step_size": null,
              "rejected_steps": null,
              "rejected_steps_available": false,
              "relative_tolerance": null,
              "schema_version": "0.1",
              "segment_count": 0,
              "termination_reason": "not_applicable",
              "time_unit": "us",
              "tolerance_applied": false
            }
          },
          "schema_version": "0.1"
        }
      ],
      "method": "state_vector",
      "resource_estimate": {
        "method": "state_vector",
        "logical_sites": 2,
        "hilbert_dimension": 4,
        "state_dimension": 4,
        "dtype": "complex128",
        "itemsize_bytes": 16,
        "trajectories": 1,
        "workers": 1,
        "state_bytes": 64,
        "operator_bytes": 128,
        "workspace_bytes": 1408,
        "worker_copy_bytes": 0,
        "sampling_bytes": 4096,
        "result_buffer_bytes": 4096,
        "estimated_peak_bytes": 9792,
        "schema_version": "cascaqit.simulation.planning.v1"
      },
      "options": {
        "method": "state_vector",
        "integrator": "fixed_step_krylov",
        "device": "auto",
        "dtype": "complex128",
        "max_memory_bytes": null,
        "memory_fraction": 0.8,
        "max_wall_time_seconds": null,
        "workers": "auto",
        "trajectories": 256,
        "target_statistical_error": null,
        "rtol": 1e-09,
        "atol": 1e-11,
        "max_steps": 32,
        "blockade_mode": "auto",
        "seed": 0,
        "metadata": {},
        "schema_version": "cascaqit.simulation.planning.v1"
      },
      "noise_model": null
    },
    {
      "case": "dephasing",
      "seed": 4881,
      "counts": {
        "01": 38,
        "00": 47,
        "11": 5,
        "10": 38
      },
      "probabilities_before_readout": {
        "00": 0.4327894017200914,
        "01": 0.23601050347734526,
        "10": 0.2900376720088961,
        "11": 0.041162422793667296
      },
      "expected_recorded_probabilities": {
        "00": 0.4327894017200914,
        "01": 0.23601050347734526,
        "10": 0.2900376720088961,
        "11": 0.041162422793667296
      },
      "frequency_00": 0.3671875,
      "observables": {
        "observable_set_hash": "dbdcda5c7aa312b23da7566b6bc7da5ac7b572b561161122735a2aeef6c5bbcc",
        "items": [
          {
            "observable": {
              "name": "Z(q0)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.33759981039487336,
            "variance": 0.8860263680213456,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q1)",
              "terms": [
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.44565414745797494,
            "variance": 0.8013923808535055,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q0)*Z(q1)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                },
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": -0.052096350972482636,
            "variance": 0.9972859702153519,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          }
        ],
        "schema_version": "cascaqit.observables.v1"
      },
      "state_chain": [
        {
          "transition_id": "transition.0.block.0000.prepare",
          "order_index": 0,
          "block_id": "block.0000.prepare",
          "program_kind": "digital",
          "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
          "kernel": "ExactDensityMatrixKernel.digital",
          "input_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
          "output_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
          "input_logical_time": 0.0,
          "output_logical_time": 0.0,
          "time_unit": "us",
          "solver_evidence_hash": "dfca8e955ca173fed5f1dce4f8b20a513e634a38ff28f78dddce9fcdaa7803dd",
          "metadata": {
            "logical_order": [
              "q0",
              "q1"
            ],
            "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
            "payload_id": "payload.0.block.0000.prepare.digital",
            "solver_evidence": {
              "absolute_tolerance": null,
              "accepted_steps": 0,
              "final_time": 0.0,
              "function_evaluations": null,
              "initial_time": 0.0,
              "integrator_requested": "fixed_step_krylov",
              "integrator_selected": "not_applicable",
              "max_step_size": null,
              "metadata": {
                "consumer": "ExactDensityMatrixKernel.digital"
              },
              "min_step_size": null,
              "rejected_steps": null,
              "rejected_steps_available": false,
              "relative_tolerance": null,
              "schema_version": "0.1",
              "segment_count": 0,
              "termination_reason": "not_applicable",
              "time_unit": "us",
              "tolerance_applied": false
            }
          },
          "schema_version": "0.1"
        },
        {
          "transition_id": "transition.1.block.0001.evolve",
          "order_index": 1,
          "block_id": "block.0001.evolve",
          "program_kind": "analog",
          "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
          "kernel": "ExactDensityMatrixKernel.analog",
          "input_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
          "output_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
          "input_logical_time": 0.0,
          "output_logical_time": 0.6,
          "time_unit": "us",
          "solver_evidence_hash": "b87033a62649f443f68ae025e7d6d4ca57efd42e54be9728595a3bf363bf4e3f",
          "metadata": {
            "logical_order": [
              "q0",
              "q1"
            ],
            "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
            "payload_id": "payload.1.block.0001.evolve.analog",
            "solver_evidence": {
              "absolute_tolerance": null,
              "accepted_steps": 32,
              "final_time": 0.6,
              "function_evaluations": null,
              "initial_time": 0.0,
              "integrator_requested": "fixed_step_krylov",
              "integrator_selected": "fixed_step_krylov",
              "max_step_size": 0.01875,
              "metadata": {
                "hermiticity_error_before_stabilization": 4.2841699744536696e-16,
                "minimum_eigenvalue_before_stabilization": 0.016080082047543128,
                "output_dtype": "complex128",
                "positivity_evidence_available": true,
                "solver": "strang_krylov_lindblad",
                "stabilization_applied": true,
                "trace_before_stabilization": {
                  "imag": -2.870804933781793e-18,
                  "real": 0.9999999999999972
                }
              },
              "min_step_size": 0.01875,
              "rejected_steps": null,
              "rejected_steps_available": false,
              "relative_tolerance": null,
              "schema_version": "0.1",
              "segment_count": 32,
              "termination_reason": "completed",
              "time_unit": "us",
              "tolerance_applied": false
            }
          },
          "schema_version": "0.1"
        },
        {
          "transition_id": "transition.2.block.0002.readout_rotation",
          "order_index": 2,
          "block_id": "block.0002.readout_rotation",
          "program_kind": "digital",
          "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
          "kernel": "ExactDensityMatrixKernel.digital",
          "input_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
          "output_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
          "input_logical_time": 0.6,
          "output_logical_time": 0.6,
          "time_unit": "us",
          "solver_evidence_hash": "8c6537a374163b7170874874c97426a424799f42a8be28e169dce0bf916296f1",
          "metadata": {
            "logical_order": [
              "q0",
              "q1"
            ],
            "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
            "payload_id": "payload.2.block.0002.readout_rotation.digital",
            "solver_evidence": {
              "absolute_tolerance": null,
              "accepted_steps": 0,
              "final_time": 0.6,
              "function_evaluations": null,
              "initial_time": 0.6,
              "integrator_requested": "fixed_step_krylov",
              "integrator_selected": "not_applicable",
              "max_step_size": null,
              "metadata": {
                "consumer": "ExactDensityMatrixKernel.digital"
              },
              "min_step_size": null,
              "rejected_steps": null,
              "rejected_steps_available": false,
              "relative_tolerance": null,
              "schema_version": "0.1",
              "segment_count": 0,
              "termination_reason": "not_applicable",
              "time_unit": "us",
              "tolerance_applied": false
            }
          },
          "schema_version": "0.1"
        }
      ],
      "method": "density_matrix",
      "resource_estimate": {
        "method": "density_matrix",
        "logical_sites": 2,
        "hilbert_dimension": 4,
        "state_dimension": 16,
        "dtype": "complex128",
        "itemsize_bytes": 16,
        "trajectories": 1,
        "workers": 1,
        "state_bytes": 256,
        "operator_bytes": 512,
        "workspace_bytes": 768,
        "worker_copy_bytes": 0,
        "sampling_bytes": 4096,
        "result_buffer_bytes": 4096,
        "estimated_peak_bytes": 9728,
        "schema_version": "cascaqit.simulation.planning.v1"
      },
      "options": {
        "method": "density_matrix",
        "integrator": "fixed_step_krylov",
        "device": "auto",
        "dtype": "complex128",
        "max_memory_bytes": null,
        "memory_fraction": 0.8,
        "max_wall_time_seconds": null,
        "workers": "auto",
        "trajectories": 256,
        "target_statistical_error": null,
        "rtol": 1e-09,
        "atol": 1e-11,
        "max_steps": 32,
        "blockade_mode": "auto",
        "seed": 0,
        "metadata": {},
        "schema_version": "cascaqit.simulation.planning.v1"
      },
      "noise_model": {
        "noise_model_id": "phase",
        "channels": [
          {
            "channel_id": "noise.dephasing",
            "channel_type": "dephasing",
            "parameters": {
              "rate": 0.8
            },
            "units": {
              "rate": "1/us"
            },
            "targets": "all",
            "model": "lindblad_phase_flip",
            "injection_point": "analog_evolution",
            "source": "user",
            "schedule_ref": null,
            "metadata": {},
            "schema_version": "cascaqit.noise.physical.v1"
          }
        ],
        "metadata": {},
        "schema_version": "cascaqit.noise.physical.v1"
      }
    },
    {
      "case": "dephasing",
      "seed": 4882,
      "counts": {
        "10": 37,
        "00": 47,
        "01": 38,
        "11": 6
      },
      "probabilities_before_readout": {
        "00": 0.4327894017200914,
        "01": 0.23601050347734526,
        "10": 0.2900376720088961,
        "11": 0.041162422793667296
      },
      "expected_recorded_probabilities": {
        "00": 0.4327894017200914,
        "01": 0.23601050347734526,
        "10": 0.2900376720088961,
        "11": 0.041162422793667296
      },
      "frequency_00": 0.3671875,
      "observables": {
        "observable_set_hash": "dbdcda5c7aa312b23da7566b6bc7da5ac7b572b561161122735a2aeef6c5bbcc",
        "items": [
          {
            "observable": {
              "name": "Z(q0)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.33759981039487336,
            "variance": 0.8860263680213456,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q1)",
              "terms": [
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.44565414745797494,
            "variance": 0.8013923808535055,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q0)*Z(q1)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                },
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": -0.052096350972482636,
            "variance": 0.9972859702153519,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          }
        ],
        "schema_version": "cascaqit.observables.v1"
      },
      "state_chain": [
        {
          "transition_id": "transition.0.block.0000.prepare",
          "order_index": 0,
          "block_id": "block.0000.prepare",
          "program_kind": "digital",
          "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
          "kernel": "ExactDensityMatrixKernel.digital",
          "input_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
          "output_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
          "input_logical_time": 0.0,
          "output_logical_time": 0.0,
          "time_unit": "us",
          "solver_evidence_hash": "dfca8e955ca173fed5f1dce4f8b20a513e634a38ff28f78dddce9fcdaa7803dd",
          "metadata": {
            "logical_order": [
              "q0",
              "q1"
            ],
            "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
            "payload_id": "payload.0.block.0000.prepare.digital",
            "solver_evidence": {
              "absolute_tolerance": null,
              "accepted_steps": 0,
              "final_time": 0.0,
              "function_evaluations": null,
              "initial_time": 0.0,
              "integrator_requested": "fixed_step_krylov",
              "integrator_selected": "not_applicable",
              "max_step_size": null,
              "metadata": {
                "consumer": "ExactDensityMatrixKernel.digital"
              },
              "min_step_size": null,
              "rejected_steps": null,
              "rejected_steps_available": false,
              "relative_tolerance": null,
              "schema_version": "0.1",
              "segment_count": 0,
              "termination_reason": "not_applicable",
              "time_unit": "us",
              "tolerance_applied": false
            }
          },
          "schema_version": "0.1"
        },
        {
          "transition_id": "transition.1.block.0001.evolve",
          "order_index": 1,
          "block_id": "block.0001.evolve",
          "program_kind": "analog",
          "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
          "kernel": "ExactDensityMatrixKernel.analog",
          "input_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
          "output_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
          "input_logical_time": 0.0,
          "output_logical_time": 0.6,
          "time_unit": "us",
          "solver_evidence_hash": "b87033a62649f443f68ae025e7d6d4ca57efd42e54be9728595a3bf363bf4e3f",
          "metadata": {
            "logical_order": [
              "q0",
              "q1"
            ],
            "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
            "payload_id": "payload.1.block.0001.evolve.analog",
            "solver_evidence": {
              "absolute_tolerance": null,
              "accepted_steps": 32,
              "final_time": 0.6,
              "function_evaluations": null,
              "initial_time": 0.0,
              "integrator_requested": "fixed_step_krylov",
              "integrator_selected": "fixed_step_krylov",
              "max_step_size": 0.01875,
              "metadata": {
                "hermiticity_error_before_stabilization": 4.2841699744536696e-16,
                "minimum_eigenvalue_before_stabilization": 0.016080082047543128,
                "output_dtype": "complex128",
                "positivity_evidence_available": true,
                "solver": "strang_krylov_lindblad",
                "stabilization_applied": true,
                "trace_before_stabilization": {
                  "imag": -2.870804933781793e-18,
                  "real": 0.9999999999999972
                }
              },
              "min_step_size": 0.01875,
              "rejected_steps": null,
              "rejected_steps_available": false,
              "relative_tolerance": null,
              "schema_version": "0.1",
              "segment_count": 32,
              "termination_reason": "completed",
              "time_unit": "us",
              "tolerance_applied": false
            }
          },
          "schema_version": "0.1"
        },
        {
          "transition_id": "transition.2.block.0002.readout_rotation",
          "order_index": 2,
          "block_id": "block.0002.readout_rotation",
          "program_kind": "digital",
          "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
          "kernel": "ExactDensityMatrixKernel.digital",
          "input_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
          "output_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
          "input_logical_time": 0.6,
          "output_logical_time": 0.6,
          "time_unit": "us",
          "solver_evidence_hash": "8c6537a374163b7170874874c97426a424799f42a8be28e169dce0bf916296f1",
          "metadata": {
            "logical_order": [
              "q0",
              "q1"
            ],
            "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
            "payload_id": "payload.2.block.0002.readout_rotation.digital",
            "solver_evidence": {
              "absolute_tolerance": null,
              "accepted_steps": 0,
              "final_time": 0.6,
              "function_evaluations": null,
              "initial_time": 0.6,
              "integrator_requested": "fixed_step_krylov",
              "integrator_selected": "not_applicable",
              "max_step_size": null,
              "metadata": {
                "consumer": "ExactDensityMatrixKernel.digital"
              },
              "min_step_size": null,
              "rejected_steps": null,
              "rejected_steps_available": false,
              "relative_tolerance": null,
              "schema_version": "0.1",
              "segment_count": 0,
              "termination_reason": "not_applicable",
              "time_unit": "us",
              "tolerance_applied": false
            }
          },
          "schema_version": "0.1"
        }
      ],
      "method": "density_matrix",
      "resource_estimate": {
        "method": "density_matrix",
        "logical_sites": 2,
        "hilbert_dimension": 4,
        "state_dimension": 16,
        "dtype": "complex128",
        "itemsize_bytes": 16,
        "trajectories": 1,
        "workers": 1,
        "state_bytes": 256,
        "operator_bytes": 512,
        "workspace_bytes": 768,
        "worker_copy_bytes": 0,
        "sampling_bytes": 4096,
        "result_buffer_bytes": 4096,
        "estimated_peak_bytes": 9728,
        "schema_version": "cascaqit.simulation.planning.v1"
      },
      "options": {
        "method": "density_matrix",
        "integrator": "fixed_step_krylov",
        "device": "auto",
        "dtype": "complex128",
        "max_memory_bytes": null,
        "memory_fraction": 0.8,
        "max_wall_time_seconds": null,
        "workers": "auto",
        "trajectories": 256,
        "target_statistical_error": null,
        "rtol": 1e-09,
        "atol": 1e-11,
        "max_steps": 32,
        "blockade_mode": "auto",
        "seed": 0,
        "metadata": {},
        "schema_version": "cascaqit.simulation.planning.v1"
      },
      "noise_model": {
        "noise_model_id": "phase",
        "channels": [
          {
            "channel_id": "noise.dephasing",
            "channel_type": "dephasing",
            "parameters": {
              "rate": 0.8
            },
            "units": {
              "rate": "1/us"
            },
            "targets": "all",
            "model": "lindblad_phase_flip",
            "injection_point": "analog_evolution",
            "source": "user",
            "schedule_ref": null,
            "metadata": {},
            "schema_version": "cascaqit.noise.physical.v1"
          }
        ],
        "metadata": {},
        "schema_version": "cascaqit.noise.physical.v1"
      }
    },
    {
      "case": "dephasing",
      "seed": 4883,
      "counts": {
        "10": 31,
        "01": 25,
        "00": 60,
        "11": 12
      },
      "probabilities_before_readout": {
        "00": 0.4327894017200914,
        "01": 0.23601050347734526,
        "10": 0.2900376720088961,
        "11": 0.041162422793667296
      },
      "expected_recorded_probabilities": {
        "00": 0.4327894017200914,
        "01": 0.23601050347734526,
        "10": 0.2900376720088961,
        "11": 0.041162422793667296
      },
      "frequency_00": 0.46875,
      "observables": {
        "observable_set_hash": "dbdcda5c7aa312b23da7566b6bc7da5ac7b572b561161122735a2aeef6c5bbcc",
        "items": [
          {
            "observable": {
              "name": "Z(q0)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.33759981039487336,
            "variance": 0.8860263680213456,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q1)",
              "terms": [
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.44565414745797494,
            "variance": 0.8013923808535055,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q0)*Z(q1)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                },
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": -0.052096350972482636,
            "variance": 0.9972859702153519,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          }
        ],
        "schema_version": "cascaqit.observables.v1"
      },
      "state_chain": [
        {
          "transition_id": "transition.0.block.0000.prepare",
          "order_index": 0,
          "block_id": "block.0000.prepare",
          "program_kind": "digital",
          "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
          "kernel": "ExactDensityMatrixKernel.digital",
          "input_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
          "output_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
          "input_logical_time": 0.0,
          "output_logical_time": 0.0,
          "time_unit": "us",
          "solver_evidence_hash": "dfca8e955ca173fed5f1dce4f8b20a513e634a38ff28f78dddce9fcdaa7803dd",
          "metadata": {
            "logical_order": [
              "q0",
              "q1"
            ],
            "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
            "payload_id": "payload.0.block.0000.prepare.digital",
            "solver_evidence": {
              "absolute_tolerance": null,
              "accepted_steps": 0,
              "final_time": 0.0,
              "function_evaluations": null,
              "initial_time": 0.0,
              "integrator_requested": "fixed_step_krylov",
              "integrator_selected": "not_applicable",
              "max_step_size": null,
              "metadata": {
                "consumer": "ExactDensityMatrixKernel.digital"
              },
              "min_step_size": null,
              "rejected_steps": null,
              "rejected_steps_available": false,
              "relative_tolerance": null,
              "schema_version": "0.1",
              "segment_count": 0,
              "termination_reason": "not_applicable",
              "time_unit": "us",
              "tolerance_applied": false
            }
          },
          "schema_version": "0.1"
        },
        {
          "transition_id": "transition.1.block.0001.evolve",
          "order_index": 1,
          "block_id": "block.0001.evolve",
          "program_kind": "analog",
          "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
          "kernel": "ExactDensityMatrixKernel.analog",
          "input_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
          "output_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
          "input_logical_time": 0.0,
          "output_logical_time": 0.6,
          "time_unit": "us",
          "solver_evidence_hash": "b87033a62649f443f68ae025e7d6d4ca57efd42e54be9728595a3bf363bf4e3f",
          "metadata": {
            "logical_order": [
              "q0",
              "q1"
            ],
            "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
            "payload_id": "payload.1.block.0001.evolve.analog",
            "solver_evidence": {
              "absolute_tolerance": null,
              "accepted_steps": 32,
              "final_time": 0.6,
              "function_evaluations": null,
              "initial_time": 0.0,
              "integrator_requested": "fixed_step_krylov",
              "integrator_selected": "fixed_step_krylov",
              "max_step_size": 0.01875,
              "metadata": {
                "hermiticity_error_before_stabilization": 4.2841699744536696e-16,
                "minimum_eigenvalue_before_stabilization": 0.016080082047543128,
                "output_dtype": "complex128",
                "positivity_evidence_available": true,
                "solver": "strang_krylov_lindblad",
                "stabilization_applied": true,
                "trace_before_stabilization": {
                  "imag": -2.870804933781793e-18,
                  "real": 0.9999999999999972
                }
              },
              "min_step_size": 0.01875,
              "rejected_steps": null,
              "rejected_steps_available": false,
              "relative_tolerance": null,
              "schema_version": "0.1",
              "segment_count": 32,
              "termination_reason": "completed",
              "time_unit": "us",
              "tolerance_applied": false
            }
          },
          "schema_version": "0.1"
        },
        {
          "transition_id": "transition.2.block.0002.readout_rotation",
          "order_index": 2,
          "block_id": "block.0002.readout_rotation",
          "program_kind": "digital",
          "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
          "kernel": "ExactDensityMatrixKernel.digital",
          "input_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
          "output_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
          "input_logical_time": 0.6,
          "output_logical_time": 0.6,
          "time_unit": "us",
          "solver_evidence_hash": "8c6537a374163b7170874874c97426a424799f42a8be28e169dce0bf916296f1",
          "metadata": {
            "logical_order": [
              "q0",
              "q1"
            ],
            "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
            "payload_id": "payload.2.block.0002.readout_rotation.digital",
            "solver_evidence": {
              "absolute_tolerance": null,
              "accepted_steps": 0,
              "final_time": 0.6,
              "function_evaluations": null,
              "initial_time": 0.6,
              "integrator_requested": "fixed_step_krylov",
              "integrator_selected": "not_applicable",
              "max_step_size": null,
              "metadata": {
                "consumer": "ExactDensityMatrixKernel.digital"
              },
              "min_step_size": null,
              "rejected_steps": null,
              "rejected_steps_available": false,
              "relative_tolerance": null,
              "schema_version": "0.1",
              "segment_count": 0,
              "termination_reason": "not_applicable",
              "time_unit": "us",
              "tolerance_applied": false
            }
          },
          "schema_version": "0.1"
        }
      ],
      "method": "density_matrix",
      "resource_estimate": {
        "method": "density_matrix",
        "logical_sites": 2,
        "hilbert_dimension": 4,
        "state_dimension": 16,
        "dtype": "complex128",
        "itemsize_bytes": 16,
        "trajectories": 1,
        "workers": 1,
        "state_bytes": 256,
        "operator_bytes": 512,
        "workspace_bytes": 768,
        "worker_copy_bytes": 0,
        "sampling_bytes": 4096,
        "result_buffer_bytes": 4096,
        "estimated_peak_bytes": 9728,
        "schema_version": "cascaqit.simulation.planning.v1"
      },
      "options": {
        "method": "density_matrix",
        "integrator": "fixed_step_krylov",
        "device": "auto",
        "dtype": "complex128",
        "max_memory_bytes": null,
        "memory_fraction": 0.8,
        "max_wall_time_seconds": null,
        "workers": "auto",
        "trajectories": 256,
        "target_statistical_error": null,
        "rtol": 1e-09,
        "atol": 1e-11,
        "max_steps": 32,
        "blockade_mode": "auto",
        "seed": 0,
        "metadata": {},
        "schema_version": "cascaqit.simulation.planning.v1"
      },
      "noise_model": {
        "noise_model_id": "phase",
        "channels": [
          {
            "channel_id": "noise.dephasing",
            "channel_type": "dephasing",
            "parameters": {
              "rate": 0.8
            },
            "units": {
              "rate": "1/us"
            },
            "targets": "all",
            "model": "lindblad_phase_flip",
            "injection_point": "analog_evolution",
            "source": "user",
            "schedule_ref": null,
            "metadata": {},
            "schema_version": "cascaqit.noise.physical.v1"
          }
        ],
        "metadata": {},
        "schema_version": "cascaqit.noise.physical.v1"
      }
    },
    {
      "case": "dephasing_readout",
      "seed": 4881,
      "counts": {
        "01": 34,
        "00": 45,
        "11": 13,
        "10": 36
      },
      "probabilities_before_readout": {
        "00": 0.4327894017200914,
        "01": 0.23601050347734526,
        "10": 0.2900376720088961,
        "11": 0.041162422793667296
      },
      "expected_recorded_probabilities": {
        "00": 0.42498140707779525,
        "01": 0.23005851708015412,
        "10": 0.2732802519053948,
        "11": 0.07167982393665592
      },
      "frequency_00": 0.3515625,
      "observables": {
        "observable_set_hash": "dbdcda5c7aa312b23da7566b6bc7da5ac7b572b561161122735a2aeef6c5bbcc",
        "items": [
          {
            "observable": {
              "name": "Z(q0)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.33759981039487336,
            "variance": 0.8860263680213456,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q1)",
              "terms": [
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.44565414745797494,
            "variance": 0.8013923808535055,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q0)*Z(q1)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                },
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": -0.052096350972482636,
            "variance": 0.9972859702153519,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          }
        ],
        "schema_version": "cascaqit.observables.v1"
      },
      "state_chain": [
        {
          "transition_id": "transition.0.block.0000.prepare",
          "order_index": 0,
          "block_id": "block.0000.prepare",
          "program_kind": "digital",
          "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
          "kernel": "ExactDensityMatrixKernel.digital",
          "input_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
          "output_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
          "input_logical_time": 0.0,
          "output_logical_time": 0.0,
          "time_unit": "us",
          "solver_evidence_hash": "dfca8e955ca173fed5f1dce4f8b20a513e634a38ff28f78dddce9fcdaa7803dd",
          "metadata": {
            "logical_order": [
              "q0",
              "q1"
            ],
            "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
            "payload_id": "payload.0.block.0000.prepare.digital",
            "solver_evidence": {
              "absolute_tolerance": null,
              "accepted_steps": 0,
              "final_time": 0.0,
              "function_evaluations": null,
              "initial_time": 0.0,
              "integrator_requested": "fixed_step_krylov",
              "integrator_selected": "not_applicable",
              "max_step_size": null,
              "metadata": {
                "consumer": "ExactDensityMatrixKernel.digital"
              },
              "min_step_size": null,
              "rejected_steps": null,
              "rejected_steps_available": false,
              "relative_tolerance": null,
              "schema_version": "0.1",
              "segment_count": 0,
              "termination_reason": "not_applicable",
              "time_unit": "us",
              "tolerance_applied": false
            }
          },
          "schema_version": "0.1"
        },
        {
          "transition_id": "transition.1.block.0001.evolve",
          "order_index": 1,
          "block_id": "block.0001.evolve",
          "program_kind": "analog",
          "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
          "kernel": "ExactDensityMatrixKernel.analog",
          "input_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
          "output_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
          "input_logical_time": 0.0,
          "output_logical_time": 0.6,
          "time_unit": "us",
          "solver_evidence_hash": "b87033a62649f443f68ae025e7d6d4ca57efd42e54be9728595a3bf363bf4e3f",
          "metadata": {
            "logical_order": [
              "q0",
              "q1"
            ],
            "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
            "payload_id": "payload.1.block.0001.evolve.analog",
            "solver_evidence": {
              "absolute_tolerance": null,
              "accepted_steps": 32,
              "final_time": 0.6,
              "function_evaluations": null,
              "initial_time": 0.0,
              "integrator_requested": "fixed_step_krylov",
              "integrator_selected": "fixed_step_krylov",
              "max_step_size": 0.01875,
              "metadata": {
                "hermiticity_error_before_stabilization": 4.2841699744536696e-16,
                "minimum_eigenvalue_before_stabilization": 0.016080082047543128,
                "output_dtype": "complex128",
                "positivity_evidence_available": true,
                "solver": "strang_krylov_lindblad",
                "stabilization_applied": true,
                "trace_before_stabilization": {
                  "imag": -2.870804933781793e-18,
                  "real": 0.9999999999999972
                }
              },
              "min_step_size": 0.01875,
              "rejected_steps": null,
              "rejected_steps_available": false,
              "relative_tolerance": null,
              "schema_version": "0.1",
              "segment_count": 32,
              "termination_reason": "completed",
              "time_unit": "us",
              "tolerance_applied": false
            }
          },
          "schema_version": "0.1"
        },
        {
          "transition_id": "transition.2.block.0002.readout_rotation",
          "order_index": 2,
          "block_id": "block.0002.readout_rotation",
          "program_kind": "digital",
          "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
          "kernel": "ExactDensityMatrixKernel.digital",
          "input_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
          "output_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
          "input_logical_time": 0.6,
          "output_logical_time": 0.6,
          "time_unit": "us",
          "solver_evidence_hash": "8c6537a374163b7170874874c97426a424799f42a8be28e169dce0bf916296f1",
          "metadata": {
            "logical_order": [
              "q0",
              "q1"
            ],
            "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
            "payload_id": "payload.2.block.0002.readout_rotation.digital",
            "solver_evidence": {
              "absolute_tolerance": null,
              "accepted_steps": 0,
              "final_time": 0.6,
              "function_evaluations": null,
              "initial_time": 0.6,
              "integrator_requested": "fixed_step_krylov",
              "integrator_selected": "not_applicable",
              "max_step_size": null,
              "metadata": {
                "consumer": "ExactDensityMatrixKernel.digital"
              },
              "min_step_size": null,
              "rejected_steps": null,
              "rejected_steps_available": false,
              "relative_tolerance": null,
              "schema_version": "0.1",
              "segment_count": 0,
              "termination_reason": "not_applicable",
              "time_unit": "us",
              "tolerance_applied": false
            }
          },
          "schema_version": "0.1"
        }
      ],
      "method": "density_matrix",
      "resource_estimate": {
        "method": "density_matrix",
        "logical_sites": 2,
        "hilbert_dimension": 4,
        "state_dimension": 16,
        "dtype": "complex128",
        "itemsize_bytes": 16,
        "trajectories": 1,
        "workers": 1,
        "state_bytes": 256,
        "operator_bytes": 512,
        "workspace_bytes": 768,
        "worker_copy_bytes": 0,
        "sampling_bytes": 4096,
        "result_buffer_bytes": 4096,
        "estimated_peak_bytes": 9728,
        "schema_version": "cascaqit.simulation.planning.v1"
      },
      "options": {
        "method": "density_matrix",
        "integrator": "fixed_step_krylov",
        "device": "auto",
        "dtype": "complex128",
        "max_memory_bytes": null,
        "memory_fraction": 0.8,
        "max_wall_time_seconds": null,
        "workers": "auto",
        "trajectories": 256,
        "target_statistical_error": null,
        "rtol": 1e-09,
        "atol": 1e-11,
        "max_steps": 32,
        "blockade_mode": "auto",
        "seed": 0,
        "metadata": {},
        "schema_version": "cascaqit.simulation.planning.v1"
      },
      "noise_model": {
        "noise_model_id": "phase.readout",
        "channels": [
          {
            "channel_id": "noise.dephasing",
            "channel_type": "dephasing",
            "parameters": {
              "rate": 0.8
            },
            "units": {
              "rate": "1/us"
            },
            "targets": "all",
            "model": "lindblad_phase_flip",
            "injection_point": "analog_evolution",
            "source": "user",
            "schedule_ref": null,
            "metadata": {},
            "schema_version": "cascaqit.noise.physical.v1"
          },
          {
            "channel_id": "noise.readout",
            "channel_type": "readout",
            "parameters": {
              "p01": 0.08,
              "p10": 0.12
            },
            "units": {
              "p01": "probability",
              "p10": "probability"
            },
            "targets": "all",
            "model": "asymmetric_confusion",
            "injection_point": "terminal_measurement",
            "source": "user",
            "schedule_ref": null,
            "metadata": {},
            "schema_version": "cascaqit.noise.physical.v1"
          }
        ],
        "metadata": {},
        "schema_version": "cascaqit.noise.physical.v1"
      }
    },
    {
      "case": "dephasing_readout",
      "seed": 4882,
      "counts": {
        "10": 38,
        "00": 42,
        "01": 39,
        "11": 9
      },
      "probabilities_before_readout": {
        "00": 0.4327894017200914,
        "01": 0.23601050347734526,
        "10": 0.2900376720088961,
        "11": 0.041162422793667296
      },
      "expected_recorded_probabilities": {
        "00": 0.42498140707779525,
        "01": 0.23005851708015412,
        "10": 0.2732802519053948,
        "11": 0.07167982393665592
      },
      "frequency_00": 0.328125,
      "observables": {
        "observable_set_hash": "dbdcda5c7aa312b23da7566b6bc7da5ac7b572b561161122735a2aeef6c5bbcc",
        "items": [
          {
            "observable": {
              "name": "Z(q0)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.33759981039487336,
            "variance": 0.8860263680213456,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q1)",
              "terms": [
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.44565414745797494,
            "variance": 0.8013923808535055,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q0)*Z(q1)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                },
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": -0.052096350972482636,
            "variance": 0.9972859702153519,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          }
        ],
        "schema_version": "cascaqit.observables.v1"
      },
      "state_chain": [
        {
          "transition_id": "transition.0.block.0000.prepare",
          "order_index": 0,
          "block_id": "block.0000.prepare",
          "program_kind": "digital",
          "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
          "kernel": "ExactDensityMatrixKernel.digital",
          "input_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
          "output_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
          "input_logical_time": 0.0,
          "output_logical_time": 0.0,
          "time_unit": "us",
          "solver_evidence_hash": "dfca8e955ca173fed5f1dce4f8b20a513e634a38ff28f78dddce9fcdaa7803dd",
          "metadata": {
            "logical_order": [
              "q0",
              "q1"
            ],
            "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
            "payload_id": "payload.0.block.0000.prepare.digital",
            "solver_evidence": {
              "absolute_tolerance": null,
              "accepted_steps": 0,
              "final_time": 0.0,
              "function_evaluations": null,
              "initial_time": 0.0,
              "integrator_requested": "fixed_step_krylov",
              "integrator_selected": "not_applicable",
              "max_step_size": null,
              "metadata": {
                "consumer": "ExactDensityMatrixKernel.digital"
              },
              "min_step_size": null,
              "rejected_steps": null,
              "rejected_steps_available": false,
              "relative_tolerance": null,
              "schema_version": "0.1",
              "segment_count": 0,
              "termination_reason": "not_applicable",
              "time_unit": "us",
              "tolerance_applied": false
            }
          },
          "schema_version": "0.1"
        },
        {
          "transition_id": "transition.1.block.0001.evolve",
          "order_index": 1,
          "block_id": "block.0001.evolve",
          "program_kind": "analog",
          "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
          "kernel": "ExactDensityMatrixKernel.analog",
          "input_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
          "output_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
          "input_logical_time": 0.0,
          "output_logical_time": 0.6,
          "time_unit": "us",
          "solver_evidence_hash": "b87033a62649f443f68ae025e7d6d4ca57efd42e54be9728595a3bf363bf4e3f",
          "metadata": {
            "logical_order": [
              "q0",
              "q1"
            ],
            "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
            "payload_id": "payload.1.block.0001.evolve.analog",
            "solver_evidence": {
              "absolute_tolerance": null,
              "accepted_steps": 32,
              "final_time": 0.6,
              "function_evaluations": null,
              "initial_time": 0.0,
              "integrator_requested": "fixed_step_krylov",
              "integrator_selected": "fixed_step_krylov",
              "max_step_size": 0.01875,
              "metadata": {
                "hermiticity_error_before_stabilization": 4.2841699744536696e-16,
                "minimum_eigenvalue_before_stabilization": 0.016080082047543128,
                "output_dtype": "complex128",
                "positivity_evidence_available": true,
                "solver": "strang_krylov_lindblad",
                "stabilization_applied": true,
                "trace_before_stabilization": {
                  "imag": -2.870804933781793e-18,
                  "real": 0.9999999999999972
                }
              },
              "min_step_size": 0.01875,
              "rejected_steps": null,
              "rejected_steps_available": false,
              "relative_tolerance": null,
              "schema_version": "0.1",
              "segment_count": 32,
              "termination_reason": "completed",
              "time_unit": "us",
              "tolerance_applied": false
            }
          },
          "schema_version": "0.1"
        },
        {
          "transition_id": "transition.2.block.0002.readout_rotation",
          "order_index": 2,
          "block_id": "block.0002.readout_rotation",
          "program_kind": "digital",
          "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
          "kernel": "ExactDensityMatrixKernel.digital",
          "input_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
          "output_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
          "input_logical_time": 0.6,
          "output_logical_time": 0.6,
          "time_unit": "us",
          "solver_evidence_hash": "8c6537a374163b7170874874c97426a424799f42a8be28e169dce0bf916296f1",
          "metadata": {
            "logical_order": [
              "q0",
              "q1"
            ],
            "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
            "payload_id": "payload.2.block.0002.readout_rotation.digital",
            "solver_evidence": {
              "absolute_tolerance": null,
              "accepted_steps": 0,
              "final_time": 0.6,
              "function_evaluations": null,
              "initial_time": 0.6,
              "integrator_requested": "fixed_step_krylov",
              "integrator_selected": "not_applicable",
              "max_step_size": null,
              "metadata": {
                "consumer": "ExactDensityMatrixKernel.digital"
              },
              "min_step_size": null,
              "rejected_steps": null,
              "rejected_steps_available": false,
              "relative_tolerance": null,
              "schema_version": "0.1",
              "segment_count": 0,
              "termination_reason": "not_applicable",
              "time_unit": "us",
              "tolerance_applied": false
            }
          },
          "schema_version": "0.1"
        }
      ],
      "method": "density_matrix",
      "resource_estimate": {
        "method": "density_matrix",
        "logical_sites": 2,
        "hilbert_dimension": 4,
        "state_dimension": 16,
        "dtype": "complex128",
        "itemsize_bytes": 16,
        "trajectories": 1,
        "workers": 1,
        "state_bytes": 256,
        "operator_bytes": 512,
        "workspace_bytes": 768,
        "worker_copy_bytes": 0,
        "sampling_bytes": 4096,
        "result_buffer_bytes": 4096,
        "estimated_peak_bytes": 9728,
        "schema_version": "cascaqit.simulation.planning.v1"
      },
      "options": {
        "method": "density_matrix",
        "integrator": "fixed_step_krylov",
        "device": "auto",
        "dtype": "complex128",
        "max_memory_bytes": null,
        "memory_fraction": 0.8,
        "max_wall_time_seconds": null,
        "workers": "auto",
        "trajectories": 256,
        "target_statistical_error": null,
        "rtol": 1e-09,
        "atol": 1e-11,
        "max_steps": 32,
        "blockade_mode": "auto",
        "seed": 0,
        "metadata": {},
        "schema_version": "cascaqit.simulation.planning.v1"
      },
      "noise_model": {
        "noise_model_id": "phase.readout",
        "channels": [
          {
            "channel_id": "noise.dephasing",
            "channel_type": "dephasing",
            "parameters": {
              "rate": 0.8
            },
            "units": {
              "rate": "1/us"
            },
            "targets": "all",
            "model": "lindblad_phase_flip",
            "injection_point": "analog_evolution",
            "source": "user",
            "schedule_ref": null,
            "metadata": {},
            "schema_version": "cascaqit.noise.physical.v1"
          },
          {
            "channel_id": "noise.readout",
            "channel_type": "readout",
            "parameters": {
              "p01": 0.08,
              "p10": 0.12
            },
            "units": {
              "p01": "probability",
              "p10": "probability"
            },
            "targets": "all",
            "model": "asymmetric_confusion",
            "injection_point": "terminal_measurement",
            "source": "user",
            "schedule_ref": null,
            "metadata": {},
            "schema_version": "cascaqit.noise.physical.v1"
          }
        ],
        "metadata": {},
        "schema_version": "cascaqit.noise.physical.v1"
      }
    },
    {
      "case": "dephasing_readout",
      "seed": 4883,
      "counts": {
        "00": 65,
        "01": 24,
        "11": 11,
        "10": 28
      },
      "probabilities_before_readout": {
        "00": 0.4327894017200914,
        "01": 0.23601050347734526,
        "10": 0.2900376720088961,
        "11": 0.041162422793667296
      },
      "expected_recorded_probabilities": {
        "00": 0.42498140707779525,
        "01": 0.23005851708015412,
        "10": 0.2732802519053948,
        "11": 0.07167982393665592
      },
      "frequency_00": 0.5078125,
      "observables": {
        "observable_set_hash": "dbdcda5c7aa312b23da7566b6bc7da5ac7b572b561161122735a2aeef6c5bbcc",
        "items": [
          {
            "observable": {
              "name": "Z(q0)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.33759981039487336,
            "variance": 0.8860263680213456,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q1)",
              "terms": [
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.44565414745797494,
            "variance": 0.8013923808535055,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q0)*Z(q1)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                },
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": -0.052096350972482636,
            "variance": 0.9972859702153519,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          }
        ],
        "schema_version": "cascaqit.observables.v1"
      },
      "state_chain": [
        {
          "transition_id": "transition.0.block.0000.prepare",
          "order_index": 0,
          "block_id": "block.0000.prepare",
          "program_kind": "digital",
          "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
          "kernel": "ExactDensityMatrixKernel.digital",
          "input_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
          "output_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
          "input_logical_time": 0.0,
          "output_logical_time": 0.0,
          "time_unit": "us",
          "solver_evidence_hash": "dfca8e955ca173fed5f1dce4f8b20a513e634a38ff28f78dddce9fcdaa7803dd",
          "metadata": {
            "logical_order": [
              "q0",
              "q1"
            ],
            "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
            "payload_id": "payload.0.block.0000.prepare.digital",
            "solver_evidence": {
              "absolute_tolerance": null,
              "accepted_steps": 0,
              "final_time": 0.0,
              "function_evaluations": null,
              "initial_time": 0.0,
              "integrator_requested": "fixed_step_krylov",
              "integrator_selected": "not_applicable",
              "max_step_size": null,
              "metadata": {
                "consumer": "ExactDensityMatrixKernel.digital"
              },
              "min_step_size": null,
              "rejected_steps": null,
              "rejected_steps_available": false,
              "relative_tolerance": null,
              "schema_version": "0.1",
              "segment_count": 0,
              "termination_reason": "not_applicable",
              "time_unit": "us",
              "tolerance_applied": false
            }
          },
          "schema_version": "0.1"
        },
        {
          "transition_id": "transition.1.block.0001.evolve",
          "order_index": 1,
          "block_id": "block.0001.evolve",
          "program_kind": "analog",
          "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
          "kernel": "ExactDensityMatrixKernel.analog",
          "input_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
          "output_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
          "input_logical_time": 0.0,
          "output_logical_time": 0.6,
          "time_unit": "us",
          "solver_evidence_hash": "b87033a62649f443f68ae025e7d6d4ca57efd42e54be9728595a3bf363bf4e3f",
          "metadata": {
            "logical_order": [
              "q0",
              "q1"
            ],
            "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
            "payload_id": "payload.1.block.0001.evolve.analog",
            "solver_evidence": {
              "absolute_tolerance": null,
              "accepted_steps": 32,
              "final_time": 0.6,
              "function_evaluations": null,
              "initial_time": 0.0,
              "integrator_requested": "fixed_step_krylov",
              "integrator_selected": "fixed_step_krylov",
              "max_step_size": 0.01875,
              "metadata": {
                "hermiticity_error_before_stabilization": 4.2841699744536696e-16,
                "minimum_eigenvalue_before_stabilization": 0.016080082047543128,
                "output_dtype": "complex128",
                "positivity_evidence_available": true,
                "solver": "strang_krylov_lindblad",
                "stabilization_applied": true,
                "trace_before_stabilization": {
                  "imag": -2.870804933781793e-18,
                  "real": 0.9999999999999972
                }
              },
              "min_step_size": 0.01875,
              "rejected_steps": null,
              "rejected_steps_available": false,
              "relative_tolerance": null,
              "schema_version": "0.1",
              "segment_count": 32,
              "termination_reason": "completed",
              "time_unit": "us",
              "tolerance_applied": false
            }
          },
          "schema_version": "0.1"
        },
        {
          "transition_id": "transition.2.block.0002.readout_rotation",
          "order_index": 2,
          "block_id": "block.0002.readout_rotation",
          "program_kind": "digital",
          "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
          "kernel": "ExactDensityMatrixKernel.digital",
          "input_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
          "output_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
          "input_logical_time": 0.6,
          "output_logical_time": 0.6,
          "time_unit": "us",
          "solver_evidence_hash": "8c6537a374163b7170874874c97426a424799f42a8be28e169dce0bf916296f1",
          "metadata": {
            "logical_order": [
              "q0",
              "q1"
            ],
            "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
            "payload_id": "payload.2.block.0002.readout_rotation.digital",
            "solver_evidence": {
              "absolute_tolerance": null,
              "accepted_steps": 0,
              "final_time": 0.6,
              "function_evaluations": null,
              "initial_time": 0.6,
              "integrator_requested": "fixed_step_krylov",
              "integrator_selected": "not_applicable",
              "max_step_size": null,
              "metadata": {
                "consumer": "ExactDensityMatrixKernel.digital"
              },
              "min_step_size": null,
              "rejected_steps": null,
              "rejected_steps_available": false,
              "relative_tolerance": null,
              "schema_version": "0.1",
              "segment_count": 0,
              "termination_reason": "not_applicable",
              "time_unit": "us",
              "tolerance_applied": false
            }
          },
          "schema_version": "0.1"
        }
      ],
      "method": "density_matrix",
      "resource_estimate": {
        "method": "density_matrix",
        "logical_sites": 2,
        "hilbert_dimension": 4,
        "state_dimension": 16,
        "dtype": "complex128",
        "itemsize_bytes": 16,
        "trajectories": 1,
        "workers": 1,
        "state_bytes": 256,
        "operator_bytes": 512,
        "workspace_bytes": 768,
        "worker_copy_bytes": 0,
        "sampling_bytes": 4096,
        "result_buffer_bytes": 4096,
        "estimated_peak_bytes": 9728,
        "schema_version": "cascaqit.simulation.planning.v1"
      },
      "options": {
        "method": "density_matrix",
        "integrator": "fixed_step_krylov",
        "device": "auto",
        "dtype": "complex128",
        "max_memory_bytes": null,
        "memory_fraction": 0.8,
        "max_wall_time_seconds": null,
        "workers": "auto",
        "trajectories": 256,
        "target_statistical_error": null,
        "rtol": 1e-09,
        "atol": 1e-11,
        "max_steps": 32,
        "blockade_mode": "auto",
        "seed": 0,
        "metadata": {},
        "schema_version": "cascaqit.simulation.planning.v1"
      },
      "noise_model": {
        "noise_model_id": "phase.readout",
        "channels": [
          {
            "channel_id": "noise.dephasing",
            "channel_type": "dephasing",
            "parameters": {
              "rate": 0.8
            },
            "units": {
              "rate": "1/us"
            },
            "targets": "all",
            "model": "lindblad_phase_flip",
            "injection_point": "analog_evolution",
            "source": "user",
            "schedule_ref": null,
            "metadata": {},
            "schema_version": "cascaqit.noise.physical.v1"
          },
          {
            "channel_id": "noise.readout",
            "channel_type": "readout",
            "parameters": {
              "p01": 0.08,
              "p10": 0.12
            },
            "units": {
              "p01": "probability",
              "p10": "probability"
            },
            "targets": "all",
            "model": "asymmetric_confusion",
            "injection_point": "terminal_measurement",
            "source": "user",
            "schedule_ref": null,
            "metadata": {},
            "schema_version": "cascaqit.noise.physical.v1"
          }
        ],
        "metadata": {},
        "schema_version": "cascaqit.noise.physical.v1"
      }
    }
  ],
  "raw_results": [
    {
      "result_id": "result.local_bundle.local_plan.project.noisy.hybrid",
      "program_hash": "3ae12596e75deff789e526006cd6fad95bd8363cc46c441de4e19eaecd54aa05",
      "target_id": "local.simulator",
      "shots": 128,
      "counts": {
        "00": 72,
        "01": 48,
        "10": 7,
        "11": 1
      },
      "samples": [
        "00",
        "00",
        "00",
        "00",
        "00",
        "00",
        "00",
        "10",
        "00",
        "01",
        "01",
        "10",
        "00",
        "01",
        "00",
        "00",
        "00",
        "01",
        "00",
        "00",
        "00",
        "00",
        "00",
        "00",
        "01",
        "01",
        "00",
        "00",
        "00",
        "01",
        "01",
        "00",
        "01",
        "00",
        "00",
        "00",
        "01",
        "00",
        "01",
        "00",
        "00",
        "10",
        "00",
        "00",
        "00",
        "01",
        "00",
        "01",
        "00",
        "01",
        "01",
        "00",
        "00",
        "01",
        "01",
        "00",
        "00",
        "01",
        "10",
        "01",
        "01",
        "00",
        "01",
        "01",
        "11",
        "00",
        "00",
        "10",
        "00",
        "01",
        "00",
        "00",
        "00",
        "01",
        "00",
        "01",
        "00",
        "01",
        "00",
        "01",
        "01",
        "00",
        "01",
        "00",
        "00",
        "01",
        "01",
        "00",
        "01",
        "00",
        "01",
        "01",
        "00",
        "00",
        "01",
        "01",
        "01",
        "00",
        "00",
        "01",
        "00",
        "01",
        "00",
        "00",
        "00",
        "00",
        "00",
        "00",
        "10",
        "01",
        "00",
        "01",
        "00",
        "10",
        "01",
        "01",
        "00",
        "01",
        "00",
        "01",
        "00",
        "00",
        "01",
        "01",
        "00",
        "01",
        "00",
        "00"
      ],
      "probabilities": {
        "00": 0.5754896316901827,
        "01": 0.36395656142510147,
        "10": 0.05808150545784879,
        "11": 0.002472301426867029
      },
      "observables": {
        "state_norm": 1.0
      },
      "observable_batch": {
        "observable_set_hash": "dbdcda5c7aa312b23da7566b6bc7da5ac7b572b561161122735a2aeef6c5bbcc",
        "items": [
          {
            "observable": {
              "name": "Z(q0)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.8788923862305684,
            "variance": 0.22754817342593736,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "state_vector",
            "source_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
            "estimator_kind": "exact_state",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q1)",
              "terms": [
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.26714227429606296,
            "variance": 0.9286350052839271,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "state_vector",
            "source_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
            "estimator_kind": "exact_state",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q0)*Z(q1)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                },
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.15592386623409932,
            "variance": 0.9756877479386107,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "state_vector",
            "source_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
            "estimator_kind": "exact_state",
            "schema_version": "cascaqit.observables.v1"
          }
        ],
        "schema_version": "cascaqit.observables.v1"
      },
      "bit_ordering": {
        "convention": "logical_order",
        "logical_order": "q0,q1"
      },
      "occupation_encoding": {
        "ground": 0,
        "rydberg": 1
      },
      "diagnostics": [
        {
          "diagnostic_id": "simulation.scalable.hybrid.completed",
          "stage": "simulation",
          "severity": "info",
          "code": "SCALABLE_IDEAL_SIMULATION_COMPLETED",
          "message": "Scalable ideal state-vector simulation completed.",
          "schema_version": "0.1",
          "object_path": "result",
          "suggestion": null,
          "metadata": {
            "program_kind": "hybrid"
          }
        }
      ],
      "schema_version": "0.1",
      "metadata": {
        "backend_called": true,
        "backend_id": "local.simulator",
        "bitstring_ordering": {
          "bitstring_index": "left_to_right_matches_logical_order",
          "convention": "logical_order",
          "logical_order": [
            "q0",
            "q1"
          ]
        },
        "block_state_chain": [
          {
            "block_id": "block.0000.prepare",
            "input_logical_time": 0.0,
            "input_state_hash": "a366dfecabfa70e226fc32395f74a800800f0dca5826459ff2c84dfbe7be5254",
            "kernel": "NumpyDigitalStateVectorKernel",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
              "payload_id": "payload.0.block.0000.prepare.digital",
              "producer": "NumpyDigitalStateVectorKernel",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.0,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "NumpyDigitalStateVectorKernel"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 0,
            "output_logical_time": 0.0,
            "output_state_hash": "6261624855ea775f2dda16925a5a04fd7e40ee305d577ef8d5cb9f75186a89fe",
            "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "e0aba1b5f620a1abc613f7065f8405f71f6e9b5d10ec348db9b3a2435fab8ff3",
            "time_unit": "us",
            "transition_id": "transition.0.block.0000.prepare"
          },
          {
            "block_id": "block.0001.evolve",
            "input_logical_time": 0.0,
            "input_state_hash": "6261624855ea775f2dda16925a5a04fd7e40ee305d577ef8d5cb9f75186a89fe",
            "kernel": "MatrixFreeAnalogStateVectorKernel",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
              "payload_id": "payload.1.block.0001.evolve.analog",
              "producer": "MatrixFreeAnalogStateVectorKernel",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 32,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "fixed_step_krylov",
                "max_step_size": 0.01875,
                "metadata": {
                  "interaction_geometry_hash": "c8f7036b5efa5324fc28833aee66676e2832be11e92fc1375477e3da34d401b3",
                  "interaction_geometry_source": "nominal_register",
                  "interaction_maximum_abs_strength": 0.0,
                  "interaction_minimum_distance": 5.0,
                  "interaction_pair_count": 0,
                  "interaction_pair_table_hash": "4f53cda18c2baa0c0354bb5f9a3ecbe5ed12ab4d8e11ba873c2f11161202b945",
                  "interaction_plan_hash": "af6e015cdee51a687043495b129b6fc3d09f4c3455ebe536dd7c4daa8e5f54a2",
                  "norm_before_normalization": 0.9999999999999981,
                  "normalization_correction": 1.887379141862766e-15,
                  "output_dtype": "complex128",
                  "output_dtype_epsilon": 2.220446049250313e-16,
                  "requested_tolerance_below_output_precision": false,
                  "solver": "scipy.sparse.linalg.expm_multiply"
                },
                "min_step_size": 0.01875,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 32,
                "termination_reason": "completed",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 1,
            "output_logical_time": 0.6,
            "output_state_hash": "f57ede75fd1a1e60a8f4b07000fddb6029e3bc52921c5de0a3168cbcec976aec",
            "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
            "program_kind": "analog",
            "schema_version": "0.1",
            "solver_evidence_hash": "5a1200248280ce6c2f930a38df841189cc608e6ad109338d0a27c18b25706de3",
            "time_unit": "us",
            "transition_id": "transition.1.block.0001.evolve"
          },
          {
            "block_id": "block.0002.readout_rotation",
            "input_logical_time": 0.6,
            "input_state_hash": "f57ede75fd1a1e60a8f4b07000fddb6029e3bc52921c5de0a3168cbcec976aec",
            "kernel": "NumpyDigitalStateVectorKernel",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
              "payload_id": "payload.2.block.0002.readout_rotation.digital",
              "producer": "NumpyDigitalStateVectorKernel",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.6,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "NumpyDigitalStateVectorKernel"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 2,
            "output_logical_time": 0.6,
            "output_state_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
            "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "19ce6d439071212a621eef9e16197494ef72777812369c752e8c2da41f550822",
            "time_unit": "us",
            "transition_id": "transition.2.block.0002.readout_rotation"
          }
        ],
        "bundle_hash": "49bf06e86bd96e992244a38daea8a830f278ddf182a63cdfd7a6605f84006ed7",
        "control_report_evidence": [
          {
            "block_id": "block.0001.evolve",
            "diagnostic_count": 4,
            "diagnostics": [
              {
                "code": "CONTROL_CONCURRENCY_SUPPORTED",
                "diagnostic_id": "control.control_concurrency_supported.rydberg.local",
                "message": "Control concurrency is within the declared group limit.",
                "metadata": {
                  "actual_max_concurrency": 1,
                  "group_id": "rydberg.local",
                  "max_concurrent_operations": 2,
                  "operation_ids": [
                    "operation.local_detuning.0"
                  ]
                },
                "object_path": "control_schedule.operations",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              },
              {
                "code": "CONTROL_BANDWIDTH_SUPPORTED",
                "diagnostic_id": "control.control_bandwidth_supported.operation.local_detuning.0",
                "message": "Waveform knot-spacing bandwidth bound is within the Target limit.",
                "metadata": {
                  "bandwidth_limit": 2.0,
                  "bandwidth_unit": "MHz",
                  "channel_id": "rydberg.detuning.local",
                  "estimate_semantics": "nyquist_bound_from_minimum_knot_spacing",
                  "estimated_bandwidth": 0.0,
                  "operation_id": "operation.local_detuning.0"
                },
                "object_path": "hamiltonian.terms.local_detuning_terms[0].waveform",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              },
              {
                "code": "CONTROL_SLEW_SUPPORTED",
                "diagnostic_id": "control.control_slew_supported.operation.local_detuning.0",
                "message": "Waveform segment slew is within the Target limit.",
                "metadata": {
                  "actual_max_slew_rate": 0.0,
                  "channel_id": "rydberg.detuning.local",
                  "estimate_semantics": "maximum_actual_waveform_segment_derivative",
                  "max_slew_rate": 30.0,
                  "operation_id": "operation.local_detuning.0",
                  "slew_rate_unit": "rad/us^2"
                },
                "object_path": "hamiltonian.terms.local_detuning_terms[0].waveform",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              },
              {
                "code": "CONTROL_CROSSTALK_NO_OVERLAP",
                "diagnostic_id": "control.control_crosstalk_no_overlap.crosstalk.rydberg.rabi.local.rydberg.rabi.global",
                "message": "Crosstalk-constrained channels do not overlap.",
                "metadata": {
                  "actual_overlap_duration": 0.0,
                  "channel_ids": [
                    "rydberg.rabi.local",
                    "rydberg.rabi.global"
                  ],
                  "constraint_id": "crosstalk.rydberg.rabi.local.rydberg.rabi.global",
                  "max_overlap_duration": null,
                  "overlap_policy": "calibration_required",
                  "time_unit": "us"
                },
                "object_path": "control_schedule.operations",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              }
            ],
            "has_errors": false,
            "production_channel_allocation_performed": false,
            "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
            "schedule": {
              "control_system_hash": "fbbc3937e5187ca6bb0a3f00e176187027581e3382a83ee377e7115bffd5a87a",
              "diagnostics": [],
              "metadata": {
                "production_channel_allocation_performed": false,
                "projection": "program_ir_control_terms",
                "time_origin": 0.0,
                "time_unit": "us"
              },
              "operations": [
                {
                  "channel_id": "rydberg.detuning.global",
                  "end_time": 0.6,
                  "metadata": {
                    "production_assigned": false,
                    "program_path": "hamiltonian.terms.detuning",
                    "time_unit": "us",
                    "value_unit": "rad/us",
                    "waveform_kind": "constant"
                  },
                  "operation_id": "operation.global_detuning",
                  "operation_kind": "global_detuning",
                  "schema_version": "0.1",
                  "source_hash": "19b3cbf48a848eccf4b459d549c9603d70c02b450b81211bb93c55010a4339ab",
                  "start_time": 0.0,
                  "target_site_ids": [
                    "q0",
                    "q1"
                  ],
                  "waveform_hash": "19b3cbf48a848eccf4b459d549c9603d70c02b450b81211bb93c55010a4339ab"
                },
                {
                  "channel_id": "rydberg.rabi.global",
                  "end_time": 0.6,
                  "metadata": {
                    "production_assigned": false,
                    "program_path": "hamiltonian.terms.rabi",
                    "time_unit": "us",
                    "value_unit": "rad/us",
                    "waveform_kind": "constant"
                  },
                  "operation_id": "operation.global_rabi",
                  "operation_kind": "global_rabi",
                  "schema_version": "0.1",
                  "source_hash": "ad464599d866805baa0f7753cf0d4ce853b1688908e85f1baa172d7740efa2da",
                  "start_time": 0.0,
                  "target_site_ids": [
                    "q0",
                    "q1"
                  ],
                  "waveform_hash": "ad464599d866805baa0f7753cf0d4ce853b1688908e85f1baa172d7740efa2da"
                },
                {
                  "channel_id": "rydberg.detuning.local",
                  "end_time": 0.6,
                  "metadata": {
                    "production_assigned": false,
                    "program_path": "hamiltonian.terms.local_detuning_terms[0].waveform",
                    "time_unit": "us",
                    "value_unit": "rad/us",
                    "waveform_kind": "constant"
                  },
                  "operation_id": "operation.local_detuning.0",
                  "operation_kind": "local_detuning",
                  "schema_version": "0.1",
                  "source_hash": "5cf7b4b36d89a2948d9ee6b9b1974f74b74438df6df8aeaaafad175c714c34ed",
                  "start_time": 0.0,
                  "target_site_ids": [
                    "q0",
                    "q1"
                  ],
                  "waveform_hash": "e1caa1faf062ab87977975eab5ad7eb6366c3974acdadba829e14493602d0665"
                }
              ],
              "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
              "schedule_id": "schedule.program.control",
              "schema_version": "0.1"
            },
            "target_id": "mock.neutral_atom.local_ahs.v0_1"
          }
        ],
        "execution_package_created": false,
        "measurement": {
          "basis": "computational",
          "key": "result",
          "targets": [
            "q0",
            "q1"
          ]
        },
        "network_accessed": false,
        "offline_deterministic": true,
        "references": {
          "bundle_hash": "49bf06e86bd96e992244a38daea8a830f278ddf182a63cdfd7a6605f84006ed7",
          "calibration_snapshot_hash": null,
          "compiled_program_hash": null,
          "discretized_program_hash": null,
          "execution_package_id": null,
          "final_state_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
          "initial_state_hash": "a366dfecabfa70e226fc32395f74a800800f0dca5826459ff2c84dfbe7be5254",
          "metadata": {
            "graph_hash": "7f1df6f7e79a08131273f5367d8b40cf1a5fab604b12a94df8efb2411a53452c"
          },
          "plan_hash": "4388febf8e9092f0d5a1bdee8ba9658cd610618a595779025d6019da97dad681",
          "program_hash": "3ae12596e75deff789e526006cd6fad95bd8363cc46c441de4e19eaecd54aa05",
          "schema_version": "0.1",
          "target_snapshot_hash": null
        },
        "register_snapshots": [
          {
            "active_atom_ids": [
              "q0",
              "q1"
            ],
            "active_site_count": 2,
            "active_site_ids": [
              "q0",
              "q1"
            ],
            "lifecycle_stage": "planned",
            "physical_site_count": 2,
            "physical_site_ids": [
              "q0",
              "q1"
            ],
            "previous_snapshot_hash": null,
            "snapshot_hash": "571e481d25fc0fb0e4962bcb62d4b574c81cc965cb8e3b4fc69565faa8be68ec",
            "snapshot_id": "register.planned",
            "status_counts": {
              "defect": 0,
              "filled": 2,
              "loading_failed": 0,
              "vacant": 0
            }
          }
        ],
        "run_trace": {
          "events": [
            {
              "event_time": "logical:0x0.0p+0",
              "message": "Completed digital state transition.",
              "metadata": {
                "state_transition": {
                  "block_id": "block.0000.prepare",
                  "input_logical_time": 0.0,
                  "input_state_hash": "a366dfecabfa70e226fc32395f74a800800f0dca5826459ff2c84dfbe7be5254",
                  "kernel": "NumpyDigitalStateVectorKernel",
                  "metadata": {
                    "logical_order": [
                      "q0",
                      "q1"
                    ],
                    "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
                    "payload_id": "payload.0.block.0000.prepare.digital",
                    "producer": "NumpyDigitalStateVectorKernel",
                    "solver_evidence": {
                      "absolute_tolerance": null,
                      "accepted_steps": 0,
                      "final_time": 0.0,
                      "function_evaluations": null,
                      "initial_time": 0.0,
                      "integrator_requested": "fixed_step_krylov",
                      "integrator_selected": "not_applicable",
                      "max_step_size": null,
                      "metadata": {
                        "consumer": "NumpyDigitalStateVectorKernel"
                      },
                      "min_step_size": null,
                      "rejected_steps": null,
                      "rejected_steps_available": false,
                      "relative_tolerance": null,
                      "schema_version": "0.1",
                      "segment_count": 0,
                      "termination_reason": "not_applicable",
                      "time_unit": "us",
                      "tolerance_applied": false
                    }
                  },
                  "order_index": 0,
                  "output_logical_time": 0.0,
                  "output_state_hash": "6261624855ea775f2dda16925a5a04fd7e40ee305d577ef8d5cb9f75186a89fe",
                  "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
                  "program_kind": "digital",
                  "schema_version": "0.1",
                  "solver_evidence_hash": "e0aba1b5f620a1abc613f7065f8405f71f6e9b5d10ec348db9b3a2435fab8ff3",
                  "time_unit": "us",
                  "transition_id": "transition.0.block.0000.prepare"
                }
              },
              "schema_version": "0.1",
              "stage": "running",
              "status": "ok"
            },
            {
              "event_time": "logical:0x1.3333333333333p-1",
              "message": "Completed analog state transition.",
              "metadata": {
                "state_transition": {
                  "block_id": "block.0001.evolve",
                  "input_logical_time": 0.0,
                  "input_state_hash": "6261624855ea775f2dda16925a5a04fd7e40ee305d577ef8d5cb9f75186a89fe",
                  "kernel": "MatrixFreeAnalogStateVectorKernel",
                  "metadata": {
                    "logical_order": [
                      "q0",
                      "q1"
                    ],
                    "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
                    "payload_id": "payload.1.block.0001.evolve.analog",
                    "producer": "MatrixFreeAnalogStateVectorKernel",
                    "solver_evidence": {
                      "absolute_tolerance": null,
                      "accepted_steps": 32,
                      "final_time": 0.6,
                      "function_evaluations": null,
                      "initial_time": 0.0,
                      "integrator_requested": "fixed_step_krylov",
                      "integrator_selected": "fixed_step_krylov",
                      "max_step_size": 0.01875,
                      "metadata": {
                        "interaction_geometry_hash": "c8f7036b5efa5324fc28833aee66676e2832be11e92fc1375477e3da34d401b3",
                        "interaction_geometry_source": "nominal_register",
                        "interaction_maximum_abs_strength": 0.0,
                        "interaction_minimum_distance": 5.0,
                        "interaction_pair_count": 0,
                        "interaction_pair_table_hash": "4f53cda18c2baa0c0354bb5f9a3ecbe5ed12ab4d8e11ba873c2f11161202b945",
                        "interaction_plan_hash": "af6e015cdee51a687043495b129b6fc3d09f4c3455ebe536dd7c4daa8e5f54a2",
                        "norm_before_normalization": 0.9999999999999981,
                        "normalization_correction": 1.887379141862766e-15,
                        "output_dtype": "complex128",
                        "output_dtype_epsilon": 2.220446049250313e-16,
                        "requested_tolerance_below_output_precision": false,
                        "solver": "scipy.sparse.linalg.expm_multiply"
                      },
                      "min_step_size": 0.01875,
                      "rejected_steps": null,
                      "rejected_steps_available": false,
                      "relative_tolerance": null,
                      "schema_version": "0.1",
                      "segment_count": 32,
                      "termination_reason": "completed",
                      "time_unit": "us",
                      "tolerance_applied": false
                    }
                  },
                  "order_index": 1,
                  "output_logical_time": 0.6,
                  "output_state_hash": "f57ede75fd1a1e60a8f4b07000fddb6029e3bc52921c5de0a3168cbcec976aec",
                  "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
                  "program_kind": "analog",
                  "schema_version": "0.1",
                  "solver_evidence_hash": "5a1200248280ce6c2f930a38df841189cc608e6ad109338d0a27c18b25706de3",
                  "time_unit": "us",
                  "transition_id": "transition.1.block.0001.evolve"
                }
              },
              "schema_version": "0.1",
              "stage": "running",
              "status": "ok"
            },
            {
              "event_time": "logical:0x1.3333333333333p-1",
              "message": "Completed digital state transition.",
              "metadata": {
                "state_transition": {
                  "block_id": "block.0002.readout_rotation",
                  "input_logical_time": 0.6,
                  "input_state_hash": "f57ede75fd1a1e60a8f4b07000fddb6029e3bc52921c5de0a3168cbcec976aec",
                  "kernel": "NumpyDigitalStateVectorKernel",
                  "metadata": {
                    "logical_order": [
                      "q0",
                      "q1"
                    ],
                    "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
                    "payload_id": "payload.2.block.0002.readout_rotation.digital",
                    "producer": "NumpyDigitalStateVectorKernel",
                    "solver_evidence": {
                      "absolute_tolerance": null,
                      "accepted_steps": 0,
                      "final_time": 0.6,
                      "function_evaluations": null,
                      "initial_time": 0.6,
                      "integrator_requested": "fixed_step_krylov",
                      "integrator_selected": "not_applicable",
                      "max_step_size": null,
                      "metadata": {
                        "consumer": "NumpyDigitalStateVectorKernel"
                      },
                      "min_step_size": null,
                      "rejected_steps": null,
                      "rejected_steps_available": false,
                      "relative_tolerance": null,
                      "schema_version": "0.1",
                      "segment_count": 0,
                      "termination_reason": "not_applicable",
                      "time_unit": "us",
                      "tolerance_applied": false
                    }
                  },
                  "order_index": 2,
                  "output_logical_time": 0.6,
                  "output_state_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
                  "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
                  "program_kind": "digital",
                  "schema_version": "0.1",
                  "solver_evidence_hash": "19ce6d439071212a621eef9e16197494ef72777812369c752e8c2da41f550822",
                  "time_unit": "us",
                  "transition_id": "transition.2.block.0002.readout_rotation"
                }
              },
              "schema_version": "0.1",
              "stage": "running",
              "status": "ok"
            },
            {
              "event_time": "logical:0x1.3333333333333p-1",
              "message": "Terminal computational-basis measurement completed.",
              "metadata": {
                "final_state_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
                "measurement_key": "result",
                "seed": 4881,
                "shots": 128
              },
              "schema_version": "0.1",
              "stage": "completed",
              "status": "ok"
            }
          ],
          "metadata": {
            "execution_mode": "local_hybrid_shared_state"
          },
          "references": {
            "bundle_hash": "49bf06e86bd96e992244a38daea8a830f278ddf182a63cdfd7a6605f84006ed7",
            "calibration_snapshot_hash": null,
            "compiled_program_hash": null,
            "discretized_program_hash": null,
            "execution_package_id": null,
            "final_state_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
            "initial_state_hash": "a366dfecabfa70e226fc32395f74a800800f0dca5826459ff2c84dfbe7be5254",
            "metadata": {
              "graph_hash": "7f1df6f7e79a08131273f5367d8b40cf1a5fab604b12a94df8efb2411a53452c"
            },
            "plan_hash": "4388febf8e9092f0d5a1bdee8ba9658cd610618a595779025d6019da97dad681",
            "program_hash": "3ae12596e75deff789e526006cd6fad95bd8363cc46c441de4e19eaecd54aa05",
            "schema_version": "0.1",
            "target_snapshot_hash": null
          },
          "schema_version": "0.1",
          "trace_id": "trace.local_bundle.local_plan.project.noisy.hybrid.scalable_hybrid"
        },
        "seed": 4881,
        "selected_simulator": "ScalableIdealEngine",
        "simulation_execution_config": {
          "absolute_tolerance": 1e-11,
          "device": "cpu",
          "dtype": "complex128",
          "execution_scope": "job",
          "integrator_requested": "fixed_step_krylov",
          "integrator_selected": "fixed_step_krylov",
          "method": "state_vector",
          "relative_tolerance": 1e-09,
          "schema_version": "0.1",
          "seed": 4881,
          "seed_semantics": "effective_seed",
          "solver_evidence_hash": "26fbcf7ffc65fd086ad31ece9408ff01f8fd0da8b2d930ee71eae79723e28b90",
          "step_semantics": "fixed_time_slices",
          "steps": 32,
          "tolerance_applied": false,
          "trajectories": null,
          "worker_semantics": "kernel_concurrency",
          "workers": 1
        },
        "simulation_plan": {
          "atol": 1e-11,
          "budget_bytes": 20615843020,
          "candidates": [
            {
              "estimate": {
                "dtype": "complex128",
                "estimated_peak_bytes": 9792,
                "hilbert_dimension": 4,
                "itemsize_bytes": 16,
                "logical_sites": 2,
                "method": "state_vector",
                "operator_bytes": 128,
                "result_buffer_bytes": 4096,
                "sampling_bytes": 4096,
                "schema_version": "cascaqit.simulation.planning.v1",
                "state_bytes": 64,
                "state_dimension": 4,
                "trajectories": 1,
                "worker_copy_bytes": 0,
                "workers": 1,
                "workspace_bytes": 1408
              },
              "method": "state_vector",
              "reason_codes": [
                "SIMULATION_METHOD_ELIGIBLE",
                "SIMULATION_METHOD_SELECTED"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "selected"
            },
            {
              "estimate": null,
              "method": "subspace",
              "reason_codes": [
                "SIMULATION_SUBSPACE_BASIS_UNAVAILABLE"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "rejected"
            },
            {
              "estimate": {
                "dtype": "complex128",
                "estimated_peak_bytes": 9728,
                "hilbert_dimension": 4,
                "itemsize_bytes": 16,
                "logical_sites": 2,
                "method": "density_matrix",
                "operator_bytes": 512,
                "result_buffer_bytes": 4096,
                "sampling_bytes": 4096,
                "schema_version": "cascaqit.simulation.planning.v1",
                "state_bytes": 256,
                "state_dimension": 16,
                "trajectories": 1,
                "worker_copy_bytes": 0,
                "workers": 1,
                "workspace_bytes": 768
              },
              "method": "density_matrix",
              "reason_codes": [
                "SIMULATION_METHOD_REQUIRES_NOISE_MODEL"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "rejected"
            },
            {
              "estimate": {
                "dtype": "complex128",
                "estimated_peak_bytes": 368768,
                "hilbert_dimension": 4,
                "itemsize_bytes": 16,
                "logical_sites": 2,
                "method": "trajectory",
                "operator_bytes": 128,
                "result_buffer_bytes": 4096,
                "sampling_bytes": 4096,
                "schema_version": "cascaqit.simulation.planning.v1",
                "state_bytes": 16384,
                "state_dimension": 1024,
                "trajectories": 256,
                "worker_copy_bytes": 229376,
                "workers": 15,
                "workspace_bytes": 114688
              },
              "method": "trajectory",
              "reason_codes": [
                "SIMULATION_METHOD_REQUIRES_NOISE_MODEL"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "rejected"
            }
          ],
          "device": "cpu",
          "dtype": "complex128",
          "estimate": {
            "dtype": "complex128",
            "estimated_peak_bytes": 9792,
            "hilbert_dimension": 4,
            "itemsize_bytes": 16,
            "logical_sites": 2,
            "method": "state_vector",
            "operator_bytes": 128,
            "result_buffer_bytes": 4096,
            "sampling_bytes": 4096,
            "schema_version": "cascaqit.simulation.planning.v1",
            "state_bytes": 64,
            "state_dimension": 4,
            "trajectories": 1,
            "worker_copy_bytes": 0,
            "workers": 1,
            "workspace_bytes": 1408
          },
          "hilbert_dimension": 4,
          "host_hash": "fc340411ec9c1fe45ae7d312ce900fdaeaa5935813f6c5c169cb18b81d90aea1",
          "integrator_requested": "fixed_step_krylov",
          "integrator_selected": "fixed_step_krylov",
          "logical_sites": 2,
          "max_steps": 32,
          "metadata": {
            "array_backend": "numpy",
            "blockade_dimension": null,
            "host_snapshot_source": "platform.effective_resource_probe",
            "max_wall_time_seconds": null,
            "memory_fraction": 0.8,
            "network_accessed": false,
            "numpy_version": "2.0.2",
            "requires_trajectory": false,
            "scipy_version": "1.17.1",
            "target_statistical_error": null,
            "time_integration_required": true,
            "workers_cpu_limit": 15,
            "workers_requested": "auto"
          },
          "method_requested": "state_vector",
          "method_selected": "state_vector",
          "noisy": false,
          "options_hash": "093b8525c0986d42fc573069d6a3404a9502db1b1bd5c3d804f1847a7c146096",
          "plan_id": "simulation_plan.hybrid.2.state_vector.fixed_step_krylov",
          "program_kind": "hybrid",
          "rtol": 1e-09,
          "schema_version": "cascaqit.simulation.planning.v1",
          "seed": 4881,
          "state_representation": "state_vector",
          "trajectories": 256,
          "truthfulness": "planning_only",
          "workers": 1
        },
        "simulation_plan_hash": "fdad61fd3328fc6d3bdaf3b566652023812c7f5499d9870de15e04e6d0e6914c",
        "simulation_plan_truthfulness": "planning_only",
        "simulation_resource_estimate": {
          "dtype": "complex128",
          "estimated_peak_bytes": 9792,
          "hilbert_dimension": 4,
          "itemsize_bytes": 16,
          "logical_sites": 2,
          "method": "state_vector",
          "operator_bytes": 128,
          "result_buffer_bytes": 4096,
          "sampling_bytes": 4096,
          "schema_version": "cascaqit.simulation.planning.v1",
          "state_bytes": 64,
          "state_dimension": 4,
          "trajectories": 1,
          "worker_copy_bytes": 0,
          "workers": 1,
          "workspace_bytes": 1408
        },
        "simulation_resource_usage": {
          "actual_peak_rss_bytes": 143736832,
          "baseline_peak_rss_bytes": 143736832,
          "estimate_error_fraction": null,
          "estimate_within_tolerance": null,
          "estimated_peak_bytes": 9792,
          "incremental_peak_rss_bytes": 0,
          "measurement_scope": "job",
          "measurement_status": "baseline_dominated",
          "rss_semantics": "process_high_water_mark",
          "schema_version": "0.1",
          "wall_time_seconds": 0.01625587500166148
        },
        "simulation_solver_evidence": {
          "absolute_tolerance": null,
          "accepted_steps": 32,
          "final_time": 0.6,
          "function_evaluations": null,
          "initial_time": 0.0,
          "integrator_requested": "fixed_step_krylov",
          "integrator_selected": "fixed_step_krylov",
          "max_step_size": 0.01875,
          "metadata": {
            "aggregation_scope": "hybrid_quantum_blocks",
            "component_count": 1,
            "component_evidence_hashes": [
              "5a1200248280ce6c2f930a38df841189cc608e6ad109338d0a27c18b25706de3"
            ]
          },
          "min_step_size": 0.01875,
          "rejected_steps": null,
          "rejected_steps_available": false,
          "relative_tolerance": null,
          "schema_version": "0.1",
          "segment_count": 32,
          "termination_reason": "completed",
          "time_unit": "us",
          "tolerance_applied": false
        },
        "simulation_solver_evidence_hash": "26fbcf7ffc65fd086ad31ece9408ff01f8fd0da8b2d930ee71eae79723e28b90",
        "simulation_state": {
          "arrays": {
            "amplitudes": {
              "content_hash": "307fb75fa3b49382f0b1cf16d9ad1f78bb24f54fc564dce43728fec68f0c2f10",
              "dtype": "complex128",
              "nbytes": 64,
              "returned_state_bytes": false,
              "shape": [
                4
              ]
            }
          },
          "basis": "logical_two_level",
          "logical_order": [
            "q0",
            "q1"
          ],
          "logical_time": 0.6,
          "metrics": {
            "norm": 1.0
          },
          "noise_context": {},
          "provenance": {
            "conversion": null,
            "metadata": {
              "algorithm": "tensor_axis",
              "operation_count": 2,
              "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf"
            },
            "parent_state_hash": "f57ede75fd1a1e60a8f4b07000fddb6029e3bc52921c5de0a3168cbcec976aec",
            "producer": "NumpyDigitalStateVectorKernel",
            "schema_version": "cascaqit.simulation.array_state.v1",
            "step_index": 3
          },
          "returned_state_bytes": false,
          "schema_version": "cascaqit.simulation.array_state.v1",
          "stable_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
          "state_kind": "state_vector",
          "time_unit": "us"
        },
        "simulation_truthfulness": "ideal_state_evolution",
        "simulator": {
          "array_backend": "numpy.cpu",
          "method": "state_vector",
          "name": "ScalableIdealEngine",
          "program_kind": "hybrid"
        },
        "state_bytes_returned": false,
        "state_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
        "state_transitions": [
          {
            "block_id": "block.0000.prepare",
            "input_logical_time": 0.0,
            "input_state_hash": "a366dfecabfa70e226fc32395f74a800800f0dca5826459ff2c84dfbe7be5254",
            "kernel": "NumpyDigitalStateVectorKernel",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
              "payload_id": "payload.0.block.0000.prepare.digital",
              "producer": "NumpyDigitalStateVectorKernel",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.0,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "NumpyDigitalStateVectorKernel"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 0,
            "output_logical_time": 0.0,
            "output_state_hash": "6261624855ea775f2dda16925a5a04fd7e40ee305d577ef8d5cb9f75186a89fe",
            "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "e0aba1b5f620a1abc613f7065f8405f71f6e9b5d10ec348db9b3a2435fab8ff3",
            "time_unit": "us",
            "transition_id": "transition.0.block.0000.prepare"
          },
          {
            "block_id": "block.0001.evolve",
            "input_logical_time": 0.0,
            "input_state_hash": "6261624855ea775f2dda16925a5a04fd7e40ee305d577ef8d5cb9f75186a89fe",
            "kernel": "MatrixFreeAnalogStateVectorKernel",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
              "payload_id": "payload.1.block.0001.evolve.analog",
              "producer": "MatrixFreeAnalogStateVectorKernel",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 32,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "fixed_step_krylov",
                "max_step_size": 0.01875,
                "metadata": {
                  "interaction_geometry_hash": "c8f7036b5efa5324fc28833aee66676e2832be11e92fc1375477e3da34d401b3",
                  "interaction_geometry_source": "nominal_register",
                  "interaction_maximum_abs_strength": 0.0,
                  "interaction_minimum_distance": 5.0,
                  "interaction_pair_count": 0,
                  "interaction_pair_table_hash": "4f53cda18c2baa0c0354bb5f9a3ecbe5ed12ab4d8e11ba873c2f11161202b945",
                  "interaction_plan_hash": "af6e015cdee51a687043495b129b6fc3d09f4c3455ebe536dd7c4daa8e5f54a2",
                  "norm_before_normalization": 0.9999999999999981,
                  "normalization_correction": 1.887379141862766e-15,
                  "output_dtype": "complex128",
                  "output_dtype_epsilon": 2.220446049250313e-16,
                  "requested_tolerance_below_output_precision": false,
                  "solver": "scipy.sparse.linalg.expm_multiply"
                },
                "min_step_size": 0.01875,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 32,
                "termination_reason": "completed",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 1,
            "output_logical_time": 0.6,
            "output_state_hash": "f57ede75fd1a1e60a8f4b07000fddb6029e3bc52921c5de0a3168cbcec976aec",
            "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
            "program_kind": "analog",
            "schema_version": "0.1",
            "solver_evidence_hash": "5a1200248280ce6c2f930a38df841189cc608e6ad109338d0a27c18b25706de3",
            "time_unit": "us",
            "transition_id": "transition.1.block.0001.evolve"
          },
          {
            "block_id": "block.0002.readout_rotation",
            "input_logical_time": 0.6,
            "input_state_hash": "f57ede75fd1a1e60a8f4b07000fddb6029e3bc52921c5de0a3168cbcec976aec",
            "kernel": "NumpyDigitalStateVectorKernel",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
              "payload_id": "payload.2.block.0002.readout_rotation.digital",
              "producer": "NumpyDigitalStateVectorKernel",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.6,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "NumpyDigitalStateVectorKernel"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 2,
            "output_logical_time": 0.6,
            "output_state_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
            "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "19ce6d439071212a621eef9e16197494ef72777812369c752e8c2da41f550822",
            "time_unit": "us",
            "transition_id": "transition.2.block.0002.readout_rotation"
          }
        ]
      }
    },
    {
      "result_id": "result.local_bundle.local_plan.project.noisy.hybrid",
      "program_hash": "3ae12596e75deff789e526006cd6fad95bd8363cc46c441de4e19eaecd54aa05",
      "target_id": "local.simulator",
      "shots": 128,
      "counts": {
        "00": 72,
        "01": 45,
        "10": 10,
        "11": 1
      },
      "samples": [
        "01",
        "00",
        "01",
        "01",
        "00",
        "00",
        "00",
        "00",
        "00",
        "00",
        "00",
        "01",
        "00",
        "01",
        "10",
        "00",
        "00",
        "01",
        "00",
        "00",
        "00",
        "00",
        "01",
        "00",
        "01",
        "01",
        "01",
        "00",
        "00",
        "00",
        "00",
        "10",
        "00",
        "01",
        "00",
        "01",
        "00",
        "10",
        "01",
        "00",
        "10",
        "00",
        "01",
        "00",
        "00",
        "00",
        "01",
        "01",
        "01",
        "10",
        "01",
        "00",
        "10",
        "00",
        "00",
        "00",
        "01",
        "00",
        "01",
        "10",
        "01",
        "01",
        "00",
        "01",
        "00",
        "01",
        "00",
        "01",
        "01",
        "01",
        "11",
        "01",
        "01",
        "00",
        "00",
        "01",
        "10",
        "00",
        "01",
        "00",
        "01",
        "01",
        "00",
        "00",
        "00",
        "00",
        "01",
        "01",
        "00",
        "01",
        "00",
        "00",
        "00",
        "01",
        "01",
        "10",
        "01",
        "00",
        "01",
        "00",
        "00",
        "01",
        "01",
        "00",
        "00",
        "00",
        "00",
        "00",
        "00",
        "01",
        "00",
        "00",
        "00",
        "00",
        "00",
        "00",
        "00",
        "01",
        "00",
        "00",
        "10",
        "00",
        "00",
        "00",
        "00",
        "00",
        "00",
        "01"
      ],
      "probabilities": {
        "00": 0.5754896316901827,
        "01": 0.36395656142510147,
        "10": 0.05808150545784879,
        "11": 0.002472301426867029
      },
      "observables": {
        "state_norm": 1.0
      },
      "observable_batch": {
        "observable_set_hash": "dbdcda5c7aa312b23da7566b6bc7da5ac7b572b561161122735a2aeef6c5bbcc",
        "items": [
          {
            "observable": {
              "name": "Z(q0)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.8788923862305684,
            "variance": 0.22754817342593736,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "state_vector",
            "source_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
            "estimator_kind": "exact_state",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q1)",
              "terms": [
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.26714227429606296,
            "variance": 0.9286350052839271,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "state_vector",
            "source_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
            "estimator_kind": "exact_state",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q0)*Z(q1)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                },
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.15592386623409932,
            "variance": 0.9756877479386107,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "state_vector",
            "source_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
            "estimator_kind": "exact_state",
            "schema_version": "cascaqit.observables.v1"
          }
        ],
        "schema_version": "cascaqit.observables.v1"
      },
      "bit_ordering": {
        "convention": "logical_order",
        "logical_order": "q0,q1"
      },
      "occupation_encoding": {
        "ground": 0,
        "rydberg": 1
      },
      "diagnostics": [
        {
          "diagnostic_id": "simulation.scalable.hybrid.completed",
          "stage": "simulation",
          "severity": "info",
          "code": "SCALABLE_IDEAL_SIMULATION_COMPLETED",
          "message": "Scalable ideal state-vector simulation completed.",
          "schema_version": "0.1",
          "object_path": "result",
          "suggestion": null,
          "metadata": {
            "program_kind": "hybrid"
          }
        }
      ],
      "schema_version": "0.1",
      "metadata": {
        "backend_called": true,
        "backend_id": "local.simulator",
        "bitstring_ordering": {
          "bitstring_index": "left_to_right_matches_logical_order",
          "convention": "logical_order",
          "logical_order": [
            "q0",
            "q1"
          ]
        },
        "block_state_chain": [
          {
            "block_id": "block.0000.prepare",
            "input_logical_time": 0.0,
            "input_state_hash": "a366dfecabfa70e226fc32395f74a800800f0dca5826459ff2c84dfbe7be5254",
            "kernel": "NumpyDigitalStateVectorKernel",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
              "payload_id": "payload.0.block.0000.prepare.digital",
              "producer": "NumpyDigitalStateVectorKernel",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.0,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "NumpyDigitalStateVectorKernel"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 0,
            "output_logical_time": 0.0,
            "output_state_hash": "6261624855ea775f2dda16925a5a04fd7e40ee305d577ef8d5cb9f75186a89fe",
            "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "e0aba1b5f620a1abc613f7065f8405f71f6e9b5d10ec348db9b3a2435fab8ff3",
            "time_unit": "us",
            "transition_id": "transition.0.block.0000.prepare"
          },
          {
            "block_id": "block.0001.evolve",
            "input_logical_time": 0.0,
            "input_state_hash": "6261624855ea775f2dda16925a5a04fd7e40ee305d577ef8d5cb9f75186a89fe",
            "kernel": "MatrixFreeAnalogStateVectorKernel",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
              "payload_id": "payload.1.block.0001.evolve.analog",
              "producer": "MatrixFreeAnalogStateVectorKernel",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 32,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "fixed_step_krylov",
                "max_step_size": 0.01875,
                "metadata": {
                  "interaction_geometry_hash": "c8f7036b5efa5324fc28833aee66676e2832be11e92fc1375477e3da34d401b3",
                  "interaction_geometry_source": "nominal_register",
                  "interaction_maximum_abs_strength": 0.0,
                  "interaction_minimum_distance": 5.0,
                  "interaction_pair_count": 0,
                  "interaction_pair_table_hash": "4f53cda18c2baa0c0354bb5f9a3ecbe5ed12ab4d8e11ba873c2f11161202b945",
                  "interaction_plan_hash": "af6e015cdee51a687043495b129b6fc3d09f4c3455ebe536dd7c4daa8e5f54a2",
                  "norm_before_normalization": 0.9999999999999981,
                  "normalization_correction": 1.887379141862766e-15,
                  "output_dtype": "complex128",
                  "output_dtype_epsilon": 2.220446049250313e-16,
                  "requested_tolerance_below_output_precision": false,
                  "solver": "scipy.sparse.linalg.expm_multiply"
                },
                "min_step_size": 0.01875,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 32,
                "termination_reason": "completed",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 1,
            "output_logical_time": 0.6,
            "output_state_hash": "f57ede75fd1a1e60a8f4b07000fddb6029e3bc52921c5de0a3168cbcec976aec",
            "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
            "program_kind": "analog",
            "schema_version": "0.1",
            "solver_evidence_hash": "5a1200248280ce6c2f930a38df841189cc608e6ad109338d0a27c18b25706de3",
            "time_unit": "us",
            "transition_id": "transition.1.block.0001.evolve"
          },
          {
            "block_id": "block.0002.readout_rotation",
            "input_logical_time": 0.6,
            "input_state_hash": "f57ede75fd1a1e60a8f4b07000fddb6029e3bc52921c5de0a3168cbcec976aec",
            "kernel": "NumpyDigitalStateVectorKernel",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
              "payload_id": "payload.2.block.0002.readout_rotation.digital",
              "producer": "NumpyDigitalStateVectorKernel",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.6,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "NumpyDigitalStateVectorKernel"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 2,
            "output_logical_time": 0.6,
            "output_state_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
            "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "19ce6d439071212a621eef9e16197494ef72777812369c752e8c2da41f550822",
            "time_unit": "us",
            "transition_id": "transition.2.block.0002.readout_rotation"
          }
        ],
        "bundle_hash": "bdc9f85447b0a582c5a90d39865e409738f6d81124016bf3a3295c6d0a94f9b4",
        "control_report_evidence": [
          {
            "block_id": "block.0001.evolve",
            "diagnostic_count": 4,
            "diagnostics": [
              {
                "code": "CONTROL_CONCURRENCY_SUPPORTED",
                "diagnostic_id": "control.control_concurrency_supported.rydberg.local",
                "message": "Control concurrency is within the declared group limit.",
                "metadata": {
                  "actual_max_concurrency": 1,
                  "group_id": "rydberg.local",
                  "max_concurrent_operations": 2,
                  "operation_ids": [
                    "operation.local_detuning.0"
                  ]
                },
                "object_path": "control_schedule.operations",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              },
              {
                "code": "CONTROL_BANDWIDTH_SUPPORTED",
                "diagnostic_id": "control.control_bandwidth_supported.operation.local_detuning.0",
                "message": "Waveform knot-spacing bandwidth bound is within the Target limit.",
                "metadata": {
                  "bandwidth_limit": 2.0,
                  "bandwidth_unit": "MHz",
                  "channel_id": "rydberg.detuning.local",
                  "estimate_semantics": "nyquist_bound_from_minimum_knot_spacing",
                  "estimated_bandwidth": 0.0,
                  "operation_id": "operation.local_detuning.0"
                },
                "object_path": "hamiltonian.terms.local_detuning_terms[0].waveform",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              },
              {
                "code": "CONTROL_SLEW_SUPPORTED",
                "diagnostic_id": "control.control_slew_supported.operation.local_detuning.0",
                "message": "Waveform segment slew is within the Target limit.",
                "metadata": {
                  "actual_max_slew_rate": 0.0,
                  "channel_id": "rydberg.detuning.local",
                  "estimate_semantics": "maximum_actual_waveform_segment_derivative",
                  "max_slew_rate": 30.0,
                  "operation_id": "operation.local_detuning.0",
                  "slew_rate_unit": "rad/us^2"
                },
                "object_path": "hamiltonian.terms.local_detuning_terms[0].waveform",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              },
              {
                "code": "CONTROL_CROSSTALK_NO_OVERLAP",
                "diagnostic_id": "control.control_crosstalk_no_overlap.crosstalk.rydberg.rabi.local.rydberg.rabi.global",
                "message": "Crosstalk-constrained channels do not overlap.",
                "metadata": {
                  "actual_overlap_duration": 0.0,
                  "channel_ids": [
                    "rydberg.rabi.local",
                    "rydberg.rabi.global"
                  ],
                  "constraint_id": "crosstalk.rydberg.rabi.local.rydberg.rabi.global",
                  "max_overlap_duration": null,
                  "overlap_policy": "calibration_required",
                  "time_unit": "us"
                },
                "object_path": "control_schedule.operations",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              }
            ],
            "has_errors": false,
            "production_channel_allocation_performed": false,
            "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
            "schedule": {
              "control_system_hash": "fbbc3937e5187ca6bb0a3f00e176187027581e3382a83ee377e7115bffd5a87a",
              "diagnostics": [],
              "metadata": {
                "production_channel_allocation_performed": false,
                "projection": "program_ir_control_terms",
                "time_origin": 0.0,
                "time_unit": "us"
              },
              "operations": [
                {
                  "channel_id": "rydberg.detuning.global",
                  "end_time": 0.6,
                  "metadata": {
                    "production_assigned": false,
                    "program_path": "hamiltonian.terms.detuning",
                    "time_unit": "us",
                    "value_unit": "rad/us",
                    "waveform_kind": "constant"
                  },
                  "operation_id": "operation.global_detuning",
                  "operation_kind": "global_detuning",
                  "schema_version": "0.1",
                  "source_hash": "19b3cbf48a848eccf4b459d549c9603d70c02b450b81211bb93c55010a4339ab",
                  "start_time": 0.0,
                  "target_site_ids": [
                    "q0",
                    "q1"
                  ],
                  "waveform_hash": "19b3cbf48a848eccf4b459d549c9603d70c02b450b81211bb93c55010a4339ab"
                },
                {
                  "channel_id": "rydberg.rabi.global",
                  "end_time": 0.6,
                  "metadata": {
                    "production_assigned": false,
                    "program_path": "hamiltonian.terms.rabi",
                    "time_unit": "us",
                    "value_unit": "rad/us",
                    "waveform_kind": "constant"
                  },
                  "operation_id": "operation.global_rabi",
                  "operation_kind": "global_rabi",
                  "schema_version": "0.1",
                  "source_hash": "ad464599d866805baa0f7753cf0d4ce853b1688908e85f1baa172d7740efa2da",
                  "start_time": 0.0,
                  "target_site_ids": [
                    "q0",
                    "q1"
                  ],
                  "waveform_hash": "ad464599d866805baa0f7753cf0d4ce853b1688908e85f1baa172d7740efa2da"
                },
                {
                  "channel_id": "rydberg.detuning.local",
                  "end_time": 0.6,
                  "metadata": {
                    "production_assigned": false,
                    "program_path": "hamiltonian.terms.local_detuning_terms[0].waveform",
                    "time_unit": "us",
                    "value_unit": "rad/us",
                    "waveform_kind": "constant"
                  },
                  "operation_id": "operation.local_detuning.0",
                  "operation_kind": "local_detuning",
                  "schema_version": "0.1",
                  "source_hash": "5cf7b4b36d89a2948d9ee6b9b1974f74b74438df6df8aeaaafad175c714c34ed",
                  "start_time": 0.0,
                  "target_site_ids": [
                    "q0",
                    "q1"
                  ],
                  "waveform_hash": "e1caa1faf062ab87977975eab5ad7eb6366c3974acdadba829e14493602d0665"
                }
              ],
              "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
              "schedule_id": "schedule.program.control",
              "schema_version": "0.1"
            },
            "target_id": "mock.neutral_atom.local_ahs.v0_1"
          }
        ],
        "execution_package_created": false,
        "measurement": {
          "basis": "computational",
          "key": "result",
          "targets": [
            "q0",
            "q1"
          ]
        },
        "network_accessed": false,
        "offline_deterministic": true,
        "references": {
          "bundle_hash": "bdc9f85447b0a582c5a90d39865e409738f6d81124016bf3a3295c6d0a94f9b4",
          "calibration_snapshot_hash": null,
          "compiled_program_hash": null,
          "discretized_program_hash": null,
          "execution_package_id": null,
          "final_state_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
          "initial_state_hash": "a366dfecabfa70e226fc32395f74a800800f0dca5826459ff2c84dfbe7be5254",
          "metadata": {
            "graph_hash": "7f1df6f7e79a08131273f5367d8b40cf1a5fab604b12a94df8efb2411a53452c"
          },
          "plan_hash": "4388febf8e9092f0d5a1bdee8ba9658cd610618a595779025d6019da97dad681",
          "program_hash": "3ae12596e75deff789e526006cd6fad95bd8363cc46c441de4e19eaecd54aa05",
          "schema_version": "0.1",
          "target_snapshot_hash": null
        },
        "register_snapshots": [
          {
            "active_atom_ids": [
              "q0",
              "q1"
            ],
            "active_site_count": 2,
            "active_site_ids": [
              "q0",
              "q1"
            ],
            "lifecycle_stage": "planned",
            "physical_site_count": 2,
            "physical_site_ids": [
              "q0",
              "q1"
            ],
            "previous_snapshot_hash": null,
            "snapshot_hash": "571e481d25fc0fb0e4962bcb62d4b574c81cc965cb8e3b4fc69565faa8be68ec",
            "snapshot_id": "register.planned",
            "status_counts": {
              "defect": 0,
              "filled": 2,
              "loading_failed": 0,
              "vacant": 0
            }
          }
        ],
        "run_trace": {
          "events": [
            {
              "event_time": "logical:0x0.0p+0",
              "message": "Completed digital state transition.",
              "metadata": {
                "state_transition": {
                  "block_id": "block.0000.prepare",
                  "input_logical_time": 0.0,
                  "input_state_hash": "a366dfecabfa70e226fc32395f74a800800f0dca5826459ff2c84dfbe7be5254",
                  "kernel": "NumpyDigitalStateVectorKernel",
                  "metadata": {
                    "logical_order": [
                      "q0",
                      "q1"
                    ],
                    "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
                    "payload_id": "payload.0.block.0000.prepare.digital",
                    "producer": "NumpyDigitalStateVectorKernel",
                    "solver_evidence": {
                      "absolute_tolerance": null,
                      "accepted_steps": 0,
                      "final_time": 0.0,
                      "function_evaluations": null,
                      "initial_time": 0.0,
                      "integrator_requested": "fixed_step_krylov",
                      "integrator_selected": "not_applicable",
                      "max_step_size": null,
                      "metadata": {
                        "consumer": "NumpyDigitalStateVectorKernel"
                      },
                      "min_step_size": null,
                      "rejected_steps": null,
                      "rejected_steps_available": false,
                      "relative_tolerance": null,
                      "schema_version": "0.1",
                      "segment_count": 0,
                      "termination_reason": "not_applicable",
                      "time_unit": "us",
                      "tolerance_applied": false
                    }
                  },
                  "order_index": 0,
                  "output_logical_time": 0.0,
                  "output_state_hash": "6261624855ea775f2dda16925a5a04fd7e40ee305d577ef8d5cb9f75186a89fe",
                  "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
                  "program_kind": "digital",
                  "schema_version": "0.1",
                  "solver_evidence_hash": "e0aba1b5f620a1abc613f7065f8405f71f6e9b5d10ec348db9b3a2435fab8ff3",
                  "time_unit": "us",
                  "transition_id": "transition.0.block.0000.prepare"
                }
              },
              "schema_version": "0.1",
              "stage": "running",
              "status": "ok"
            },
            {
              "event_time": "logical:0x1.3333333333333p-1",
              "message": "Completed analog state transition.",
              "metadata": {
                "state_transition": {
                  "block_id": "block.0001.evolve",
                  "input_logical_time": 0.0,
                  "input_state_hash": "6261624855ea775f2dda16925a5a04fd7e40ee305d577ef8d5cb9f75186a89fe",
                  "kernel": "MatrixFreeAnalogStateVectorKernel",
                  "metadata": {
                    "logical_order": [
                      "q0",
                      "q1"
                    ],
                    "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
                    "payload_id": "payload.1.block.0001.evolve.analog",
                    "producer": "MatrixFreeAnalogStateVectorKernel",
                    "solver_evidence": {
                      "absolute_tolerance": null,
                      "accepted_steps": 32,
                      "final_time": 0.6,
                      "function_evaluations": null,
                      "initial_time": 0.0,
                      "integrator_requested": "fixed_step_krylov",
                      "integrator_selected": "fixed_step_krylov",
                      "max_step_size": 0.01875,
                      "metadata": {
                        "interaction_geometry_hash": "c8f7036b5efa5324fc28833aee66676e2832be11e92fc1375477e3da34d401b3",
                        "interaction_geometry_source": "nominal_register",
                        "interaction_maximum_abs_strength": 0.0,
                        "interaction_minimum_distance": 5.0,
                        "interaction_pair_count": 0,
                        "interaction_pair_table_hash": "4f53cda18c2baa0c0354bb5f9a3ecbe5ed12ab4d8e11ba873c2f11161202b945",
                        "interaction_plan_hash": "af6e015cdee51a687043495b129b6fc3d09f4c3455ebe536dd7c4daa8e5f54a2",
                        "norm_before_normalization": 0.9999999999999981,
                        "normalization_correction": 1.887379141862766e-15,
                        "output_dtype": "complex128",
                        "output_dtype_epsilon": 2.220446049250313e-16,
                        "requested_tolerance_below_output_precision": false,
                        "solver": "scipy.sparse.linalg.expm_multiply"
                      },
                      "min_step_size": 0.01875,
                      "rejected_steps": null,
                      "rejected_steps_available": false,
                      "relative_tolerance": null,
                      "schema_version": "0.1",
                      "segment_count": 32,
                      "termination_reason": "completed",
                      "time_unit": "us",
                      "tolerance_applied": false
                    }
                  },
                  "order_index": 1,
                  "output_logical_time": 0.6,
                  "output_state_hash": "f57ede75fd1a1e60a8f4b07000fddb6029e3bc52921c5de0a3168cbcec976aec",
                  "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
                  "program_kind": "analog",
                  "schema_version": "0.1",
                  "solver_evidence_hash": "5a1200248280ce6c2f930a38df841189cc608e6ad109338d0a27c18b25706de3",
                  "time_unit": "us",
                  "transition_id": "transition.1.block.0001.evolve"
                }
              },
              "schema_version": "0.1",
              "stage": "running",
              "status": "ok"
            },
            {
              "event_time": "logical:0x1.3333333333333p-1",
              "message": "Completed digital state transition.",
              "metadata": {
                "state_transition": {
                  "block_id": "block.0002.readout_rotation",
                  "input_logical_time": 0.6,
                  "input_state_hash": "f57ede75fd1a1e60a8f4b07000fddb6029e3bc52921c5de0a3168cbcec976aec",
                  "kernel": "NumpyDigitalStateVectorKernel",
                  "metadata": {
                    "logical_order": [
                      "q0",
                      "q1"
                    ],
                    "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
                    "payload_id": "payload.2.block.0002.readout_rotation.digital",
                    "producer": "NumpyDigitalStateVectorKernel",
                    "solver_evidence": {
                      "absolute_tolerance": null,
                      "accepted_steps": 0,
                      "final_time": 0.6,
                      "function_evaluations": null,
                      "initial_time": 0.6,
                      "integrator_requested": "fixed_step_krylov",
                      "integrator_selected": "not_applicable",
                      "max_step_size": null,
                      "metadata": {
                        "consumer": "NumpyDigitalStateVectorKernel"
                      },
                      "min_step_size": null,
                      "rejected_steps": null,
                      "rejected_steps_available": false,
                      "relative_tolerance": null,
                      "schema_version": "0.1",
                      "segment_count": 0,
                      "termination_reason": "not_applicable",
                      "time_unit": "us",
                      "tolerance_applied": false
                    }
                  },
                  "order_index": 2,
                  "output_logical_time": 0.6,
                  "output_state_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
                  "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
                  "program_kind": "digital",
                  "schema_version": "0.1",
                  "solver_evidence_hash": "19ce6d439071212a621eef9e16197494ef72777812369c752e8c2da41f550822",
                  "time_unit": "us",
                  "transition_id": "transition.2.block.0002.readout_rotation"
                }
              },
              "schema_version": "0.1",
              "stage": "running",
              "status": "ok"
            },
            {
              "event_time": "logical:0x1.3333333333333p-1",
              "message": "Terminal computational-basis measurement completed.",
              "metadata": {
                "final_state_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
                "measurement_key": "result",
                "seed": 4882,
                "shots": 128
              },
              "schema_version": "0.1",
              "stage": "completed",
              "status": "ok"
            }
          ],
          "metadata": {
            "execution_mode": "local_hybrid_shared_state"
          },
          "references": {
            "bundle_hash": "bdc9f85447b0a582c5a90d39865e409738f6d81124016bf3a3295c6d0a94f9b4",
            "calibration_snapshot_hash": null,
            "compiled_program_hash": null,
            "discretized_program_hash": null,
            "execution_package_id": null,
            "final_state_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
            "initial_state_hash": "a366dfecabfa70e226fc32395f74a800800f0dca5826459ff2c84dfbe7be5254",
            "metadata": {
              "graph_hash": "7f1df6f7e79a08131273f5367d8b40cf1a5fab604b12a94df8efb2411a53452c"
            },
            "plan_hash": "4388febf8e9092f0d5a1bdee8ba9658cd610618a595779025d6019da97dad681",
            "program_hash": "3ae12596e75deff789e526006cd6fad95bd8363cc46c441de4e19eaecd54aa05",
            "schema_version": "0.1",
            "target_snapshot_hash": null
          },
          "schema_version": "0.1",
          "trace_id": "trace.local_bundle.local_plan.project.noisy.hybrid.scalable_hybrid"
        },
        "seed": 4882,
        "selected_simulator": "ScalableIdealEngine",
        "simulation_execution_config": {
          "absolute_tolerance": 1e-11,
          "device": "cpu",
          "dtype": "complex128",
          "execution_scope": "job",
          "integrator_requested": "fixed_step_krylov",
          "integrator_selected": "fixed_step_krylov",
          "method": "state_vector",
          "relative_tolerance": 1e-09,
          "schema_version": "0.1",
          "seed": 4882,
          "seed_semantics": "effective_seed",
          "solver_evidence_hash": "26fbcf7ffc65fd086ad31ece9408ff01f8fd0da8b2d930ee71eae79723e28b90",
          "step_semantics": "fixed_time_slices",
          "steps": 32,
          "tolerance_applied": false,
          "trajectories": null,
          "worker_semantics": "kernel_concurrency",
          "workers": 1
        },
        "simulation_plan": {
          "atol": 1e-11,
          "budget_bytes": 20615843020,
          "candidates": [
            {
              "estimate": {
                "dtype": "complex128",
                "estimated_peak_bytes": 9792,
                "hilbert_dimension": 4,
                "itemsize_bytes": 16,
                "logical_sites": 2,
                "method": "state_vector",
                "operator_bytes": 128,
                "result_buffer_bytes": 4096,
                "sampling_bytes": 4096,
                "schema_version": "cascaqit.simulation.planning.v1",
                "state_bytes": 64,
                "state_dimension": 4,
                "trajectories": 1,
                "worker_copy_bytes": 0,
                "workers": 1,
                "workspace_bytes": 1408
              },
              "method": "state_vector",
              "reason_codes": [
                "SIMULATION_METHOD_ELIGIBLE",
                "SIMULATION_METHOD_SELECTED"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "selected"
            },
            {
              "estimate": null,
              "method": "subspace",
              "reason_codes": [
                "SIMULATION_SUBSPACE_BASIS_UNAVAILABLE"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "rejected"
            },
            {
              "estimate": {
                "dtype": "complex128",
                "estimated_peak_bytes": 9728,
                "hilbert_dimension": 4,
                "itemsize_bytes": 16,
                "logical_sites": 2,
                "method": "density_matrix",
                "operator_bytes": 512,
                "result_buffer_bytes": 4096,
                "sampling_bytes": 4096,
                "schema_version": "cascaqit.simulation.planning.v1",
                "state_bytes": 256,
                "state_dimension": 16,
                "trajectories": 1,
                "worker_copy_bytes": 0,
                "workers": 1,
                "workspace_bytes": 768
              },
              "method": "density_matrix",
              "reason_codes": [
                "SIMULATION_METHOD_REQUIRES_NOISE_MODEL"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "rejected"
            },
            {
              "estimate": {
                "dtype": "complex128",
                "estimated_peak_bytes": 368768,
                "hilbert_dimension": 4,
                "itemsize_bytes": 16,
                "logical_sites": 2,
                "method": "trajectory",
                "operator_bytes": 128,
                "result_buffer_bytes": 4096,
                "sampling_bytes": 4096,
                "schema_version": "cascaqit.simulation.planning.v1",
                "state_bytes": 16384,
                "state_dimension": 1024,
                "trajectories": 256,
                "worker_copy_bytes": 229376,
                "workers": 15,
                "workspace_bytes": 114688
              },
              "method": "trajectory",
              "reason_codes": [
                "SIMULATION_METHOD_REQUIRES_NOISE_MODEL"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "rejected"
            }
          ],
          "device": "cpu",
          "dtype": "complex128",
          "estimate": {
            "dtype": "complex128",
            "estimated_peak_bytes": 9792,
            "hilbert_dimension": 4,
            "itemsize_bytes": 16,
            "logical_sites": 2,
            "method": "state_vector",
            "operator_bytes": 128,
            "result_buffer_bytes": 4096,
            "sampling_bytes": 4096,
            "schema_version": "cascaqit.simulation.planning.v1",
            "state_bytes": 64,
            "state_dimension": 4,
            "trajectories": 1,
            "worker_copy_bytes": 0,
            "workers": 1,
            "workspace_bytes": 1408
          },
          "hilbert_dimension": 4,
          "host_hash": "fc340411ec9c1fe45ae7d312ce900fdaeaa5935813f6c5c169cb18b81d90aea1",
          "integrator_requested": "fixed_step_krylov",
          "integrator_selected": "fixed_step_krylov",
          "logical_sites": 2,
          "max_steps": 32,
          "metadata": {
            "array_backend": "numpy",
            "blockade_dimension": null,
            "host_snapshot_source": "platform.effective_resource_probe",
            "max_wall_time_seconds": null,
            "memory_fraction": 0.8,
            "network_accessed": false,
            "numpy_version": "2.0.2",
            "requires_trajectory": false,
            "scipy_version": "1.17.1",
            "target_statistical_error": null,
            "time_integration_required": true,
            "workers_cpu_limit": 15,
            "workers_requested": "auto"
          },
          "method_requested": "state_vector",
          "method_selected": "state_vector",
          "noisy": false,
          "options_hash": "f6c9a4c1639ebcb40c6e2a5068f9515fa622c0f9a805910604160020cd095cd2",
          "plan_id": "simulation_plan.hybrid.2.state_vector.fixed_step_krylov",
          "program_kind": "hybrid",
          "rtol": 1e-09,
          "schema_version": "cascaqit.simulation.planning.v1",
          "seed": 4882,
          "state_representation": "state_vector",
          "trajectories": 256,
          "truthfulness": "planning_only",
          "workers": 1
        },
        "simulation_plan_hash": "cbbfcae1994cb67eb67d6b7b176d1abb68025689c904285b85edbcd2c5b103f7",
        "simulation_plan_truthfulness": "planning_only",
        "simulation_resource_estimate": {
          "dtype": "complex128",
          "estimated_peak_bytes": 9792,
          "hilbert_dimension": 4,
          "itemsize_bytes": 16,
          "logical_sites": 2,
          "method": "state_vector",
          "operator_bytes": 128,
          "result_buffer_bytes": 4096,
          "sampling_bytes": 4096,
          "schema_version": "cascaqit.simulation.planning.v1",
          "state_bytes": 64,
          "state_dimension": 4,
          "trajectories": 1,
          "worker_copy_bytes": 0,
          "workers": 1,
          "workspace_bytes": 1408
        },
        "simulation_resource_usage": {
          "actual_peak_rss_bytes": 143736832,
          "baseline_peak_rss_bytes": 143736832,
          "estimate_error_fraction": null,
          "estimate_within_tolerance": null,
          "estimated_peak_bytes": 9792,
          "incremental_peak_rss_bytes": 0,
          "measurement_scope": "job",
          "measurement_status": "baseline_dominated",
          "rss_semantics": "process_high_water_mark",
          "schema_version": "0.1",
          "wall_time_seconds": 0.01371320802718401
        },
        "simulation_solver_evidence": {
          "absolute_tolerance": null,
          "accepted_steps": 32,
          "final_time": 0.6,
          "function_evaluations": null,
          "initial_time": 0.0,
          "integrator_requested": "fixed_step_krylov",
          "integrator_selected": "fixed_step_krylov",
          "max_step_size": 0.01875,
          "metadata": {
            "aggregation_scope": "hybrid_quantum_blocks",
            "component_count": 1,
            "component_evidence_hashes": [
              "5a1200248280ce6c2f930a38df841189cc608e6ad109338d0a27c18b25706de3"
            ]
          },
          "min_step_size": 0.01875,
          "rejected_steps": null,
          "rejected_steps_available": false,
          "relative_tolerance": null,
          "schema_version": "0.1",
          "segment_count": 32,
          "termination_reason": "completed",
          "time_unit": "us",
          "tolerance_applied": false
        },
        "simulation_solver_evidence_hash": "26fbcf7ffc65fd086ad31ece9408ff01f8fd0da8b2d930ee71eae79723e28b90",
        "simulation_state": {
          "arrays": {
            "amplitudes": {
              "content_hash": "307fb75fa3b49382f0b1cf16d9ad1f78bb24f54fc564dce43728fec68f0c2f10",
              "dtype": "complex128",
              "nbytes": 64,
              "returned_state_bytes": false,
              "shape": [
                4
              ]
            }
          },
          "basis": "logical_two_level",
          "logical_order": [
            "q0",
            "q1"
          ],
          "logical_time": 0.6,
          "metrics": {
            "norm": 1.0
          },
          "noise_context": {},
          "provenance": {
            "conversion": null,
            "metadata": {
              "algorithm": "tensor_axis",
              "operation_count": 2,
              "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf"
            },
            "parent_state_hash": "f57ede75fd1a1e60a8f4b07000fddb6029e3bc52921c5de0a3168cbcec976aec",
            "producer": "NumpyDigitalStateVectorKernel",
            "schema_version": "cascaqit.simulation.array_state.v1",
            "step_index": 3
          },
          "returned_state_bytes": false,
          "schema_version": "cascaqit.simulation.array_state.v1",
          "stable_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
          "state_kind": "state_vector",
          "time_unit": "us"
        },
        "simulation_truthfulness": "ideal_state_evolution",
        "simulator": {
          "array_backend": "numpy.cpu",
          "method": "state_vector",
          "name": "ScalableIdealEngine",
          "program_kind": "hybrid"
        },
        "state_bytes_returned": false,
        "state_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
        "state_transitions": [
          {
            "block_id": "block.0000.prepare",
            "input_logical_time": 0.0,
            "input_state_hash": "a366dfecabfa70e226fc32395f74a800800f0dca5826459ff2c84dfbe7be5254",
            "kernel": "NumpyDigitalStateVectorKernel",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
              "payload_id": "payload.0.block.0000.prepare.digital",
              "producer": "NumpyDigitalStateVectorKernel",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.0,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "NumpyDigitalStateVectorKernel"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 0,
            "output_logical_time": 0.0,
            "output_state_hash": "6261624855ea775f2dda16925a5a04fd7e40ee305d577ef8d5cb9f75186a89fe",
            "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "e0aba1b5f620a1abc613f7065f8405f71f6e9b5d10ec348db9b3a2435fab8ff3",
            "time_unit": "us",
            "transition_id": "transition.0.block.0000.prepare"
          },
          {
            "block_id": "block.0001.evolve",
            "input_logical_time": 0.0,
            "input_state_hash": "6261624855ea775f2dda16925a5a04fd7e40ee305d577ef8d5cb9f75186a89fe",
            "kernel": "MatrixFreeAnalogStateVectorKernel",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
              "payload_id": "payload.1.block.0001.evolve.analog",
              "producer": "MatrixFreeAnalogStateVectorKernel",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 32,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "fixed_step_krylov",
                "max_step_size": 0.01875,
                "metadata": {
                  "interaction_geometry_hash": "c8f7036b5efa5324fc28833aee66676e2832be11e92fc1375477e3da34d401b3",
                  "interaction_geometry_source": "nominal_register",
                  "interaction_maximum_abs_strength": 0.0,
                  "interaction_minimum_distance": 5.0,
                  "interaction_pair_count": 0,
                  "interaction_pair_table_hash": "4f53cda18c2baa0c0354bb5f9a3ecbe5ed12ab4d8e11ba873c2f11161202b945",
                  "interaction_plan_hash": "af6e015cdee51a687043495b129b6fc3d09f4c3455ebe536dd7c4daa8e5f54a2",
                  "norm_before_normalization": 0.9999999999999981,
                  "normalization_correction": 1.887379141862766e-15,
                  "output_dtype": "complex128",
                  "output_dtype_epsilon": 2.220446049250313e-16,
                  "requested_tolerance_below_output_precision": false,
                  "solver": "scipy.sparse.linalg.expm_multiply"
                },
                "min_step_size": 0.01875,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 32,
                "termination_reason": "completed",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 1,
            "output_logical_time": 0.6,
            "output_state_hash": "f57ede75fd1a1e60a8f4b07000fddb6029e3bc52921c5de0a3168cbcec976aec",
            "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
            "program_kind": "analog",
            "schema_version": "0.1",
            "solver_evidence_hash": "5a1200248280ce6c2f930a38df841189cc608e6ad109338d0a27c18b25706de3",
            "time_unit": "us",
            "transition_id": "transition.1.block.0001.evolve"
          },
          {
            "block_id": "block.0002.readout_rotation",
            "input_logical_time": 0.6,
            "input_state_hash": "f57ede75fd1a1e60a8f4b07000fddb6029e3bc52921c5de0a3168cbcec976aec",
            "kernel": "NumpyDigitalStateVectorKernel",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
              "payload_id": "payload.2.block.0002.readout_rotation.digital",
              "producer": "NumpyDigitalStateVectorKernel",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.6,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "NumpyDigitalStateVectorKernel"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 2,
            "output_logical_time": 0.6,
            "output_state_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
            "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "19ce6d439071212a621eef9e16197494ef72777812369c752e8c2da41f550822",
            "time_unit": "us",
            "transition_id": "transition.2.block.0002.readout_rotation"
          }
        ]
      }
    },
    {
      "result_id": "result.local_bundle.local_plan.project.noisy.hybrid",
      "program_hash": "3ae12596e75deff789e526006cd6fad95bd8363cc46c441de4e19eaecd54aa05",
      "target_id": "local.simulator",
      "shots": 128,
      "counts": {
        "00": 75,
        "01": 38,
        "10": 14,
        "11": 1
      },
      "samples": [
        "01",
        "00",
        "01",
        "00",
        "00",
        "00",
        "10",
        "00",
        "01",
        "01",
        "01",
        "01",
        "00",
        "00",
        "00",
        "01",
        "10",
        "01",
        "00",
        "00",
        "00",
        "01",
        "01",
        "01",
        "00",
        "01",
        "00",
        "00",
        "00",
        "00",
        "00",
        "10",
        "10",
        "00",
        "01",
        "01",
        "00",
        "00",
        "00",
        "00",
        "00",
        "00",
        "00",
        "11",
        "00",
        "10",
        "01",
        "10",
        "00",
        "00",
        "00",
        "00",
        "01",
        "00",
        "00",
        "10",
        "01",
        "01",
        "00",
        "01",
        "01",
        "00",
        "00",
        "00",
        "00",
        "01",
        "00",
        "00",
        "10",
        "10",
        "01",
        "00",
        "10",
        "00",
        "10",
        "00",
        "00",
        "00",
        "00",
        "00",
        "00",
        "00",
        "00",
        "10",
        "10",
        "00",
        "01",
        "00",
        "00",
        "00",
        "00",
        "00",
        "00",
        "00",
        "01",
        "01",
        "00",
        "01",
        "10",
        "01",
        "01",
        "00",
        "00",
        "01",
        "01",
        "01",
        "00",
        "00",
        "00",
        "00",
        "01",
        "01",
        "00",
        "01",
        "00",
        "01",
        "00",
        "00",
        "01",
        "00",
        "00",
        "01",
        "00",
        "00",
        "00",
        "01",
        "00",
        "00"
      ],
      "probabilities": {
        "00": 0.5754896316901827,
        "01": 0.36395656142510147,
        "10": 0.05808150545784879,
        "11": 0.002472301426867029
      },
      "observables": {
        "state_norm": 1.0
      },
      "observable_batch": {
        "observable_set_hash": "dbdcda5c7aa312b23da7566b6bc7da5ac7b572b561161122735a2aeef6c5bbcc",
        "items": [
          {
            "observable": {
              "name": "Z(q0)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.8788923862305684,
            "variance": 0.22754817342593736,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "state_vector",
            "source_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
            "estimator_kind": "exact_state",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q1)",
              "terms": [
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.26714227429606296,
            "variance": 0.9286350052839271,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "state_vector",
            "source_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
            "estimator_kind": "exact_state",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q0)*Z(q1)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                },
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.15592386623409932,
            "variance": 0.9756877479386107,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "state_vector",
            "source_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
            "estimator_kind": "exact_state",
            "schema_version": "cascaqit.observables.v1"
          }
        ],
        "schema_version": "cascaqit.observables.v1"
      },
      "bit_ordering": {
        "convention": "logical_order",
        "logical_order": "q0,q1"
      },
      "occupation_encoding": {
        "ground": 0,
        "rydberg": 1
      },
      "diagnostics": [
        {
          "diagnostic_id": "simulation.scalable.hybrid.completed",
          "stage": "simulation",
          "severity": "info",
          "code": "SCALABLE_IDEAL_SIMULATION_COMPLETED",
          "message": "Scalable ideal state-vector simulation completed.",
          "schema_version": "0.1",
          "object_path": "result",
          "suggestion": null,
          "metadata": {
            "program_kind": "hybrid"
          }
        }
      ],
      "schema_version": "0.1",
      "metadata": {
        "backend_called": true,
        "backend_id": "local.simulator",
        "bitstring_ordering": {
          "bitstring_index": "left_to_right_matches_logical_order",
          "convention": "logical_order",
          "logical_order": [
            "q0",
            "q1"
          ]
        },
        "block_state_chain": [
          {
            "block_id": "block.0000.prepare",
            "input_logical_time": 0.0,
            "input_state_hash": "a366dfecabfa70e226fc32395f74a800800f0dca5826459ff2c84dfbe7be5254",
            "kernel": "NumpyDigitalStateVectorKernel",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
              "payload_id": "payload.0.block.0000.prepare.digital",
              "producer": "NumpyDigitalStateVectorKernel",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.0,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "NumpyDigitalStateVectorKernel"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 0,
            "output_logical_time": 0.0,
            "output_state_hash": "6261624855ea775f2dda16925a5a04fd7e40ee305d577ef8d5cb9f75186a89fe",
            "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "e0aba1b5f620a1abc613f7065f8405f71f6e9b5d10ec348db9b3a2435fab8ff3",
            "time_unit": "us",
            "transition_id": "transition.0.block.0000.prepare"
          },
          {
            "block_id": "block.0001.evolve",
            "input_logical_time": 0.0,
            "input_state_hash": "6261624855ea775f2dda16925a5a04fd7e40ee305d577ef8d5cb9f75186a89fe",
            "kernel": "MatrixFreeAnalogStateVectorKernel",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
              "payload_id": "payload.1.block.0001.evolve.analog",
              "producer": "MatrixFreeAnalogStateVectorKernel",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 32,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "fixed_step_krylov",
                "max_step_size": 0.01875,
                "metadata": {
                  "interaction_geometry_hash": "c8f7036b5efa5324fc28833aee66676e2832be11e92fc1375477e3da34d401b3",
                  "interaction_geometry_source": "nominal_register",
                  "interaction_maximum_abs_strength": 0.0,
                  "interaction_minimum_distance": 5.0,
                  "interaction_pair_count": 0,
                  "interaction_pair_table_hash": "4f53cda18c2baa0c0354bb5f9a3ecbe5ed12ab4d8e11ba873c2f11161202b945",
                  "interaction_plan_hash": "af6e015cdee51a687043495b129b6fc3d09f4c3455ebe536dd7c4daa8e5f54a2",
                  "norm_before_normalization": 0.9999999999999981,
                  "normalization_correction": 1.887379141862766e-15,
                  "output_dtype": "complex128",
                  "output_dtype_epsilon": 2.220446049250313e-16,
                  "requested_tolerance_below_output_precision": false,
                  "solver": "scipy.sparse.linalg.expm_multiply"
                },
                "min_step_size": 0.01875,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 32,
                "termination_reason": "completed",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 1,
            "output_logical_time": 0.6,
            "output_state_hash": "f57ede75fd1a1e60a8f4b07000fddb6029e3bc52921c5de0a3168cbcec976aec",
            "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
            "program_kind": "analog",
            "schema_version": "0.1",
            "solver_evidence_hash": "5a1200248280ce6c2f930a38df841189cc608e6ad109338d0a27c18b25706de3",
            "time_unit": "us",
            "transition_id": "transition.1.block.0001.evolve"
          },
          {
            "block_id": "block.0002.readout_rotation",
            "input_logical_time": 0.6,
            "input_state_hash": "f57ede75fd1a1e60a8f4b07000fddb6029e3bc52921c5de0a3168cbcec976aec",
            "kernel": "NumpyDigitalStateVectorKernel",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
              "payload_id": "payload.2.block.0002.readout_rotation.digital",
              "producer": "NumpyDigitalStateVectorKernel",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.6,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "NumpyDigitalStateVectorKernel"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 2,
            "output_logical_time": 0.6,
            "output_state_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
            "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "19ce6d439071212a621eef9e16197494ef72777812369c752e8c2da41f550822",
            "time_unit": "us",
            "transition_id": "transition.2.block.0002.readout_rotation"
          }
        ],
        "bundle_hash": "42234f4fd9d09c4d8102e6dc8d5f703c5ec76e567a4a89e630381577a0768e05",
        "control_report_evidence": [
          {
            "block_id": "block.0001.evolve",
            "diagnostic_count": 4,
            "diagnostics": [
              {
                "code": "CONTROL_CONCURRENCY_SUPPORTED",
                "diagnostic_id": "control.control_concurrency_supported.rydberg.local",
                "message": "Control concurrency is within the declared group limit.",
                "metadata": {
                  "actual_max_concurrency": 1,
                  "group_id": "rydberg.local",
                  "max_concurrent_operations": 2,
                  "operation_ids": [
                    "operation.local_detuning.0"
                  ]
                },
                "object_path": "control_schedule.operations",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              },
              {
                "code": "CONTROL_BANDWIDTH_SUPPORTED",
                "diagnostic_id": "control.control_bandwidth_supported.operation.local_detuning.0",
                "message": "Waveform knot-spacing bandwidth bound is within the Target limit.",
                "metadata": {
                  "bandwidth_limit": 2.0,
                  "bandwidth_unit": "MHz",
                  "channel_id": "rydberg.detuning.local",
                  "estimate_semantics": "nyquist_bound_from_minimum_knot_spacing",
                  "estimated_bandwidth": 0.0,
                  "operation_id": "operation.local_detuning.0"
                },
                "object_path": "hamiltonian.terms.local_detuning_terms[0].waveform",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              },
              {
                "code": "CONTROL_SLEW_SUPPORTED",
                "diagnostic_id": "control.control_slew_supported.operation.local_detuning.0",
                "message": "Waveform segment slew is within the Target limit.",
                "metadata": {
                  "actual_max_slew_rate": 0.0,
                  "channel_id": "rydberg.detuning.local",
                  "estimate_semantics": "maximum_actual_waveform_segment_derivative",
                  "max_slew_rate": 30.0,
                  "operation_id": "operation.local_detuning.0",
                  "slew_rate_unit": "rad/us^2"
                },
                "object_path": "hamiltonian.terms.local_detuning_terms[0].waveform",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              },
              {
                "code": "CONTROL_CROSSTALK_NO_OVERLAP",
                "diagnostic_id": "control.control_crosstalk_no_overlap.crosstalk.rydberg.rabi.local.rydberg.rabi.global",
                "message": "Crosstalk-constrained channels do not overlap.",
                "metadata": {
                  "actual_overlap_duration": 0.0,
                  "channel_ids": [
                    "rydberg.rabi.local",
                    "rydberg.rabi.global"
                  ],
                  "constraint_id": "crosstalk.rydberg.rabi.local.rydberg.rabi.global",
                  "max_overlap_duration": null,
                  "overlap_policy": "calibration_required",
                  "time_unit": "us"
                },
                "object_path": "control_schedule.operations",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              }
            ],
            "has_errors": false,
            "production_channel_allocation_performed": false,
            "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
            "schedule": {
              "control_system_hash": "fbbc3937e5187ca6bb0a3f00e176187027581e3382a83ee377e7115bffd5a87a",
              "diagnostics": [],
              "metadata": {
                "production_channel_allocation_performed": false,
                "projection": "program_ir_control_terms",
                "time_origin": 0.0,
                "time_unit": "us"
              },
              "operations": [
                {
                  "channel_id": "rydberg.detuning.global",
                  "end_time": 0.6,
                  "metadata": {
                    "production_assigned": false,
                    "program_path": "hamiltonian.terms.detuning",
                    "time_unit": "us",
                    "value_unit": "rad/us",
                    "waveform_kind": "constant"
                  },
                  "operation_id": "operation.global_detuning",
                  "operation_kind": "global_detuning",
                  "schema_version": "0.1",
                  "source_hash": "19b3cbf48a848eccf4b459d549c9603d70c02b450b81211bb93c55010a4339ab",
                  "start_time": 0.0,
                  "target_site_ids": [
                    "q0",
                    "q1"
                  ],
                  "waveform_hash": "19b3cbf48a848eccf4b459d549c9603d70c02b450b81211bb93c55010a4339ab"
                },
                {
                  "channel_id": "rydberg.rabi.global",
                  "end_time": 0.6,
                  "metadata": {
                    "production_assigned": false,
                    "program_path": "hamiltonian.terms.rabi",
                    "time_unit": "us",
                    "value_unit": "rad/us",
                    "waveform_kind": "constant"
                  },
                  "operation_id": "operation.global_rabi",
                  "operation_kind": "global_rabi",
                  "schema_version": "0.1",
                  "source_hash": "ad464599d866805baa0f7753cf0d4ce853b1688908e85f1baa172d7740efa2da",
                  "start_time": 0.0,
                  "target_site_ids": [
                    "q0",
                    "q1"
                  ],
                  "waveform_hash": "ad464599d866805baa0f7753cf0d4ce853b1688908e85f1baa172d7740efa2da"
                },
                {
                  "channel_id": "rydberg.detuning.local",
                  "end_time": 0.6,
                  "metadata": {
                    "production_assigned": false,
                    "program_path": "hamiltonian.terms.local_detuning_terms[0].waveform",
                    "time_unit": "us",
                    "value_unit": "rad/us",
                    "waveform_kind": "constant"
                  },
                  "operation_id": "operation.local_detuning.0",
                  "operation_kind": "local_detuning",
                  "schema_version": "0.1",
                  "source_hash": "5cf7b4b36d89a2948d9ee6b9b1974f74b74438df6df8aeaaafad175c714c34ed",
                  "start_time": 0.0,
                  "target_site_ids": [
                    "q0",
                    "q1"
                  ],
                  "waveform_hash": "e1caa1faf062ab87977975eab5ad7eb6366c3974acdadba829e14493602d0665"
                }
              ],
              "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
              "schedule_id": "schedule.program.control",
              "schema_version": "0.1"
            },
            "target_id": "mock.neutral_atom.local_ahs.v0_1"
          }
        ],
        "execution_package_created": false,
        "measurement": {
          "basis": "computational",
          "key": "result",
          "targets": [
            "q0",
            "q1"
          ]
        },
        "network_accessed": false,
        "offline_deterministic": true,
        "references": {
          "bundle_hash": "42234f4fd9d09c4d8102e6dc8d5f703c5ec76e567a4a89e630381577a0768e05",
          "calibration_snapshot_hash": null,
          "compiled_program_hash": null,
          "discretized_program_hash": null,
          "execution_package_id": null,
          "final_state_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
          "initial_state_hash": "a366dfecabfa70e226fc32395f74a800800f0dca5826459ff2c84dfbe7be5254",
          "metadata": {
            "graph_hash": "7f1df6f7e79a08131273f5367d8b40cf1a5fab604b12a94df8efb2411a53452c"
          },
          "plan_hash": "4388febf8e9092f0d5a1bdee8ba9658cd610618a595779025d6019da97dad681",
          "program_hash": "3ae12596e75deff789e526006cd6fad95bd8363cc46c441de4e19eaecd54aa05",
          "schema_version": "0.1",
          "target_snapshot_hash": null
        },
        "register_snapshots": [
          {
            "active_atom_ids": [
              "q0",
              "q1"
            ],
            "active_site_count": 2,
            "active_site_ids": [
              "q0",
              "q1"
            ],
            "lifecycle_stage": "planned",
            "physical_site_count": 2,
            "physical_site_ids": [
              "q0",
              "q1"
            ],
            "previous_snapshot_hash": null,
            "snapshot_hash": "571e481d25fc0fb0e4962bcb62d4b574c81cc965cb8e3b4fc69565faa8be68ec",
            "snapshot_id": "register.planned",
            "status_counts": {
              "defect": 0,
              "filled": 2,
              "loading_failed": 0,
              "vacant": 0
            }
          }
        ],
        "run_trace": {
          "events": [
            {
              "event_time": "logical:0x0.0p+0",
              "message": "Completed digital state transition.",
              "metadata": {
                "state_transition": {
                  "block_id": "block.0000.prepare",
                  "input_logical_time": 0.0,
                  "input_state_hash": "a366dfecabfa70e226fc32395f74a800800f0dca5826459ff2c84dfbe7be5254",
                  "kernel": "NumpyDigitalStateVectorKernel",
                  "metadata": {
                    "logical_order": [
                      "q0",
                      "q1"
                    ],
                    "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
                    "payload_id": "payload.0.block.0000.prepare.digital",
                    "producer": "NumpyDigitalStateVectorKernel",
                    "solver_evidence": {
                      "absolute_tolerance": null,
                      "accepted_steps": 0,
                      "final_time": 0.0,
                      "function_evaluations": null,
                      "initial_time": 0.0,
                      "integrator_requested": "fixed_step_krylov",
                      "integrator_selected": "not_applicable",
                      "max_step_size": null,
                      "metadata": {
                        "consumer": "NumpyDigitalStateVectorKernel"
                      },
                      "min_step_size": null,
                      "rejected_steps": null,
                      "rejected_steps_available": false,
                      "relative_tolerance": null,
                      "schema_version": "0.1",
                      "segment_count": 0,
                      "termination_reason": "not_applicable",
                      "time_unit": "us",
                      "tolerance_applied": false
                    }
                  },
                  "order_index": 0,
                  "output_logical_time": 0.0,
                  "output_state_hash": "6261624855ea775f2dda16925a5a04fd7e40ee305d577ef8d5cb9f75186a89fe",
                  "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
                  "program_kind": "digital",
                  "schema_version": "0.1",
                  "solver_evidence_hash": "e0aba1b5f620a1abc613f7065f8405f71f6e9b5d10ec348db9b3a2435fab8ff3",
                  "time_unit": "us",
                  "transition_id": "transition.0.block.0000.prepare"
                }
              },
              "schema_version": "0.1",
              "stage": "running",
              "status": "ok"
            },
            {
              "event_time": "logical:0x1.3333333333333p-1",
              "message": "Completed analog state transition.",
              "metadata": {
                "state_transition": {
                  "block_id": "block.0001.evolve",
                  "input_logical_time": 0.0,
                  "input_state_hash": "6261624855ea775f2dda16925a5a04fd7e40ee305d577ef8d5cb9f75186a89fe",
                  "kernel": "MatrixFreeAnalogStateVectorKernel",
                  "metadata": {
                    "logical_order": [
                      "q0",
                      "q1"
                    ],
                    "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
                    "payload_id": "payload.1.block.0001.evolve.analog",
                    "producer": "MatrixFreeAnalogStateVectorKernel",
                    "solver_evidence": {
                      "absolute_tolerance": null,
                      "accepted_steps": 32,
                      "final_time": 0.6,
                      "function_evaluations": null,
                      "initial_time": 0.0,
                      "integrator_requested": "fixed_step_krylov",
                      "integrator_selected": "fixed_step_krylov",
                      "max_step_size": 0.01875,
                      "metadata": {
                        "interaction_geometry_hash": "c8f7036b5efa5324fc28833aee66676e2832be11e92fc1375477e3da34d401b3",
                        "interaction_geometry_source": "nominal_register",
                        "interaction_maximum_abs_strength": 0.0,
                        "interaction_minimum_distance": 5.0,
                        "interaction_pair_count": 0,
                        "interaction_pair_table_hash": "4f53cda18c2baa0c0354bb5f9a3ecbe5ed12ab4d8e11ba873c2f11161202b945",
                        "interaction_plan_hash": "af6e015cdee51a687043495b129b6fc3d09f4c3455ebe536dd7c4daa8e5f54a2",
                        "norm_before_normalization": 0.9999999999999981,
                        "normalization_correction": 1.887379141862766e-15,
                        "output_dtype": "complex128",
                        "output_dtype_epsilon": 2.220446049250313e-16,
                        "requested_tolerance_below_output_precision": false,
                        "solver": "scipy.sparse.linalg.expm_multiply"
                      },
                      "min_step_size": 0.01875,
                      "rejected_steps": null,
                      "rejected_steps_available": false,
                      "relative_tolerance": null,
                      "schema_version": "0.1",
                      "segment_count": 32,
                      "termination_reason": "completed",
                      "time_unit": "us",
                      "tolerance_applied": false
                    }
                  },
                  "order_index": 1,
                  "output_logical_time": 0.6,
                  "output_state_hash": "f57ede75fd1a1e60a8f4b07000fddb6029e3bc52921c5de0a3168cbcec976aec",
                  "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
                  "program_kind": "analog",
                  "schema_version": "0.1",
                  "solver_evidence_hash": "5a1200248280ce6c2f930a38df841189cc608e6ad109338d0a27c18b25706de3",
                  "time_unit": "us",
                  "transition_id": "transition.1.block.0001.evolve"
                }
              },
              "schema_version": "0.1",
              "stage": "running",
              "status": "ok"
            },
            {
              "event_time": "logical:0x1.3333333333333p-1",
              "message": "Completed digital state transition.",
              "metadata": {
                "state_transition": {
                  "block_id": "block.0002.readout_rotation",
                  "input_logical_time": 0.6,
                  "input_state_hash": "f57ede75fd1a1e60a8f4b07000fddb6029e3bc52921c5de0a3168cbcec976aec",
                  "kernel": "NumpyDigitalStateVectorKernel",
                  "metadata": {
                    "logical_order": [
                      "q0",
                      "q1"
                    ],
                    "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
                    "payload_id": "payload.2.block.0002.readout_rotation.digital",
                    "producer": "NumpyDigitalStateVectorKernel",
                    "solver_evidence": {
                      "absolute_tolerance": null,
                      "accepted_steps": 0,
                      "final_time": 0.6,
                      "function_evaluations": null,
                      "initial_time": 0.6,
                      "integrator_requested": "fixed_step_krylov",
                      "integrator_selected": "not_applicable",
                      "max_step_size": null,
                      "metadata": {
                        "consumer": "NumpyDigitalStateVectorKernel"
                      },
                      "min_step_size": null,
                      "rejected_steps": null,
                      "rejected_steps_available": false,
                      "relative_tolerance": null,
                      "schema_version": "0.1",
                      "segment_count": 0,
                      "termination_reason": "not_applicable",
                      "time_unit": "us",
                      "tolerance_applied": false
                    }
                  },
                  "order_index": 2,
                  "output_logical_time": 0.6,
                  "output_state_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
                  "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
                  "program_kind": "digital",
                  "schema_version": "0.1",
                  "solver_evidence_hash": "19ce6d439071212a621eef9e16197494ef72777812369c752e8c2da41f550822",
                  "time_unit": "us",
                  "transition_id": "transition.2.block.0002.readout_rotation"
                }
              },
              "schema_version": "0.1",
              "stage": "running",
              "status": "ok"
            },
            {
              "event_time": "logical:0x1.3333333333333p-1",
              "message": "Terminal computational-basis measurement completed.",
              "metadata": {
                "final_state_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
                "measurement_key": "result",
                "seed": 4883,
                "shots": 128
              },
              "schema_version": "0.1",
              "stage": "completed",
              "status": "ok"
            }
          ],
          "metadata": {
            "execution_mode": "local_hybrid_shared_state"
          },
          "references": {
            "bundle_hash": "42234f4fd9d09c4d8102e6dc8d5f703c5ec76e567a4a89e630381577a0768e05",
            "calibration_snapshot_hash": null,
            "compiled_program_hash": null,
            "discretized_program_hash": null,
            "execution_package_id": null,
            "final_state_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
            "initial_state_hash": "a366dfecabfa70e226fc32395f74a800800f0dca5826459ff2c84dfbe7be5254",
            "metadata": {
              "graph_hash": "7f1df6f7e79a08131273f5367d8b40cf1a5fab604b12a94df8efb2411a53452c"
            },
            "plan_hash": "4388febf8e9092f0d5a1bdee8ba9658cd610618a595779025d6019da97dad681",
            "program_hash": "3ae12596e75deff789e526006cd6fad95bd8363cc46c441de4e19eaecd54aa05",
            "schema_version": "0.1",
            "target_snapshot_hash": null
          },
          "schema_version": "0.1",
          "trace_id": "trace.local_bundle.local_plan.project.noisy.hybrid.scalable_hybrid"
        },
        "seed": 4883,
        "selected_simulator": "ScalableIdealEngine",
        "simulation_execution_config": {
          "absolute_tolerance": 1e-11,
          "device": "cpu",
          "dtype": "complex128",
          "execution_scope": "job",
          "integrator_requested": "fixed_step_krylov",
          "integrator_selected": "fixed_step_krylov",
          "method": "state_vector",
          "relative_tolerance": 1e-09,
          "schema_version": "0.1",
          "seed": 4883,
          "seed_semantics": "effective_seed",
          "solver_evidence_hash": "26fbcf7ffc65fd086ad31ece9408ff01f8fd0da8b2d930ee71eae79723e28b90",
          "step_semantics": "fixed_time_slices",
          "steps": 32,
          "tolerance_applied": false,
          "trajectories": null,
          "worker_semantics": "kernel_concurrency",
          "workers": 1
        },
        "simulation_plan": {
          "atol": 1e-11,
          "budget_bytes": 20615843020,
          "candidates": [
            {
              "estimate": {
                "dtype": "complex128",
                "estimated_peak_bytes": 9792,
                "hilbert_dimension": 4,
                "itemsize_bytes": 16,
                "logical_sites": 2,
                "method": "state_vector",
                "operator_bytes": 128,
                "result_buffer_bytes": 4096,
                "sampling_bytes": 4096,
                "schema_version": "cascaqit.simulation.planning.v1",
                "state_bytes": 64,
                "state_dimension": 4,
                "trajectories": 1,
                "worker_copy_bytes": 0,
                "workers": 1,
                "workspace_bytes": 1408
              },
              "method": "state_vector",
              "reason_codes": [
                "SIMULATION_METHOD_ELIGIBLE",
                "SIMULATION_METHOD_SELECTED"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "selected"
            },
            {
              "estimate": null,
              "method": "subspace",
              "reason_codes": [
                "SIMULATION_SUBSPACE_BASIS_UNAVAILABLE"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "rejected"
            },
            {
              "estimate": {
                "dtype": "complex128",
                "estimated_peak_bytes": 9728,
                "hilbert_dimension": 4,
                "itemsize_bytes": 16,
                "logical_sites": 2,
                "method": "density_matrix",
                "operator_bytes": 512,
                "result_buffer_bytes": 4096,
                "sampling_bytes": 4096,
                "schema_version": "cascaqit.simulation.planning.v1",
                "state_bytes": 256,
                "state_dimension": 16,
                "trajectories": 1,
                "worker_copy_bytes": 0,
                "workers": 1,
                "workspace_bytes": 768
              },
              "method": "density_matrix",
              "reason_codes": [
                "SIMULATION_METHOD_REQUIRES_NOISE_MODEL"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "rejected"
            },
            {
              "estimate": {
                "dtype": "complex128",
                "estimated_peak_bytes": 368768,
                "hilbert_dimension": 4,
                "itemsize_bytes": 16,
                "logical_sites": 2,
                "method": "trajectory",
                "operator_bytes": 128,
                "result_buffer_bytes": 4096,
                "sampling_bytes": 4096,
                "schema_version": "cascaqit.simulation.planning.v1",
                "state_bytes": 16384,
                "state_dimension": 1024,
                "trajectories": 256,
                "worker_copy_bytes": 229376,
                "workers": 15,
                "workspace_bytes": 114688
              },
              "method": "trajectory",
              "reason_codes": [
                "SIMULATION_METHOD_REQUIRES_NOISE_MODEL"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "rejected"
            }
          ],
          "device": "cpu",
          "dtype": "complex128",
          "estimate": {
            "dtype": "complex128",
            "estimated_peak_bytes": 9792,
            "hilbert_dimension": 4,
            "itemsize_bytes": 16,
            "logical_sites": 2,
            "method": "state_vector",
            "operator_bytes": 128,
            "result_buffer_bytes": 4096,
            "sampling_bytes": 4096,
            "schema_version": "cascaqit.simulation.planning.v1",
            "state_bytes": 64,
            "state_dimension": 4,
            "trajectories": 1,
            "worker_copy_bytes": 0,
            "workers": 1,
            "workspace_bytes": 1408
          },
          "hilbert_dimension": 4,
          "host_hash": "fc340411ec9c1fe45ae7d312ce900fdaeaa5935813f6c5c169cb18b81d90aea1",
          "integrator_requested": "fixed_step_krylov",
          "integrator_selected": "fixed_step_krylov",
          "logical_sites": 2,
          "max_steps": 32,
          "metadata": {
            "array_backend": "numpy",
            "blockade_dimension": null,
            "host_snapshot_source": "platform.effective_resource_probe",
            "max_wall_time_seconds": null,
            "memory_fraction": 0.8,
            "network_accessed": false,
            "numpy_version": "2.0.2",
            "requires_trajectory": false,
            "scipy_version": "1.17.1",
            "target_statistical_error": null,
            "time_integration_required": true,
            "workers_cpu_limit": 15,
            "workers_requested": "auto"
          },
          "method_requested": "state_vector",
          "method_selected": "state_vector",
          "noisy": false,
          "options_hash": "7ba8889c5c03606c2adf135430cd6cea394c55f6e848cee74843c36c64bfaae5",
          "plan_id": "simulation_plan.hybrid.2.state_vector.fixed_step_krylov",
          "program_kind": "hybrid",
          "rtol": 1e-09,
          "schema_version": "cascaqit.simulation.planning.v1",
          "seed": 4883,
          "state_representation": "state_vector",
          "trajectories": 256,
          "truthfulness": "planning_only",
          "workers": 1
        },
        "simulation_plan_hash": "7435a9972fa6c39fbcb07632560544b37c22047b7bc6fb5fa982284672e09629",
        "simulation_plan_truthfulness": "planning_only",
        "simulation_resource_estimate": {
          "dtype": "complex128",
          "estimated_peak_bytes": 9792,
          "hilbert_dimension": 4,
          "itemsize_bytes": 16,
          "logical_sites": 2,
          "method": "state_vector",
          "operator_bytes": 128,
          "result_buffer_bytes": 4096,
          "sampling_bytes": 4096,
          "schema_version": "cascaqit.simulation.planning.v1",
          "state_bytes": 64,
          "state_dimension": 4,
          "trajectories": 1,
          "worker_copy_bytes": 0,
          "workers": 1,
          "workspace_bytes": 1408
        },
        "simulation_resource_usage": {
          "actual_peak_rss_bytes": 143736832,
          "baseline_peak_rss_bytes": 143736832,
          "estimate_error_fraction": null,
          "estimate_within_tolerance": null,
          "estimated_peak_bytes": 9792,
          "incremental_peak_rss_bytes": 0,
          "measurement_scope": "job",
          "measurement_status": "baseline_dominated",
          "rss_semantics": "process_high_water_mark",
          "schema_version": "0.1",
          "wall_time_seconds": 0.013312541996128857
        },
        "simulation_solver_evidence": {
          "absolute_tolerance": null,
          "accepted_steps": 32,
          "final_time": 0.6,
          "function_evaluations": null,
          "initial_time": 0.0,
          "integrator_requested": "fixed_step_krylov",
          "integrator_selected": "fixed_step_krylov",
          "max_step_size": 0.01875,
          "metadata": {
            "aggregation_scope": "hybrid_quantum_blocks",
            "component_count": 1,
            "component_evidence_hashes": [
              "5a1200248280ce6c2f930a38df841189cc608e6ad109338d0a27c18b25706de3"
            ]
          },
          "min_step_size": 0.01875,
          "rejected_steps": null,
          "rejected_steps_available": false,
          "relative_tolerance": null,
          "schema_version": "0.1",
          "segment_count": 32,
          "termination_reason": "completed",
          "time_unit": "us",
          "tolerance_applied": false
        },
        "simulation_solver_evidence_hash": "26fbcf7ffc65fd086ad31ece9408ff01f8fd0da8b2d930ee71eae79723e28b90",
        "simulation_state": {
          "arrays": {
            "amplitudes": {
              "content_hash": "307fb75fa3b49382f0b1cf16d9ad1f78bb24f54fc564dce43728fec68f0c2f10",
              "dtype": "complex128",
              "nbytes": 64,
              "returned_state_bytes": false,
              "shape": [
                4
              ]
            }
          },
          "basis": "logical_two_level",
          "logical_order": [
            "q0",
            "q1"
          ],
          "logical_time": 0.6,
          "metrics": {
            "norm": 1.0
          },
          "noise_context": {},
          "provenance": {
            "conversion": null,
            "metadata": {
              "algorithm": "tensor_axis",
              "operation_count": 2,
              "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf"
            },
            "parent_state_hash": "f57ede75fd1a1e60a8f4b07000fddb6029e3bc52921c5de0a3168cbcec976aec",
            "producer": "NumpyDigitalStateVectorKernel",
            "schema_version": "cascaqit.simulation.array_state.v1",
            "step_index": 3
          },
          "returned_state_bytes": false,
          "schema_version": "cascaqit.simulation.array_state.v1",
          "stable_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
          "state_kind": "state_vector",
          "time_unit": "us"
        },
        "simulation_truthfulness": "ideal_state_evolution",
        "simulator": {
          "array_backend": "numpy.cpu",
          "method": "state_vector",
          "name": "ScalableIdealEngine",
          "program_kind": "hybrid"
        },
        "state_bytes_returned": false,
        "state_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
        "state_transitions": [
          {
            "block_id": "block.0000.prepare",
            "input_logical_time": 0.0,
            "input_state_hash": "a366dfecabfa70e226fc32395f74a800800f0dca5826459ff2c84dfbe7be5254",
            "kernel": "NumpyDigitalStateVectorKernel",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
              "payload_id": "payload.0.block.0000.prepare.digital",
              "producer": "NumpyDigitalStateVectorKernel",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.0,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "NumpyDigitalStateVectorKernel"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 0,
            "output_logical_time": 0.0,
            "output_state_hash": "6261624855ea775f2dda16925a5a04fd7e40ee305d577ef8d5cb9f75186a89fe",
            "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "e0aba1b5f620a1abc613f7065f8405f71f6e9b5d10ec348db9b3a2435fab8ff3",
            "time_unit": "us",
            "transition_id": "transition.0.block.0000.prepare"
          },
          {
            "block_id": "block.0001.evolve",
            "input_logical_time": 0.0,
            "input_state_hash": "6261624855ea775f2dda16925a5a04fd7e40ee305d577ef8d5cb9f75186a89fe",
            "kernel": "MatrixFreeAnalogStateVectorKernel",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
              "payload_id": "payload.1.block.0001.evolve.analog",
              "producer": "MatrixFreeAnalogStateVectorKernel",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 32,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "fixed_step_krylov",
                "max_step_size": 0.01875,
                "metadata": {
                  "interaction_geometry_hash": "c8f7036b5efa5324fc28833aee66676e2832be11e92fc1375477e3da34d401b3",
                  "interaction_geometry_source": "nominal_register",
                  "interaction_maximum_abs_strength": 0.0,
                  "interaction_minimum_distance": 5.0,
                  "interaction_pair_count": 0,
                  "interaction_pair_table_hash": "4f53cda18c2baa0c0354bb5f9a3ecbe5ed12ab4d8e11ba873c2f11161202b945",
                  "interaction_plan_hash": "af6e015cdee51a687043495b129b6fc3d09f4c3455ebe536dd7c4daa8e5f54a2",
                  "norm_before_normalization": 0.9999999999999981,
                  "normalization_correction": 1.887379141862766e-15,
                  "output_dtype": "complex128",
                  "output_dtype_epsilon": 2.220446049250313e-16,
                  "requested_tolerance_below_output_precision": false,
                  "solver": "scipy.sparse.linalg.expm_multiply"
                },
                "min_step_size": 0.01875,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 32,
                "termination_reason": "completed",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 1,
            "output_logical_time": 0.6,
            "output_state_hash": "f57ede75fd1a1e60a8f4b07000fddb6029e3bc52921c5de0a3168cbcec976aec",
            "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
            "program_kind": "analog",
            "schema_version": "0.1",
            "solver_evidence_hash": "5a1200248280ce6c2f930a38df841189cc608e6ad109338d0a27c18b25706de3",
            "time_unit": "us",
            "transition_id": "transition.1.block.0001.evolve"
          },
          {
            "block_id": "block.0002.readout_rotation",
            "input_logical_time": 0.6,
            "input_state_hash": "f57ede75fd1a1e60a8f4b07000fddb6029e3bc52921c5de0a3168cbcec976aec",
            "kernel": "NumpyDigitalStateVectorKernel",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
              "payload_id": "payload.2.block.0002.readout_rotation.digital",
              "producer": "NumpyDigitalStateVectorKernel",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.6,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "NumpyDigitalStateVectorKernel"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 2,
            "output_logical_time": 0.6,
            "output_state_hash": "6cef2e41d9072423b6fa6832b34bba694ed206ccd467820ce3f79a88d5661838",
            "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "19ce6d439071212a621eef9e16197494ef72777812369c752e8c2da41f550822",
            "time_unit": "us",
            "transition_id": "transition.2.block.0002.readout_rotation"
          }
        ]
      }
    },
    {
      "result_id": "result.local_bundle.local_plan.project.noisy.hybrid.physical_noise",
      "program_hash": "3ae12596e75deff789e526006cd6fad95bd8363cc46c441de4e19eaecd54aa05",
      "target_id": "local.simulator",
      "shots": 128,
      "counts": {
        "00": 47,
        "01": 38,
        "10": 38,
        "11": 5
      },
      "samples": [
        "01",
        "00",
        "01",
        "01",
        "00",
        "00",
        "00",
        "11",
        "00",
        "01",
        "10",
        "10",
        "00",
        "01",
        "00",
        "00",
        "00",
        "01",
        "01",
        "00",
        "00",
        "00",
        "00",
        "00",
        "01",
        "10",
        "00",
        "01",
        "00",
        "10",
        "10",
        "00",
        "10",
        "01",
        "01",
        "00",
        "01",
        "00",
        "10",
        "00",
        "01",
        "10",
        "00",
        "00",
        "01",
        "01",
        "00",
        "10",
        "01",
        "10",
        "01",
        "00",
        "00",
        "10",
        "10",
        "01",
        "00",
        "10",
        "11",
        "10",
        "01",
        "00",
        "10",
        "01",
        "11",
        "00",
        "00",
        "10",
        "01",
        "10",
        "00",
        "00",
        "01",
        "10",
        "00",
        "01",
        "01",
        "10",
        "00",
        "10",
        "10",
        "00",
        "10",
        "00",
        "00",
        "10",
        "10",
        "00",
        "10",
        "01",
        "10",
        "01",
        "01",
        "01",
        "10",
        "10",
        "10",
        "00",
        "01",
        "10",
        "00",
        "10",
        "01",
        "00",
        "00",
        "00",
        "01",
        "01",
        "11",
        "01",
        "00",
        "10",
        "00",
        "11",
        "10",
        "10",
        "00",
        "01",
        "01",
        "10",
        "01",
        "00",
        "10",
        "10",
        "01",
        "10",
        "00",
        "01"
      ],
      "probabilities": {
        "00": 0.4327894017200914,
        "01": 0.23601050347734526,
        "10": 0.2900376720088961,
        "11": 0.041162422793667296
      },
      "observables": {
        "minimum_eigenvalue": 0.016080082047543194,
        "purity": 0.5302271049763567,
        "trace": 1.0
      },
      "observable_batch": {
        "observable_set_hash": "dbdcda5c7aa312b23da7566b6bc7da5ac7b572b561161122735a2aeef6c5bbcc",
        "items": [
          {
            "observable": {
              "name": "Z(q0)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.33759981039487336,
            "variance": 0.8860263680213456,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q1)",
              "terms": [
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.44565414745797494,
            "variance": 0.8013923808535055,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q0)*Z(q1)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                },
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": -0.052096350972482636,
            "variance": 0.9972859702153519,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          }
        ],
        "schema_version": "cascaqit.observables.v1"
      },
      "bit_ordering": {
        "convention": "logical_order",
        "logical_order": "q0,q1"
      },
      "occupation_encoding": {
        "ground": 0,
        "rydberg": 1
      },
      "diagnostics": [
        {
          "diagnostic_id": "simulation.noise.physical.completed",
          "stage": "simulation",
          "severity": "info",
          "code": "PHYSICAL_NOISE_SIMULATION_COMPLETED",
          "message": "Canonical physical noise simulation completed.",
          "schema_version": "0.1",
          "object_path": "result",
          "suggestion": null,
          "metadata": {
            "channel_count": 1,
            "method": "density_matrix"
          }
        }
      ],
      "schema_version": "0.1",
      "metadata": {
        "backend_called": true,
        "backend_id": "local.simulator",
        "block_state_chain": [
          {
            "block_id": "block.0000.prepare",
            "input_logical_time": 0.0,
            "input_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
            "kernel": "ExactDensityMatrixKernel.digital",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
              "payload_id": "payload.0.block.0000.prepare.digital",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.0,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "ExactDensityMatrixKernel.digital"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 0,
            "output_logical_time": 0.0,
            "output_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
            "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "dfca8e955ca173fed5f1dce4f8b20a513e634a38ff28f78dddce9fcdaa7803dd",
            "time_unit": "us",
            "transition_id": "transition.0.block.0000.prepare"
          },
          {
            "block_id": "block.0001.evolve",
            "input_logical_time": 0.0,
            "input_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
            "kernel": "ExactDensityMatrixKernel.analog",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
              "payload_id": "payload.1.block.0001.evolve.analog",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 32,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "fixed_step_krylov",
                "max_step_size": 0.01875,
                "metadata": {
                  "hermiticity_error_before_stabilization": 4.2841699744536696e-16,
                  "minimum_eigenvalue_before_stabilization": 0.016080082047543128,
                  "output_dtype": "complex128",
                  "positivity_evidence_available": true,
                  "solver": "strang_krylov_lindblad",
                  "stabilization_applied": true,
                  "trace_before_stabilization": {
                    "imag": -2.870804933781793e-18,
                    "real": 0.9999999999999972
                  }
                },
                "min_step_size": 0.01875,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 32,
                "termination_reason": "completed",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 1,
            "output_logical_time": 0.6,
            "output_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
            "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
            "program_kind": "analog",
            "schema_version": "0.1",
            "solver_evidence_hash": "b87033a62649f443f68ae025e7d6d4ca57efd42e54be9728595a3bf363bf4e3f",
            "time_unit": "us",
            "transition_id": "transition.1.block.0001.evolve"
          },
          {
            "block_id": "block.0002.readout_rotation",
            "input_logical_time": 0.6,
            "input_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
            "kernel": "ExactDensityMatrixKernel.digital",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
              "payload_id": "payload.2.block.0002.readout_rotation.digital",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.6,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "ExactDensityMatrixKernel.digital"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 2,
            "output_logical_time": 0.6,
            "output_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "8c6537a374163b7170874874c97426a424799f42a8be28e169dce0bf916296f1",
            "time_unit": "us",
            "transition_id": "transition.2.block.0002.readout_rotation"
          }
        ],
        "control_report_evidence": [
          {
            "block_id": "block.0001.evolve",
            "diagnostic_count": 4,
            "diagnostics": [
              {
                "code": "CONTROL_CONCURRENCY_SUPPORTED",
                "diagnostic_id": "control.control_concurrency_supported.rydberg.local",
                "message": "Control concurrency is within the declared group limit.",
                "metadata": {
                  "actual_max_concurrency": 1,
                  "group_id": "rydberg.local",
                  "max_concurrent_operations": 2,
                  "operation_ids": [
                    "operation.local_detuning.0"
                  ]
                },
                "object_path": "control_schedule.operations",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              },
              {
                "code": "CONTROL_BANDWIDTH_SUPPORTED",
                "diagnostic_id": "control.control_bandwidth_supported.operation.local_detuning.0",
                "message": "Waveform knot-spacing bandwidth bound is within the Target limit.",
                "metadata": {
                  "bandwidth_limit": 2.0,
                  "bandwidth_unit": "MHz",
                  "channel_id": "rydberg.detuning.local",
                  "estimate_semantics": "nyquist_bound_from_minimum_knot_spacing",
                  "estimated_bandwidth": 0.0,
                  "operation_id": "operation.local_detuning.0"
                },
                "object_path": "hamiltonian.terms.local_detuning_terms[0].waveform",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              },
              {
                "code": "CONTROL_SLEW_SUPPORTED",
                "diagnostic_id": "control.control_slew_supported.operation.local_detuning.0",
                "message": "Waveform segment slew is within the Target limit.",
                "metadata": {
                  "actual_max_slew_rate": 0.0,
                  "channel_id": "rydberg.detuning.local",
                  "estimate_semantics": "maximum_actual_waveform_segment_derivative",
                  "max_slew_rate": 30.0,
                  "operation_id": "operation.local_detuning.0",
                  "slew_rate_unit": "rad/us^2"
                },
                "object_path": "hamiltonian.terms.local_detuning_terms[0].waveform",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              },
              {
                "code": "CONTROL_CROSSTALK_NO_OVERLAP",
                "diagnostic_id": "control.control_crosstalk_no_overlap.crosstalk.rydberg.rabi.local.rydberg.rabi.global",
                "message": "Crosstalk-constrained channels do not overlap.",
                "metadata": {
                  "actual_overlap_duration": 0.0,
                  "channel_ids": [
                    "rydberg.rabi.local",
                    "rydberg.rabi.global"
                  ],
                  "constraint_id": "crosstalk.rydberg.rabi.local.rydberg.rabi.global",
                  "max_overlap_duration": null,
                  "overlap_policy": "calibration_required",
                  "time_unit": "us"
                },
                "object_path": "control_schedule.operations",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              }
            ],
            "has_errors": false,
            "production_channel_allocation_performed": false,
            "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
            "schedule": {
              "control_system_hash": "fbbc3937e5187ca6bb0a3f00e176187027581e3382a83ee377e7115bffd5a87a",
              "diagnostics": [],
              "metadata": {
                "production_channel_allocation_performed": false,
                "projection": "program_ir_control_terms",
                "time_origin": 0.0,
                "time_unit": "us"
              },
              "operations": [
                {
                  "channel_id": "rydberg.detuning.global",
                  "end_time": 0.6,
                  "metadata": {
                    "production_assigned": false,
                    "program_path": "hamiltonian.terms.detuning",
                    "time_unit": "us",
                    "value_unit": "rad/us",
                    "waveform_kind": "constant"
                  },
                  "operation_id": "operation.global_detuning",
                  "operation_kind": "global_detuning",
                  "schema_version": "0.1",
                  "source_hash": "19b3cbf48a848eccf4b459d549c9603d70c02b450b81211bb93c55010a4339ab",
                  "start_time": 0.0,
                  "target_site_ids": [
                    "q0",
                    "q1"
                  ],
                  "waveform_hash": "19b3cbf48a848eccf4b459d549c9603d70c02b450b81211bb93c55010a4339ab"
                },
                {
                  "channel_id": "rydberg.rabi.global",
                  "end_time": 0.6,
                  "metadata": {
                    "production_assigned": false,
                    "program_path": "hamiltonian.terms.rabi",
                    "time_unit": "us",
                    "value_unit": "rad/us",
                    "waveform_kind": "constant"
                  },
                  "operation_id": "operation.global_rabi",
                  "operation_kind": "global_rabi",
                  "schema_version": "0.1",
                  "source_hash": "ad464599d866805baa0f7753cf0d4ce853b1688908e85f1baa172d7740efa2da",
                  "start_time": 0.0,
                  "target_site_ids": [
                    "q0",
                    "q1"
                  ],
                  "waveform_hash": "ad464599d866805baa0f7753cf0d4ce853b1688908e85f1baa172d7740efa2da"
                },
                {
                  "channel_id": "rydberg.detuning.local",
                  "end_time": 0.6,
                  "metadata": {
                    "production_assigned": false,
                    "program_path": "hamiltonian.terms.local_detuning_terms[0].waveform",
                    "time_unit": "us",
                    "value_unit": "rad/us",
                    "waveform_kind": "constant"
                  },
                  "operation_id": "operation.local_detuning.0",
                  "operation_kind": "local_detuning",
                  "schema_version": "0.1",
                  "source_hash": "5cf7b4b36d89a2948d9ee6b9b1974f74b74438df6df8aeaaafad175c714c34ed",
                  "start_time": 0.0,
                  "target_site_ids": [
                    "q0",
                    "q1"
                  ],
                  "waveform_hash": "e1caa1faf062ab87977975eab5ad7eb6366c3974acdadba829e14493602d0665"
                }
              ],
              "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
              "schedule_id": "schedule.program.control",
              "schema_version": "0.1"
            },
            "target_id": "mock.neutral_atom.local_ahs.v0_1"
          }
        ],
        "execution_package_created": false,
        "network_accessed": false,
        "noise_model_hash": "597cc0c9128c4662d67f002310b8179ca1a8a02b1202d622a4347fb08e70061e",
        "noise_report": {
          "applied_channel_types": [
            "dephasing"
          ],
          "measurement_application_count": 0,
          "method": "density_matrix",
          "noise_model_hash": "597cc0c9128c4662d67f002310b8179ca1a8a02b1202d622a4347fb08e70061e",
          "noise_model_id": "phase",
          "physical_application_count": 1,
          "records": [
            {
              "channel_id": "noise.dephasing",
              "channel_type": "dephasing",
              "injection_point": "analog_evolution",
              "input_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
              "metadata": {
                "model": "lindblad_phase_flip",
                "parameters": {
                  "rate": 0.8
                },
                "schedule_ref": null
              },
              "output_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
              "targets": [
                "q0",
                "q1"
              ],
              "truthfulness": "physical_state_evolution"
            }
          ],
          "truthfulness": "physical_state_evolution"
        },
        "noise_report_hash": "9caa728416d5f767fc1fbb0397f0a0086d6be2c8158d2a48eaeb9244f691f285",
        "offline_deterministic": true,
        "references": {
          "bundle_hash": "49bf06e86bd96e992244a38daea8a830f278ddf182a63cdfd7a6605f84006ed7",
          "calibration_snapshot_hash": null,
          "compiled_program_hash": null,
          "discretized_program_hash": null,
          "execution_package_id": null,
          "final_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
          "initial_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
          "metadata": {
            "graph_hash": "7f1df6f7e79a08131273f5367d8b40cf1a5fab604b12a94df8efb2411a53452c"
          },
          "plan_hash": "4388febf8e9092f0d5a1bdee8ba9658cd610618a595779025d6019da97dad681",
          "program_hash": "3ae12596e75deff789e526006cd6fad95bd8363cc46c441de4e19eaecd54aa05",
          "schema_version": "0.1",
          "target_snapshot_hash": null
        },
        "register_snapshots": [
          {
            "active_atom_ids": [
              "q0",
              "q1"
            ],
            "active_site_count": 2,
            "active_site_ids": [
              "q0",
              "q1"
            ],
            "lifecycle_stage": "planned",
            "physical_site_count": 2,
            "physical_site_ids": [
              "q0",
              "q1"
            ],
            "previous_snapshot_hash": null,
            "snapshot_hash": "571e481d25fc0fb0e4962bcb62d4b574c81cc965cb8e3b4fc69565faa8be68ec",
            "snapshot_id": "register.planned",
            "status_counts": {
              "defect": 0,
              "filled": 2,
              "loading_failed": 0,
              "vacant": 0
            }
          }
        ],
        "run_trace": {
          "events": [
            {
              "event_time": "logical:0x0.0p+0",
              "message": "Completed digital state transition.",
              "metadata": {
                "state_transition": {
                  "block_id": "block.0000.prepare",
                  "input_logical_time": 0.0,
                  "input_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
                  "kernel": "ExactDensityMatrixKernel.digital",
                  "metadata": {
                    "logical_order": [
                      "q0",
                      "q1"
                    ],
                    "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
                    "payload_id": "payload.0.block.0000.prepare.digital",
                    "solver_evidence": {
                      "absolute_tolerance": null,
                      "accepted_steps": 0,
                      "final_time": 0.0,
                      "function_evaluations": null,
                      "initial_time": 0.0,
                      "integrator_requested": "fixed_step_krylov",
                      "integrator_selected": "not_applicable",
                      "max_step_size": null,
                      "metadata": {
                        "consumer": "ExactDensityMatrixKernel.digital"
                      },
                      "min_step_size": null,
                      "rejected_steps": null,
                      "rejected_steps_available": false,
                      "relative_tolerance": null,
                      "schema_version": "0.1",
                      "segment_count": 0,
                      "termination_reason": "not_applicable",
                      "time_unit": "us",
                      "tolerance_applied": false
                    }
                  },
                  "order_index": 0,
                  "output_logical_time": 0.0,
                  "output_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
                  "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
                  "program_kind": "digital",
                  "schema_version": "0.1",
                  "solver_evidence_hash": "dfca8e955ca173fed5f1dce4f8b20a513e634a38ff28f78dddce9fcdaa7803dd",
                  "time_unit": "us",
                  "transition_id": "transition.0.block.0000.prepare"
                }
              },
              "schema_version": "0.1",
              "stage": "running",
              "status": "ok"
            },
            {
              "event_time": "logical:0x1.3333333333333p-1",
              "message": "Completed analog state transition.",
              "metadata": {
                "state_transition": {
                  "block_id": "block.0001.evolve",
                  "input_logical_time": 0.0,
                  "input_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
                  "kernel": "ExactDensityMatrixKernel.analog",
                  "metadata": {
                    "logical_order": [
                      "q0",
                      "q1"
                    ],
                    "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
                    "payload_id": "payload.1.block.0001.evolve.analog",
                    "solver_evidence": {
                      "absolute_tolerance": null,
                      "accepted_steps": 32,
                      "final_time": 0.6,
                      "function_evaluations": null,
                      "initial_time": 0.0,
                      "integrator_requested": "fixed_step_krylov",
                      "integrator_selected": "fixed_step_krylov",
                      "max_step_size": 0.01875,
                      "metadata": {
                        "hermiticity_error_before_stabilization": 4.2841699744536696e-16,
                        "minimum_eigenvalue_before_stabilization": 0.016080082047543128,
                        "output_dtype": "complex128",
                        "positivity_evidence_available": true,
                        "solver": "strang_krylov_lindblad",
                        "stabilization_applied": true,
                        "trace_before_stabilization": {
                          "imag": -2.870804933781793e-18,
                          "real": 0.9999999999999972
                        }
                      },
                      "min_step_size": 0.01875,
                      "rejected_steps": null,
                      "rejected_steps_available": false,
                      "relative_tolerance": null,
                      "schema_version": "0.1",
                      "segment_count": 32,
                      "termination_reason": "completed",
                      "time_unit": "us",
                      "tolerance_applied": false
                    }
                  },
                  "order_index": 1,
                  "output_logical_time": 0.6,
                  "output_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
                  "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
                  "program_kind": "analog",
                  "schema_version": "0.1",
                  "solver_evidence_hash": "b87033a62649f443f68ae025e7d6d4ca57efd42e54be9728595a3bf363bf4e3f",
                  "time_unit": "us",
                  "transition_id": "transition.1.block.0001.evolve"
                }
              },
              "schema_version": "0.1",
              "stage": "running",
              "status": "ok"
            },
            {
              "event_time": "logical:0x1.3333333333333p-1",
              "message": "Completed digital state transition.",
              "metadata": {
                "state_transition": {
                  "block_id": "block.0002.readout_rotation",
                  "input_logical_time": 0.6,
                  "input_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
                  "kernel": "ExactDensityMatrixKernel.digital",
                  "metadata": {
                    "logical_order": [
                      "q0",
                      "q1"
                    ],
                    "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
                    "payload_id": "payload.2.block.0002.readout_rotation.digital",
                    "solver_evidence": {
                      "absolute_tolerance": null,
                      "accepted_steps": 0,
                      "final_time": 0.6,
                      "function_evaluations": null,
                      "initial_time": 0.6,
                      "integrator_requested": "fixed_step_krylov",
                      "integrator_selected": "not_applicable",
                      "max_step_size": null,
                      "metadata": {
                        "consumer": "ExactDensityMatrixKernel.digital"
                      },
                      "min_step_size": null,
                      "rejected_steps": null,
                      "rejected_steps_available": false,
                      "relative_tolerance": null,
                      "schema_version": "0.1",
                      "segment_count": 0,
                      "termination_reason": "not_applicable",
                      "time_unit": "us",
                      "tolerance_applied": false
                    }
                  },
                  "order_index": 2,
                  "output_logical_time": 0.6,
                  "output_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
                  "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
                  "program_kind": "digital",
                  "schema_version": "0.1",
                  "solver_evidence_hash": "8c6537a374163b7170874874c97426a424799f42a8be28e169dce0bf916296f1",
                  "time_unit": "us",
                  "transition_id": "transition.2.block.0002.readout_rotation"
                }
              },
              "schema_version": "0.1",
              "stage": "running",
              "status": "ok"
            },
            {
              "event_time": "logical:0x1.3333333333333p-1",
              "message": "Terminal noisy sampling completed.",
              "metadata": {
                "final_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
                "measurement_key": "result",
                "seed": 4881,
                "shots": 128
              },
              "schema_version": "0.1",
              "stage": "completed",
              "status": "ok"
            }
          ],
          "metadata": {
            "execution_mode": "local_hybrid_density_matrix"
          },
          "references": {
            "bundle_hash": "49bf06e86bd96e992244a38daea8a830f278ddf182a63cdfd7a6605f84006ed7",
            "calibration_snapshot_hash": null,
            "compiled_program_hash": null,
            "discretized_program_hash": null,
            "execution_package_id": null,
            "final_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "initial_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
            "metadata": {
              "graph_hash": "7f1df6f7e79a08131273f5367d8b40cf1a5fab604b12a94df8efb2411a53452c"
            },
            "plan_hash": "4388febf8e9092f0d5a1bdee8ba9658cd610618a595779025d6019da97dad681",
            "program_hash": "3ae12596e75deff789e526006cd6fad95bd8363cc46c441de4e19eaecd54aa05",
            "schema_version": "0.1",
            "target_snapshot_hash": null
          },
          "schema_version": "0.1",
          "trace_id": "trace.local_bundle.local_plan.project.noisy.hybrid.physical_noise"
        },
        "selected_simulator": "ExactDensityNoiseEngine",
        "simulation_execution_config": {
          "absolute_tolerance": 1e-11,
          "device": "cpu",
          "dtype": "complex128",
          "execution_scope": "job",
          "integrator_requested": "fixed_step_krylov",
          "integrator_selected": "fixed_step_krylov",
          "method": "density_matrix",
          "relative_tolerance": 1e-09,
          "schema_version": "0.1",
          "seed": 4881,
          "seed_semantics": "effective_seed",
          "solver_evidence_hash": "ef94260e54386e61fba4be5fe71dd918dd8b4fe0e55d432adf91e8b7ac110708",
          "step_semantics": "fixed_time_slices",
          "steps": 32,
          "tolerance_applied": false,
          "trajectories": null,
          "worker_semantics": "kernel_concurrency",
          "workers": 1
        },
        "simulation_plan": {
          "atol": 1e-11,
          "budget_bytes": 20615843020,
          "candidates": [
            {
              "estimate": {
                "dtype": "complex128",
                "estimated_peak_bytes": 9792,
                "hilbert_dimension": 4,
                "itemsize_bytes": 16,
                "logical_sites": 2,
                "method": "state_vector",
                "operator_bytes": 128,
                "result_buffer_bytes": 4096,
                "sampling_bytes": 4096,
                "schema_version": "cascaqit.simulation.planning.v1",
                "state_bytes": 64,
                "state_dimension": 4,
                "trajectories": 1,
                "worker_copy_bytes": 0,
                "workers": 1,
                "workspace_bytes": 1408
              },
              "method": "state_vector",
              "reason_codes": [
                "SIMULATION_METHOD_REQUIRES_IDEAL_MODEL"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "rejected"
            },
            {
              "estimate": null,
              "method": "subspace",
              "reason_codes": [
                "SIMULATION_METHOD_REQUIRES_IDEAL_MODEL"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "rejected"
            },
            {
              "estimate": {
                "dtype": "complex128",
                "estimated_peak_bytes": 9728,
                "hilbert_dimension": 4,
                "itemsize_bytes": 16,
                "logical_sites": 2,
                "method": "density_matrix",
                "operator_bytes": 512,
                "result_buffer_bytes": 4096,
                "sampling_bytes": 4096,
                "schema_version": "cascaqit.simulation.planning.v1",
                "state_bytes": 256,
                "state_dimension": 16,
                "trajectories": 1,
                "worker_copy_bytes": 0,
                "workers": 1,
                "workspace_bytes": 768
              },
              "method": "density_matrix",
              "reason_codes": [
                "SIMULATION_METHOD_ELIGIBLE",
                "SIMULATION_METHOD_SELECTED"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "selected"
            },
            {
              "estimate": {
                "dtype": "complex128",
                "estimated_peak_bytes": 368768,
                "hilbert_dimension": 4,
                "itemsize_bytes": 16,
                "logical_sites": 2,
                "method": "trajectory",
                "operator_bytes": 128,
                "result_buffer_bytes": 4096,
                "sampling_bytes": 4096,
                "schema_version": "cascaqit.simulation.planning.v1",
                "state_bytes": 16384,
                "state_dimension": 1024,
                "trajectories": 256,
                "worker_copy_bytes": 229376,
                "workers": 15,
                "workspace_bytes": 114688
              },
              "method": "trajectory",
              "reason_codes": [
                "SIMULATION_METHOD_ELIGIBLE"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "eligible"
            }
          ],
          "device": "cpu",
          "dtype": "complex128",
          "estimate": {
            "dtype": "complex128",
            "estimated_peak_bytes": 9728,
            "hilbert_dimension": 4,
            "itemsize_bytes": 16,
            "logical_sites": 2,
            "method": "density_matrix",
            "operator_bytes": 512,
            "result_buffer_bytes": 4096,
            "sampling_bytes": 4096,
            "schema_version": "cascaqit.simulation.planning.v1",
            "state_bytes": 256,
            "state_dimension": 16,
            "trajectories": 1,
            "worker_copy_bytes": 0,
            "workers": 1,
            "workspace_bytes": 768
          },
          "hilbert_dimension": 4,
          "host_hash": "fc340411ec9c1fe45ae7d312ce900fdaeaa5935813f6c5c169cb18b81d90aea1",
          "integrator_requested": "fixed_step_krylov",
          "integrator_selected": "fixed_step_krylov",
          "logical_sites": 2,
          "max_steps": 32,
          "metadata": {
            "array_backend": "numpy",
            "blockade_dimension": null,
            "host_snapshot_source": "platform.effective_resource_probe",
            "max_wall_time_seconds": null,
            "memory_fraction": 0.8,
            "network_accessed": false,
            "numpy_version": "2.0.2",
            "requires_trajectory": false,
            "scipy_version": "1.17.1",
            "target_statistical_error": null,
            "time_integration_required": true,
            "workers_cpu_limit": 15,
            "workers_requested": "auto"
          },
          "method_requested": "density_matrix",
          "method_selected": "density_matrix",
          "noisy": true,
          "options_hash": "2a941fe55d2238532ebd3114677c2cbbf495f4dfb815cb1a7caf566a75ffa99f",
          "plan_id": "simulation_plan.hybrid.2.density_matrix.fixed_step_krylov",
          "program_kind": "hybrid",
          "rtol": 1e-09,
          "schema_version": "cascaqit.simulation.planning.v1",
          "seed": 4881,
          "state_representation": "density_matrix",
          "trajectories": 256,
          "truthfulness": "planning_only",
          "workers": 1
        },
        "simulation_plan_hash": "ebb59f2ca97625a39f64ab5f58854cb4655e72e400495fa82a4e7e10ee92c493",
        "simulation_plan_truthfulness": "planning_only",
        "simulation_resource_estimate": {
          "dtype": "complex128",
          "estimated_peak_bytes": 9728,
          "hilbert_dimension": 4,
          "itemsize_bytes": 16,
          "logical_sites": 2,
          "method": "density_matrix",
          "operator_bytes": 512,
          "result_buffer_bytes": 4096,
          "sampling_bytes": 4096,
          "schema_version": "cascaqit.simulation.planning.v1",
          "state_bytes": 256,
          "state_dimension": 16,
          "trajectories": 1,
          "worker_copy_bytes": 0,
          "workers": 1,
          "workspace_bytes": 768
        },
        "simulation_resource_usage": {
          "actual_peak_rss_bytes": 143736832,
          "baseline_peak_rss_bytes": 143736832,
          "estimate_error_fraction": null,
          "estimate_within_tolerance": null,
          "estimated_peak_bytes": 9728,
          "incremental_peak_rss_bytes": 0,
          "measurement_scope": "job",
          "measurement_status": "baseline_dominated",
          "rss_semantics": "process_high_water_mark",
          "schema_version": "0.1",
          "wall_time_seconds": 0.028014332987368107
        },
        "simulation_solver_evidence": {
          "absolute_tolerance": null,
          "accepted_steps": 32,
          "final_time": 0.6,
          "function_evaluations": null,
          "initial_time": 0.0,
          "integrator_requested": "fixed_step_krylov",
          "integrator_selected": "fixed_step_krylov",
          "max_step_size": 0.01875,
          "metadata": {
            "aggregation_scope": "physical_density_hybrid_blocks",
            "component_count": 1,
            "component_evidence_hashes": [
              "b87033a62649f443f68ae025e7d6d4ca57efd42e54be9728595a3bf363bf4e3f"
            ]
          },
          "min_step_size": 0.01875,
          "rejected_steps": null,
          "rejected_steps_available": false,
          "relative_tolerance": null,
          "schema_version": "0.1",
          "segment_count": 32,
          "termination_reason": "completed",
          "time_unit": "us",
          "tolerance_applied": false
        },
        "simulation_solver_evidence_hash": "ef94260e54386e61fba4be5fe71dd918dd8b4fe0e55d432adf91e8b7ac110708",
        "simulation_state": {
          "arrays": {
            "rho": {
              "content_hash": "6e3ff60d8eb326639015a4e1b4fe7d8db257751cc3bf160b0d7c7d54572ddced",
              "dtype": "complex128",
              "nbytes": 256,
              "returned_state_bytes": false,
              "shape": [
                4,
                4
              ]
            }
          },
          "basis": "logical_two_level",
          "logical_order": [
            "q0",
            "q1"
          ],
          "logical_time": 0.6,
          "metrics": {
            "minimum_eigenvalue": 0.016080082047543194,
            "purity": 0.5302271049763567,
            "trace": 1.0
          },
          "noise_context": {},
          "provenance": {
            "conversion": null,
            "metadata": {
              "dephasing_duration": 0.0,
              "dephasing_rate": 0.0,
              "operation_count": 1,
              "program_hash": "c439c000a20062942c65081686f9e97ff09b1930f870b6090c842f0a4b79d040"
            },
            "parent_state_hash": "0f00ee3c858716b93a944d7fcc02114b6b0bdb5ae272180533083453d4776c76",
            "producer": "ExactDensityMatrixKernel.digital",
            "schema_version": "cascaqit.simulation.array_state.v1",
            "step_index": 5
          },
          "returned_state_bytes": false,
          "schema_version": "cascaqit.simulation.array_state.v1",
          "stable_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
          "state_kind": "density_matrix",
          "time_unit": "us"
        },
        "simulation_truthfulness": "physical_state_evolution",
        "state_bytes_returned": false,
        "state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
        "state_transitions": [
          {
            "block_id": "block.0000.prepare",
            "input_logical_time": 0.0,
            "input_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
            "kernel": "ExactDensityMatrixKernel.digital",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
              "payload_id": "payload.0.block.0000.prepare.digital",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.0,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "ExactDensityMatrixKernel.digital"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 0,
            "output_logical_time": 0.0,
            "output_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
            "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "dfca8e955ca173fed5f1dce4f8b20a513e634a38ff28f78dddce9fcdaa7803dd",
            "time_unit": "us",
            "transition_id": "transition.0.block.0000.prepare"
          },
          {
            "block_id": "block.0001.evolve",
            "input_logical_time": 0.0,
            "input_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
            "kernel": "ExactDensityMatrixKernel.analog",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
              "payload_id": "payload.1.block.0001.evolve.analog",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 32,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "fixed_step_krylov",
                "max_step_size": 0.01875,
                "metadata": {
                  "hermiticity_error_before_stabilization": 4.2841699744536696e-16,
                  "minimum_eigenvalue_before_stabilization": 0.016080082047543128,
                  "output_dtype": "complex128",
                  "positivity_evidence_available": true,
                  "solver": "strang_krylov_lindblad",
                  "stabilization_applied": true,
                  "trace_before_stabilization": {
                    "imag": -2.870804933781793e-18,
                    "real": 0.9999999999999972
                  }
                },
                "min_step_size": 0.01875,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 32,
                "termination_reason": "completed",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 1,
            "output_logical_time": 0.6,
            "output_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
            "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
            "program_kind": "analog",
            "schema_version": "0.1",
            "solver_evidence_hash": "b87033a62649f443f68ae025e7d6d4ca57efd42e54be9728595a3bf363bf4e3f",
            "time_unit": "us",
            "transition_id": "transition.1.block.0001.evolve"
          },
          {
            "block_id": "block.0002.readout_rotation",
            "input_logical_time": 0.6,
            "input_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
            "kernel": "ExactDensityMatrixKernel.digital",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
              "payload_id": "payload.2.block.0002.readout_rotation.digital",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.6,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "ExactDensityMatrixKernel.digital"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 2,
            "output_logical_time": 0.6,
            "output_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "8c6537a374163b7170874874c97426a424799f42a8be28e169dce0bf916296f1",
            "time_unit": "us",
            "transition_id": "transition.2.block.0002.readout_rotation"
          }
        ]
      }
    },
    {
      "result_id": "result.local_bundle.local_plan.project.noisy.hybrid.physical_noise",
      "program_hash": "3ae12596e75deff789e526006cd6fad95bd8363cc46c441de4e19eaecd54aa05",
      "target_id": "local.simulator",
      "shots": 128,
      "counts": {
        "00": 47,
        "01": 38,
        "10": 37,
        "11": 6
      },
      "samples": [
        "10",
        "00",
        "10",
        "10",
        "00",
        "01",
        "01",
        "00",
        "01",
        "00",
        "01",
        "10",
        "00",
        "10",
        "10",
        "01",
        "00",
        "10",
        "00",
        "00",
        "00",
        "01",
        "10",
        "01",
        "01",
        "10",
        "01",
        "00",
        "00",
        "01",
        "01",
        "11",
        "00",
        "10",
        "01",
        "01",
        "00",
        "10",
        "10",
        "00",
        "11",
        "01",
        "10",
        "01",
        "00",
        "00",
        "01",
        "10",
        "10",
        "10",
        "10",
        "01",
        "11",
        "00",
        "01",
        "00",
        "01",
        "00",
        "10",
        "10",
        "10",
        "10",
        "01",
        "01",
        "00",
        "10",
        "00",
        "10",
        "10",
        "10",
        "11",
        "10",
        "10",
        "00",
        "00",
        "10",
        "11",
        "01",
        "10",
        "00",
        "01",
        "01",
        "01",
        "00",
        "01",
        "00",
        "10",
        "01",
        "00",
        "01",
        "00",
        "00",
        "00",
        "10",
        "10",
        "10",
        "01",
        "01",
        "10",
        "00",
        "00",
        "01",
        "10",
        "00",
        "00",
        "00",
        "00",
        "01",
        "01",
        "01",
        "00",
        "01",
        "00",
        "00",
        "01",
        "00",
        "01",
        "10",
        "00",
        "00",
        "11",
        "00",
        "01",
        "00",
        "00",
        "00",
        "00",
        "10"
      ],
      "probabilities": {
        "00": 0.4327894017200914,
        "01": 0.23601050347734526,
        "10": 0.2900376720088961,
        "11": 0.041162422793667296
      },
      "observables": {
        "minimum_eigenvalue": 0.016080082047543194,
        "purity": 0.5302271049763567,
        "trace": 1.0
      },
      "observable_batch": {
        "observable_set_hash": "dbdcda5c7aa312b23da7566b6bc7da5ac7b572b561161122735a2aeef6c5bbcc",
        "items": [
          {
            "observable": {
              "name": "Z(q0)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.33759981039487336,
            "variance": 0.8860263680213456,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q1)",
              "terms": [
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.44565414745797494,
            "variance": 0.8013923808535055,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q0)*Z(q1)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                },
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": -0.052096350972482636,
            "variance": 0.9972859702153519,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          }
        ],
        "schema_version": "cascaqit.observables.v1"
      },
      "bit_ordering": {
        "convention": "logical_order",
        "logical_order": "q0,q1"
      },
      "occupation_encoding": {
        "ground": 0,
        "rydberg": 1
      },
      "diagnostics": [
        {
          "diagnostic_id": "simulation.noise.physical.completed",
          "stage": "simulation",
          "severity": "info",
          "code": "PHYSICAL_NOISE_SIMULATION_COMPLETED",
          "message": "Canonical physical noise simulation completed.",
          "schema_version": "0.1",
          "object_path": "result",
          "suggestion": null,
          "metadata": {
            "channel_count": 1,
            "method": "density_matrix"
          }
        }
      ],
      "schema_version": "0.1",
      "metadata": {
        "backend_called": true,
        "backend_id": "local.simulator",
        "block_state_chain": [
          {
            "block_id": "block.0000.prepare",
            "input_logical_time": 0.0,
            "input_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
            "kernel": "ExactDensityMatrixKernel.digital",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
              "payload_id": "payload.0.block.0000.prepare.digital",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.0,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "ExactDensityMatrixKernel.digital"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 0,
            "output_logical_time": 0.0,
            "output_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
            "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "dfca8e955ca173fed5f1dce4f8b20a513e634a38ff28f78dddce9fcdaa7803dd",
            "time_unit": "us",
            "transition_id": "transition.0.block.0000.prepare"
          },
          {
            "block_id": "block.0001.evolve",
            "input_logical_time": 0.0,
            "input_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
            "kernel": "ExactDensityMatrixKernel.analog",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
              "payload_id": "payload.1.block.0001.evolve.analog",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 32,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "fixed_step_krylov",
                "max_step_size": 0.01875,
                "metadata": {
                  "hermiticity_error_before_stabilization": 4.2841699744536696e-16,
                  "minimum_eigenvalue_before_stabilization": 0.016080082047543128,
                  "output_dtype": "complex128",
                  "positivity_evidence_available": true,
                  "solver": "strang_krylov_lindblad",
                  "stabilization_applied": true,
                  "trace_before_stabilization": {
                    "imag": -2.870804933781793e-18,
                    "real": 0.9999999999999972
                  }
                },
                "min_step_size": 0.01875,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 32,
                "termination_reason": "completed",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 1,
            "output_logical_time": 0.6,
            "output_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
            "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
            "program_kind": "analog",
            "schema_version": "0.1",
            "solver_evidence_hash": "b87033a62649f443f68ae025e7d6d4ca57efd42e54be9728595a3bf363bf4e3f",
            "time_unit": "us",
            "transition_id": "transition.1.block.0001.evolve"
          },
          {
            "block_id": "block.0002.readout_rotation",
            "input_logical_time": 0.6,
            "input_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
            "kernel": "ExactDensityMatrixKernel.digital",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
              "payload_id": "payload.2.block.0002.readout_rotation.digital",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.6,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "ExactDensityMatrixKernel.digital"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 2,
            "output_logical_time": 0.6,
            "output_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "8c6537a374163b7170874874c97426a424799f42a8be28e169dce0bf916296f1",
            "time_unit": "us",
            "transition_id": "transition.2.block.0002.readout_rotation"
          }
        ],
        "control_report_evidence": [
          {
            "block_id": "block.0001.evolve",
            "diagnostic_count": 4,
            "diagnostics": [
              {
                "code": "CONTROL_CONCURRENCY_SUPPORTED",
                "diagnostic_id": "control.control_concurrency_supported.rydberg.local",
                "message": "Control concurrency is within the declared group limit.",
                "metadata": {
                  "actual_max_concurrency": 1,
                  "group_id": "rydberg.local",
                  "max_concurrent_operations": 2,
                  "operation_ids": [
                    "operation.local_detuning.0"
                  ]
                },
                "object_path": "control_schedule.operations",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              },
              {
                "code": "CONTROL_BANDWIDTH_SUPPORTED",
                "diagnostic_id": "control.control_bandwidth_supported.operation.local_detuning.0",
                "message": "Waveform knot-spacing bandwidth bound is within the Target limit.",
                "metadata": {
                  "bandwidth_limit": 2.0,
                  "bandwidth_unit": "MHz",
                  "channel_id": "rydberg.detuning.local",
                  "estimate_semantics": "nyquist_bound_from_minimum_knot_spacing",
                  "estimated_bandwidth": 0.0,
                  "operation_id": "operation.local_detuning.0"
                },
                "object_path": "hamiltonian.terms.local_detuning_terms[0].waveform",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              },
              {
                "code": "CONTROL_SLEW_SUPPORTED",
                "diagnostic_id": "control.control_slew_supported.operation.local_detuning.0",
                "message": "Waveform segment slew is within the Target limit.",
                "metadata": {
                  "actual_max_slew_rate": 0.0,
                  "channel_id": "rydberg.detuning.local",
                  "estimate_semantics": "maximum_actual_waveform_segment_derivative",
                  "max_slew_rate": 30.0,
                  "operation_id": "operation.local_detuning.0",
                  "slew_rate_unit": "rad/us^2"
                },
                "object_path": "hamiltonian.terms.local_detuning_terms[0].waveform",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              },
              {
                "code": "CONTROL_CROSSTALK_NO_OVERLAP",
                "diagnostic_id": "control.control_crosstalk_no_overlap.crosstalk.rydberg.rabi.local.rydberg.rabi.global",
                "message": "Crosstalk-constrained channels do not overlap.",
                "metadata": {
                  "actual_overlap_duration": 0.0,
                  "channel_ids": [
                    "rydberg.rabi.local",
                    "rydberg.rabi.global"
                  ],
                  "constraint_id": "crosstalk.rydberg.rabi.local.rydberg.rabi.global",
                  "max_overlap_duration": null,
                  "overlap_policy": "calibration_required",
                  "time_unit": "us"
                },
                "object_path": "control_schedule.operations",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              }
            ],
            "has_errors": false,
            "production_channel_allocation_performed": false,
            "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
            "schedule": {
              "control_system_hash": "fbbc3937e5187ca6bb0a3f00e176187027581e3382a83ee377e7115bffd5a87a",
              "diagnostics": [],
              "metadata": {
                "production_channel_allocation_performed": false,
                "projection": "program_ir_control_terms",
                "time_origin": 0.0,
                "time_unit": "us"
              },
              "operations": [
                {
                  "channel_id": "rydberg.detuning.global",
                  "end_time": 0.6,
                  "metadata": {
                    "production_assigned": false,
                    "program_path": "hamiltonian.terms.detuning",
                    "time_unit": "us",
                    "value_unit": "rad/us",
                    "waveform_kind": "constant"
                  },
                  "operation_id": "operation.global_detuning",
                  "operation_kind": "global_detuning",
                  "schema_version": "0.1",
                  "source_hash": "19b3cbf48a848eccf4b459d549c9603d70c02b450b81211bb93c55010a4339ab",
                  "start_time": 0.0,
                  "target_site_ids": [
                    "q0",
                    "q1"
                  ],
                  "waveform_hash": "19b3cbf48a848eccf4b459d549c9603d70c02b450b81211bb93c55010a4339ab"
                },
                {
                  "channel_id": "rydberg.rabi.global",
                  "end_time": 0.6,
                  "metadata": {
                    "production_assigned": false,
                    "program_path": "hamiltonian.terms.rabi",
                    "time_unit": "us",
                    "value_unit": "rad/us",
                    "waveform_kind": "constant"
                  },
                  "operation_id": "operation.global_rabi",
                  "operation_kind": "global_rabi",
                  "schema_version": "0.1",
                  "source_hash": "ad464599d866805baa0f7753cf0d4ce853b1688908e85f1baa172d7740efa2da",
                  "start_time": 0.0,
                  "target_site_ids": [
                    "q0",
                    "q1"
                  ],
                  "waveform_hash": "ad464599d866805baa0f7753cf0d4ce853b1688908e85f1baa172d7740efa2da"
                },
                {
                  "channel_id": "rydberg.detuning.local",
                  "end_time": 0.6,
                  "metadata": {
                    "production_assigned": false,
                    "program_path": "hamiltonian.terms.local_detuning_terms[0].waveform",
                    "time_unit": "us",
                    "value_unit": "rad/us",
                    "waveform_kind": "constant"
                  },
                  "operation_id": "operation.local_detuning.0",
                  "operation_kind": "local_detuning",
                  "schema_version": "0.1",
                  "source_hash": "5cf7b4b36d89a2948d9ee6b9b1974f74b74438df6df8aeaaafad175c714c34ed",
                  "start_time": 0.0,
                  "target_site_ids": [
                    "q0",
                    "q1"
                  ],
                  "waveform_hash": "e1caa1faf062ab87977975eab5ad7eb6366c3974acdadba829e14493602d0665"
                }
              ],
              "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
              "schedule_id": "schedule.program.control",
              "schema_version": "0.1"
            },
            "target_id": "mock.neutral_atom.local_ahs.v0_1"
          }
        ],
        "execution_package_created": false,
        "network_accessed": false,
        "noise_model_hash": "597cc0c9128c4662d67f002310b8179ca1a8a02b1202d622a4347fb08e70061e",
        "noise_report": {
          "applied_channel_types": [
            "dephasing"
          ],
          "measurement_application_count": 0,
          "method": "density_matrix",
          "noise_model_hash": "597cc0c9128c4662d67f002310b8179ca1a8a02b1202d622a4347fb08e70061e",
          "noise_model_id": "phase",
          "physical_application_count": 1,
          "records": [
            {
              "channel_id": "noise.dephasing",
              "channel_type": "dephasing",
              "injection_point": "analog_evolution",
              "input_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
              "metadata": {
                "model": "lindblad_phase_flip",
                "parameters": {
                  "rate": 0.8
                },
                "schedule_ref": null
              },
              "output_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
              "targets": [
                "q0",
                "q1"
              ],
              "truthfulness": "physical_state_evolution"
            }
          ],
          "truthfulness": "physical_state_evolution"
        },
        "noise_report_hash": "9caa728416d5f767fc1fbb0397f0a0086d6be2c8158d2a48eaeb9244f691f285",
        "offline_deterministic": true,
        "references": {
          "bundle_hash": "bdc9f85447b0a582c5a90d39865e409738f6d81124016bf3a3295c6d0a94f9b4",
          "calibration_snapshot_hash": null,
          "compiled_program_hash": null,
          "discretized_program_hash": null,
          "execution_package_id": null,
          "final_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
          "initial_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
          "metadata": {
            "graph_hash": "7f1df6f7e79a08131273f5367d8b40cf1a5fab604b12a94df8efb2411a53452c"
          },
          "plan_hash": "4388febf8e9092f0d5a1bdee8ba9658cd610618a595779025d6019da97dad681",
          "program_hash": "3ae12596e75deff789e526006cd6fad95bd8363cc46c441de4e19eaecd54aa05",
          "schema_version": "0.1",
          "target_snapshot_hash": null
        },
        "register_snapshots": [
          {
            "active_atom_ids": [
              "q0",
              "q1"
            ],
            "active_site_count": 2,
            "active_site_ids": [
              "q0",
              "q1"
            ],
            "lifecycle_stage": "planned",
            "physical_site_count": 2,
            "physical_site_ids": [
              "q0",
              "q1"
            ],
            "previous_snapshot_hash": null,
            "snapshot_hash": "571e481d25fc0fb0e4962bcb62d4b574c81cc965cb8e3b4fc69565faa8be68ec",
            "snapshot_id": "register.planned",
            "status_counts": {
              "defect": 0,
              "filled": 2,
              "loading_failed": 0,
              "vacant": 0
            }
          }
        ],
        "run_trace": {
          "events": [
            {
              "event_time": "logical:0x0.0p+0",
              "message": "Completed digital state transition.",
              "metadata": {
                "state_transition": {
                  "block_id": "block.0000.prepare",
                  "input_logical_time": 0.0,
                  "input_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
                  "kernel": "ExactDensityMatrixKernel.digital",
                  "metadata": {
                    "logical_order": [
                      "q0",
                      "q1"
                    ],
                    "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
                    "payload_id": "payload.0.block.0000.prepare.digital",
                    "solver_evidence": {
                      "absolute_tolerance": null,
                      "accepted_steps": 0,
                      "final_time": 0.0,
                      "function_evaluations": null,
                      "initial_time": 0.0,
                      "integrator_requested": "fixed_step_krylov",
                      "integrator_selected": "not_applicable",
                      "max_step_size": null,
                      "metadata": {
                        "consumer": "ExactDensityMatrixKernel.digital"
                      },
                      "min_step_size": null,
                      "rejected_steps": null,
                      "rejected_steps_available": false,
                      "relative_tolerance": null,
                      "schema_version": "0.1",
                      "segment_count": 0,
                      "termination_reason": "not_applicable",
                      "time_unit": "us",
                      "tolerance_applied": false
                    }
                  },
                  "order_index": 0,
                  "output_logical_time": 0.0,
                  "output_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
                  "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
                  "program_kind": "digital",
                  "schema_version": "0.1",
                  "solver_evidence_hash": "dfca8e955ca173fed5f1dce4f8b20a513e634a38ff28f78dddce9fcdaa7803dd",
                  "time_unit": "us",
                  "transition_id": "transition.0.block.0000.prepare"
                }
              },
              "schema_version": "0.1",
              "stage": "running",
              "status": "ok"
            },
            {
              "event_time": "logical:0x1.3333333333333p-1",
              "message": "Completed analog state transition.",
              "metadata": {
                "state_transition": {
                  "block_id": "block.0001.evolve",
                  "input_logical_time": 0.0,
                  "input_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
                  "kernel": "ExactDensityMatrixKernel.analog",
                  "metadata": {
                    "logical_order": [
                      "q0",
                      "q1"
                    ],
                    "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
                    "payload_id": "payload.1.block.0001.evolve.analog",
                    "solver_evidence": {
                      "absolute_tolerance": null,
                      "accepted_steps": 32,
                      "final_time": 0.6,
                      "function_evaluations": null,
                      "initial_time": 0.0,
                      "integrator_requested": "fixed_step_krylov",
                      "integrator_selected": "fixed_step_krylov",
                      "max_step_size": 0.01875,
                      "metadata": {
                        "hermiticity_error_before_stabilization": 4.2841699744536696e-16,
                        "minimum_eigenvalue_before_stabilization": 0.016080082047543128,
                        "output_dtype": "complex128",
                        "positivity_evidence_available": true,
                        "solver": "strang_krylov_lindblad",
                        "stabilization_applied": true,
                        "trace_before_stabilization": {
                          "imag": -2.870804933781793e-18,
                          "real": 0.9999999999999972
                        }
                      },
                      "min_step_size": 0.01875,
                      "rejected_steps": null,
                      "rejected_steps_available": false,
                      "relative_tolerance": null,
                      "schema_version": "0.1",
                      "segment_count": 32,
                      "termination_reason": "completed",
                      "time_unit": "us",
                      "tolerance_applied": false
                    }
                  },
                  "order_index": 1,
                  "output_logical_time": 0.6,
                  "output_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
                  "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
                  "program_kind": "analog",
                  "schema_version": "0.1",
                  "solver_evidence_hash": "b87033a62649f443f68ae025e7d6d4ca57efd42e54be9728595a3bf363bf4e3f",
                  "time_unit": "us",
                  "transition_id": "transition.1.block.0001.evolve"
                }
              },
              "schema_version": "0.1",
              "stage": "running",
              "status": "ok"
            },
            {
              "event_time": "logical:0x1.3333333333333p-1",
              "message": "Completed digital state transition.",
              "metadata": {
                "state_transition": {
                  "block_id": "block.0002.readout_rotation",
                  "input_logical_time": 0.6,
                  "input_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
                  "kernel": "ExactDensityMatrixKernel.digital",
                  "metadata": {
                    "logical_order": [
                      "q0",
                      "q1"
                    ],
                    "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
                    "payload_id": "payload.2.block.0002.readout_rotation.digital",
                    "solver_evidence": {
                      "absolute_tolerance": null,
                      "accepted_steps": 0,
                      "final_time": 0.6,
                      "function_evaluations": null,
                      "initial_time": 0.6,
                      "integrator_requested": "fixed_step_krylov",
                      "integrator_selected": "not_applicable",
                      "max_step_size": null,
                      "metadata": {
                        "consumer": "ExactDensityMatrixKernel.digital"
                      },
                      "min_step_size": null,
                      "rejected_steps": null,
                      "rejected_steps_available": false,
                      "relative_tolerance": null,
                      "schema_version": "0.1",
                      "segment_count": 0,
                      "termination_reason": "not_applicable",
                      "time_unit": "us",
                      "tolerance_applied": false
                    }
                  },
                  "order_index": 2,
                  "output_logical_time": 0.6,
                  "output_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
                  "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
                  "program_kind": "digital",
                  "schema_version": "0.1",
                  "solver_evidence_hash": "8c6537a374163b7170874874c97426a424799f42a8be28e169dce0bf916296f1",
                  "time_unit": "us",
                  "transition_id": "transition.2.block.0002.readout_rotation"
                }
              },
              "schema_version": "0.1",
              "stage": "running",
              "status": "ok"
            },
            {
              "event_time": "logical:0x1.3333333333333p-1",
              "message": "Terminal noisy sampling completed.",
              "metadata": {
                "final_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
                "measurement_key": "result",
                "seed": 4882,
                "shots": 128
              },
              "schema_version": "0.1",
              "stage": "completed",
              "status": "ok"
            }
          ],
          "metadata": {
            "execution_mode": "local_hybrid_density_matrix"
          },
          "references": {
            "bundle_hash": "bdc9f85447b0a582c5a90d39865e409738f6d81124016bf3a3295c6d0a94f9b4",
            "calibration_snapshot_hash": null,
            "compiled_program_hash": null,
            "discretized_program_hash": null,
            "execution_package_id": null,
            "final_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "initial_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
            "metadata": {
              "graph_hash": "7f1df6f7e79a08131273f5367d8b40cf1a5fab604b12a94df8efb2411a53452c"
            },
            "plan_hash": "4388febf8e9092f0d5a1bdee8ba9658cd610618a595779025d6019da97dad681",
            "program_hash": "3ae12596e75deff789e526006cd6fad95bd8363cc46c441de4e19eaecd54aa05",
            "schema_version": "0.1",
            "target_snapshot_hash": null
          },
          "schema_version": "0.1",
          "trace_id": "trace.local_bundle.local_plan.project.noisy.hybrid.physical_noise"
        },
        "selected_simulator": "ExactDensityNoiseEngine",
        "simulation_execution_config": {
          "absolute_tolerance": 1e-11,
          "device": "cpu",
          "dtype": "complex128",
          "execution_scope": "job",
          "integrator_requested": "fixed_step_krylov",
          "integrator_selected": "fixed_step_krylov",
          "method": "density_matrix",
          "relative_tolerance": 1e-09,
          "schema_version": "0.1",
          "seed": 4882,
          "seed_semantics": "effective_seed",
          "solver_evidence_hash": "ef94260e54386e61fba4be5fe71dd918dd8b4fe0e55d432adf91e8b7ac110708",
          "step_semantics": "fixed_time_slices",
          "steps": 32,
          "tolerance_applied": false,
          "trajectories": null,
          "worker_semantics": "kernel_concurrency",
          "workers": 1
        },
        "simulation_plan": {
          "atol": 1e-11,
          "budget_bytes": 20615843020,
          "candidates": [
            {
              "estimate": {
                "dtype": "complex128",
                "estimated_peak_bytes": 9792,
                "hilbert_dimension": 4,
                "itemsize_bytes": 16,
                "logical_sites": 2,
                "method": "state_vector",
                "operator_bytes": 128,
                "result_buffer_bytes": 4096,
                "sampling_bytes": 4096,
                "schema_version": "cascaqit.simulation.planning.v1",
                "state_bytes": 64,
                "state_dimension": 4,
                "trajectories": 1,
                "worker_copy_bytes": 0,
                "workers": 1,
                "workspace_bytes": 1408
              },
              "method": "state_vector",
              "reason_codes": [
                "SIMULATION_METHOD_REQUIRES_IDEAL_MODEL"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "rejected"
            },
            {
              "estimate": null,
              "method": "subspace",
              "reason_codes": [
                "SIMULATION_METHOD_REQUIRES_IDEAL_MODEL"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "rejected"
            },
            {
              "estimate": {
                "dtype": "complex128",
                "estimated_peak_bytes": 9728,
                "hilbert_dimension": 4,
                "itemsize_bytes": 16,
                "logical_sites": 2,
                "method": "density_matrix",
                "operator_bytes": 512,
                "result_buffer_bytes": 4096,
                "sampling_bytes": 4096,
                "schema_version": "cascaqit.simulation.planning.v1",
                "state_bytes": 256,
                "state_dimension": 16,
                "trajectories": 1,
                "worker_copy_bytes": 0,
                "workers": 1,
                "workspace_bytes": 768
              },
              "method": "density_matrix",
              "reason_codes": [
                "SIMULATION_METHOD_ELIGIBLE",
                "SIMULATION_METHOD_SELECTED"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "selected"
            },
            {
              "estimate": {
                "dtype": "complex128",
                "estimated_peak_bytes": 368768,
                "hilbert_dimension": 4,
                "itemsize_bytes": 16,
                "logical_sites": 2,
                "method": "trajectory",
                "operator_bytes": 128,
                "result_buffer_bytes": 4096,
                "sampling_bytes": 4096,
                "schema_version": "cascaqit.simulation.planning.v1",
                "state_bytes": 16384,
                "state_dimension": 1024,
                "trajectories": 256,
                "worker_copy_bytes": 229376,
                "workers": 15,
                "workspace_bytes": 114688
              },
              "method": "trajectory",
              "reason_codes": [
                "SIMULATION_METHOD_ELIGIBLE"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "eligible"
            }
          ],
          "device": "cpu",
          "dtype": "complex128",
          "estimate": {
            "dtype": "complex128",
            "estimated_peak_bytes": 9728,
            "hilbert_dimension": 4,
            "itemsize_bytes": 16,
            "logical_sites": 2,
            "method": "density_matrix",
            "operator_bytes": 512,
            "result_buffer_bytes": 4096,
            "sampling_bytes": 4096,
            "schema_version": "cascaqit.simulation.planning.v1",
            "state_bytes": 256,
            "state_dimension": 16,
            "trajectories": 1,
            "worker_copy_bytes": 0,
            "workers": 1,
            "workspace_bytes": 768
          },
          "hilbert_dimension": 4,
          "host_hash": "fc340411ec9c1fe45ae7d312ce900fdaeaa5935813f6c5c169cb18b81d90aea1",
          "integrator_requested": "fixed_step_krylov",
          "integrator_selected": "fixed_step_krylov",
          "logical_sites": 2,
          "max_steps": 32,
          "metadata": {
            "array_backend": "numpy",
            "blockade_dimension": null,
            "host_snapshot_source": "platform.effective_resource_probe",
            "max_wall_time_seconds": null,
            "memory_fraction": 0.8,
            "network_accessed": false,
            "numpy_version": "2.0.2",
            "requires_trajectory": false,
            "scipy_version": "1.17.1",
            "target_statistical_error": null,
            "time_integration_required": true,
            "workers_cpu_limit": 15,
            "workers_requested": "auto"
          },
          "method_requested": "density_matrix",
          "method_selected": "density_matrix",
          "noisy": true,
          "options_hash": "da08e4479dfebca841e152f623e8f6fedcb92e41b4999609317fd27be0fdd0f2",
          "plan_id": "simulation_plan.hybrid.2.density_matrix.fixed_step_krylov",
          "program_kind": "hybrid",
          "rtol": 1e-09,
          "schema_version": "cascaqit.simulation.planning.v1",
          "seed": 4882,
          "state_representation": "density_matrix",
          "trajectories": 256,
          "truthfulness": "planning_only",
          "workers": 1
        },
        "simulation_plan_hash": "63cde3827ecd111f55bd79cd26a4f6be3f2fbac6b2f1bb94497f87cc1aa21e58",
        "simulation_plan_truthfulness": "planning_only",
        "simulation_resource_estimate": {
          "dtype": "complex128",
          "estimated_peak_bytes": 9728,
          "hilbert_dimension": 4,
          "itemsize_bytes": 16,
          "logical_sites": 2,
          "method": "density_matrix",
          "operator_bytes": 512,
          "result_buffer_bytes": 4096,
          "sampling_bytes": 4096,
          "schema_version": "cascaqit.simulation.planning.v1",
          "state_bytes": 256,
          "state_dimension": 16,
          "trajectories": 1,
          "worker_copy_bytes": 0,
          "workers": 1,
          "workspace_bytes": 768
        },
        "simulation_resource_usage": {
          "actual_peak_rss_bytes": 143736832,
          "baseline_peak_rss_bytes": 143736832,
          "estimate_error_fraction": null,
          "estimate_within_tolerance": null,
          "estimated_peak_bytes": 9728,
          "incremental_peak_rss_bytes": 0,
          "measurement_scope": "job",
          "measurement_status": "baseline_dominated",
          "rss_semantics": "process_high_water_mark",
          "schema_version": "0.1",
          "wall_time_seconds": 0.0257848339388147
        },
        "simulation_solver_evidence": {
          "absolute_tolerance": null,
          "accepted_steps": 32,
          "final_time": 0.6,
          "function_evaluations": null,
          "initial_time": 0.0,
          "integrator_requested": "fixed_step_krylov",
          "integrator_selected": "fixed_step_krylov",
          "max_step_size": 0.01875,
          "metadata": {
            "aggregation_scope": "physical_density_hybrid_blocks",
            "component_count": 1,
            "component_evidence_hashes": [
              "b87033a62649f443f68ae025e7d6d4ca57efd42e54be9728595a3bf363bf4e3f"
            ]
          },
          "min_step_size": 0.01875,
          "rejected_steps": null,
          "rejected_steps_available": false,
          "relative_tolerance": null,
          "schema_version": "0.1",
          "segment_count": 32,
          "termination_reason": "completed",
          "time_unit": "us",
          "tolerance_applied": false
        },
        "simulation_solver_evidence_hash": "ef94260e54386e61fba4be5fe71dd918dd8b4fe0e55d432adf91e8b7ac110708",
        "simulation_state": {
          "arrays": {
            "rho": {
              "content_hash": "6e3ff60d8eb326639015a4e1b4fe7d8db257751cc3bf160b0d7c7d54572ddced",
              "dtype": "complex128",
              "nbytes": 256,
              "returned_state_bytes": false,
              "shape": [
                4,
                4
              ]
            }
          },
          "basis": "logical_two_level",
          "logical_order": [
            "q0",
            "q1"
          ],
          "logical_time": 0.6,
          "metrics": {
            "minimum_eigenvalue": 0.016080082047543194,
            "purity": 0.5302271049763567,
            "trace": 1.0
          },
          "noise_context": {},
          "provenance": {
            "conversion": null,
            "metadata": {
              "dephasing_duration": 0.0,
              "dephasing_rate": 0.0,
              "operation_count": 1,
              "program_hash": "c439c000a20062942c65081686f9e97ff09b1930f870b6090c842f0a4b79d040"
            },
            "parent_state_hash": "0f00ee3c858716b93a944d7fcc02114b6b0bdb5ae272180533083453d4776c76",
            "producer": "ExactDensityMatrixKernel.digital",
            "schema_version": "cascaqit.simulation.array_state.v1",
            "step_index": 5
          },
          "returned_state_bytes": false,
          "schema_version": "cascaqit.simulation.array_state.v1",
          "stable_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
          "state_kind": "density_matrix",
          "time_unit": "us"
        },
        "simulation_truthfulness": "physical_state_evolution",
        "state_bytes_returned": false,
        "state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
        "state_transitions": [
          {
            "block_id": "block.0000.prepare",
            "input_logical_time": 0.0,
            "input_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
            "kernel": "ExactDensityMatrixKernel.digital",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
              "payload_id": "payload.0.block.0000.prepare.digital",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.0,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "ExactDensityMatrixKernel.digital"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 0,
            "output_logical_time": 0.0,
            "output_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
            "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "dfca8e955ca173fed5f1dce4f8b20a513e634a38ff28f78dddce9fcdaa7803dd",
            "time_unit": "us",
            "transition_id": "transition.0.block.0000.prepare"
          },
          {
            "block_id": "block.0001.evolve",
            "input_logical_time": 0.0,
            "input_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
            "kernel": "ExactDensityMatrixKernel.analog",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
              "payload_id": "payload.1.block.0001.evolve.analog",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 32,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "fixed_step_krylov",
                "max_step_size": 0.01875,
                "metadata": {
                  "hermiticity_error_before_stabilization": 4.2841699744536696e-16,
                  "minimum_eigenvalue_before_stabilization": 0.016080082047543128,
                  "output_dtype": "complex128",
                  "positivity_evidence_available": true,
                  "solver": "strang_krylov_lindblad",
                  "stabilization_applied": true,
                  "trace_before_stabilization": {
                    "imag": -2.870804933781793e-18,
                    "real": 0.9999999999999972
                  }
                },
                "min_step_size": 0.01875,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 32,
                "termination_reason": "completed",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 1,
            "output_logical_time": 0.6,
            "output_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
            "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
            "program_kind": "analog",
            "schema_version": "0.1",
            "solver_evidence_hash": "b87033a62649f443f68ae025e7d6d4ca57efd42e54be9728595a3bf363bf4e3f",
            "time_unit": "us",
            "transition_id": "transition.1.block.0001.evolve"
          },
          {
            "block_id": "block.0002.readout_rotation",
            "input_logical_time": 0.6,
            "input_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
            "kernel": "ExactDensityMatrixKernel.digital",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
              "payload_id": "payload.2.block.0002.readout_rotation.digital",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.6,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "ExactDensityMatrixKernel.digital"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 2,
            "output_logical_time": 0.6,
            "output_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "8c6537a374163b7170874874c97426a424799f42a8be28e169dce0bf916296f1",
            "time_unit": "us",
            "transition_id": "transition.2.block.0002.readout_rotation"
          }
        ]
      }
    },
    {
      "result_id": "result.local_bundle.local_plan.project.noisy.hybrid.physical_noise",
      "program_hash": "3ae12596e75deff789e526006cd6fad95bd8363cc46c441de4e19eaecd54aa05",
      "target_id": "local.simulator",
      "shots": 128,
      "counts": {
        "00": 60,
        "01": 25,
        "10": 31,
        "11": 12
      },
      "samples": [
        "10",
        "01",
        "10",
        "00",
        "00",
        "00",
        "11",
        "00",
        "10",
        "10",
        "10",
        "10",
        "00",
        "00",
        "00",
        "10",
        "11",
        "10",
        "01",
        "00",
        "00",
        "01",
        "10",
        "10",
        "00",
        "10",
        "00",
        "00",
        "00",
        "00",
        "00",
        "10",
        "11",
        "00",
        "10",
        "10",
        "00",
        "00",
        "00",
        "00",
        "00",
        "01",
        "00",
        "11",
        "01",
        "11",
        "10",
        "10",
        "00",
        "00",
        "01",
        "00",
        "10",
        "00",
        "00",
        "11",
        "01",
        "10",
        "00",
        "01",
        "10",
        "00",
        "00",
        "01",
        "01",
        "10",
        "01",
        "00",
        "11",
        "11",
        "10",
        "00",
        "11",
        "01",
        "11",
        "00",
        "00",
        "00",
        "00",
        "00",
        "00",
        "00",
        "00",
        "10",
        "11",
        "00",
        "10",
        "00",
        "00",
        "01",
        "00",
        "00",
        "00",
        "01",
        "10",
        "01",
        "00",
        "01",
        "11",
        "01",
        "01",
        "00",
        "00",
        "10",
        "10",
        "10",
        "00",
        "01",
        "01",
        "00",
        "01",
        "10",
        "01",
        "10",
        "00",
        "01",
        "00",
        "01",
        "01",
        "00",
        "00",
        "10",
        "00",
        "00",
        "00",
        "10",
        "00",
        "00"
      ],
      "probabilities": {
        "00": 0.4327894017200914,
        "01": 0.23601050347734526,
        "10": 0.2900376720088961,
        "11": 0.041162422793667296
      },
      "observables": {
        "minimum_eigenvalue": 0.016080082047543194,
        "purity": 0.5302271049763567,
        "trace": 1.0
      },
      "observable_batch": {
        "observable_set_hash": "dbdcda5c7aa312b23da7566b6bc7da5ac7b572b561161122735a2aeef6c5bbcc",
        "items": [
          {
            "observable": {
              "name": "Z(q0)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.33759981039487336,
            "variance": 0.8860263680213456,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q1)",
              "terms": [
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.44565414745797494,
            "variance": 0.8013923808535055,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q0)*Z(q1)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                },
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": -0.052096350972482636,
            "variance": 0.9972859702153519,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          }
        ],
        "schema_version": "cascaqit.observables.v1"
      },
      "bit_ordering": {
        "convention": "logical_order",
        "logical_order": "q0,q1"
      },
      "occupation_encoding": {
        "ground": 0,
        "rydberg": 1
      },
      "diagnostics": [
        {
          "diagnostic_id": "simulation.noise.physical.completed",
          "stage": "simulation",
          "severity": "info",
          "code": "PHYSICAL_NOISE_SIMULATION_COMPLETED",
          "message": "Canonical physical noise simulation completed.",
          "schema_version": "0.1",
          "object_path": "result",
          "suggestion": null,
          "metadata": {
            "channel_count": 1,
            "method": "density_matrix"
          }
        }
      ],
      "schema_version": "0.1",
      "metadata": {
        "backend_called": true,
        "backend_id": "local.simulator",
        "block_state_chain": [
          {
            "block_id": "block.0000.prepare",
            "input_logical_time": 0.0,
            "input_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
            "kernel": "ExactDensityMatrixKernel.digital",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
              "payload_id": "payload.0.block.0000.prepare.digital",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.0,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "ExactDensityMatrixKernel.digital"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 0,
            "output_logical_time": 0.0,
            "output_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
            "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "dfca8e955ca173fed5f1dce4f8b20a513e634a38ff28f78dddce9fcdaa7803dd",
            "time_unit": "us",
            "transition_id": "transition.0.block.0000.prepare"
          },
          {
            "block_id": "block.0001.evolve",
            "input_logical_time": 0.0,
            "input_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
            "kernel": "ExactDensityMatrixKernel.analog",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
              "payload_id": "payload.1.block.0001.evolve.analog",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 32,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "fixed_step_krylov",
                "max_step_size": 0.01875,
                "metadata": {
                  "hermiticity_error_before_stabilization": 4.2841699744536696e-16,
                  "minimum_eigenvalue_before_stabilization": 0.016080082047543128,
                  "output_dtype": "complex128",
                  "positivity_evidence_available": true,
                  "solver": "strang_krylov_lindblad",
                  "stabilization_applied": true,
                  "trace_before_stabilization": {
                    "imag": -2.870804933781793e-18,
                    "real": 0.9999999999999972
                  }
                },
                "min_step_size": 0.01875,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 32,
                "termination_reason": "completed",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 1,
            "output_logical_time": 0.6,
            "output_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
            "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
            "program_kind": "analog",
            "schema_version": "0.1",
            "solver_evidence_hash": "b87033a62649f443f68ae025e7d6d4ca57efd42e54be9728595a3bf363bf4e3f",
            "time_unit": "us",
            "transition_id": "transition.1.block.0001.evolve"
          },
          {
            "block_id": "block.0002.readout_rotation",
            "input_logical_time": 0.6,
            "input_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
            "kernel": "ExactDensityMatrixKernel.digital",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
              "payload_id": "payload.2.block.0002.readout_rotation.digital",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.6,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "ExactDensityMatrixKernel.digital"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 2,
            "output_logical_time": 0.6,
            "output_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "8c6537a374163b7170874874c97426a424799f42a8be28e169dce0bf916296f1",
            "time_unit": "us",
            "transition_id": "transition.2.block.0002.readout_rotation"
          }
        ],
        "control_report_evidence": [
          {
            "block_id": "block.0001.evolve",
            "diagnostic_count": 4,
            "diagnostics": [
              {
                "code": "CONTROL_CONCURRENCY_SUPPORTED",
                "diagnostic_id": "control.control_concurrency_supported.rydberg.local",
                "message": "Control concurrency is within the declared group limit.",
                "metadata": {
                  "actual_max_concurrency": 1,
                  "group_id": "rydberg.local",
                  "max_concurrent_operations": 2,
                  "operation_ids": [
                    "operation.local_detuning.0"
                  ]
                },
                "object_path": "control_schedule.operations",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              },
              {
                "code": "CONTROL_BANDWIDTH_SUPPORTED",
                "diagnostic_id": "control.control_bandwidth_supported.operation.local_detuning.0",
                "message": "Waveform knot-spacing bandwidth bound is within the Target limit.",
                "metadata": {
                  "bandwidth_limit": 2.0,
                  "bandwidth_unit": "MHz",
                  "channel_id": "rydberg.detuning.local",
                  "estimate_semantics": "nyquist_bound_from_minimum_knot_spacing",
                  "estimated_bandwidth": 0.0,
                  "operation_id": "operation.local_detuning.0"
                },
                "object_path": "hamiltonian.terms.local_detuning_terms[0].waveform",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              },
              {
                "code": "CONTROL_SLEW_SUPPORTED",
                "diagnostic_id": "control.control_slew_supported.operation.local_detuning.0",
                "message": "Waveform segment slew is within the Target limit.",
                "metadata": {
                  "actual_max_slew_rate": 0.0,
                  "channel_id": "rydberg.detuning.local",
                  "estimate_semantics": "maximum_actual_waveform_segment_derivative",
                  "max_slew_rate": 30.0,
                  "operation_id": "operation.local_detuning.0",
                  "slew_rate_unit": "rad/us^2"
                },
                "object_path": "hamiltonian.terms.local_detuning_terms[0].waveform",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              },
              {
                "code": "CONTROL_CROSSTALK_NO_OVERLAP",
                "diagnostic_id": "control.control_crosstalk_no_overlap.crosstalk.rydberg.rabi.local.rydberg.rabi.global",
                "message": "Crosstalk-constrained channels do not overlap.",
                "metadata": {
                  "actual_overlap_duration": 0.0,
                  "channel_ids": [
                    "rydberg.rabi.local",
                    "rydberg.rabi.global"
                  ],
                  "constraint_id": "crosstalk.rydberg.rabi.local.rydberg.rabi.global",
                  "max_overlap_duration": null,
                  "overlap_policy": "calibration_required",
                  "time_unit": "us"
                },
                "object_path": "control_schedule.operations",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              }
            ],
            "has_errors": false,
            "production_channel_allocation_performed": false,
            "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
            "schedule": {
              "control_system_hash": "fbbc3937e5187ca6bb0a3f00e176187027581e3382a83ee377e7115bffd5a87a",
              "diagnostics": [],
              "metadata": {
                "production_channel_allocation_performed": false,
                "projection": "program_ir_control_terms",
                "time_origin": 0.0,
                "time_unit": "us"
              },
              "operations": [
                {
                  "channel_id": "rydberg.detuning.global",
                  "end_time": 0.6,
                  "metadata": {
                    "production_assigned": false,
                    "program_path": "hamiltonian.terms.detuning",
                    "time_unit": "us",
                    "value_unit": "rad/us",
                    "waveform_kind": "constant"
                  },
                  "operation_id": "operation.global_detuning",
                  "operation_kind": "global_detuning",
                  "schema_version": "0.1",
                  "source_hash": "19b3cbf48a848eccf4b459d549c9603d70c02b450b81211bb93c55010a4339ab",
                  "start_time": 0.0,
                  "target_site_ids": [
                    "q0",
                    "q1"
                  ],
                  "waveform_hash": "19b3cbf48a848eccf4b459d549c9603d70c02b450b81211bb93c55010a4339ab"
                },
                {
                  "channel_id": "rydberg.rabi.global",
                  "end_time": 0.6,
                  "metadata": {
                    "production_assigned": false,
                    "program_path": "hamiltonian.terms.rabi",
                    "time_unit": "us",
                    "value_unit": "rad/us",
                    "waveform_kind": "constant"
                  },
                  "operation_id": "operation.global_rabi",
                  "operation_kind": "global_rabi",
                  "schema_version": "0.1",
                  "source_hash": "ad464599d866805baa0f7753cf0d4ce853b1688908e85f1baa172d7740efa2da",
                  "start_time": 0.0,
                  "target_site_ids": [
                    "q0",
                    "q1"
                  ],
                  "waveform_hash": "ad464599d866805baa0f7753cf0d4ce853b1688908e85f1baa172d7740efa2da"
                },
                {
                  "channel_id": "rydberg.detuning.local",
                  "end_time": 0.6,
                  "metadata": {
                    "production_assigned": false,
                    "program_path": "hamiltonian.terms.local_detuning_terms[0].waveform",
                    "time_unit": "us",
                    "value_unit": "rad/us",
                    "waveform_kind": "constant"
                  },
                  "operation_id": "operation.local_detuning.0",
                  "operation_kind": "local_detuning",
                  "schema_version": "0.1",
                  "source_hash": "5cf7b4b36d89a2948d9ee6b9b1974f74b74438df6df8aeaaafad175c714c34ed",
                  "start_time": 0.0,
                  "target_site_ids": [
                    "q0",
                    "q1"
                  ],
                  "waveform_hash": "e1caa1faf062ab87977975eab5ad7eb6366c3974acdadba829e14493602d0665"
                }
              ],
              "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
              "schedule_id": "schedule.program.control",
              "schema_version": "0.1"
            },
            "target_id": "mock.neutral_atom.local_ahs.v0_1"
          }
        ],
        "execution_package_created": false,
        "network_accessed": false,
        "noise_model_hash": "597cc0c9128c4662d67f002310b8179ca1a8a02b1202d622a4347fb08e70061e",
        "noise_report": {
          "applied_channel_types": [
            "dephasing"
          ],
          "measurement_application_count": 0,
          "method": "density_matrix",
          "noise_model_hash": "597cc0c9128c4662d67f002310b8179ca1a8a02b1202d622a4347fb08e70061e",
          "noise_model_id": "phase",
          "physical_application_count": 1,
          "records": [
            {
              "channel_id": "noise.dephasing",
              "channel_type": "dephasing",
              "injection_point": "analog_evolution",
              "input_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
              "metadata": {
                "model": "lindblad_phase_flip",
                "parameters": {
                  "rate": 0.8
                },
                "schedule_ref": null
              },
              "output_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
              "targets": [
                "q0",
                "q1"
              ],
              "truthfulness": "physical_state_evolution"
            }
          ],
          "truthfulness": "physical_state_evolution"
        },
        "noise_report_hash": "9caa728416d5f767fc1fbb0397f0a0086d6be2c8158d2a48eaeb9244f691f285",
        "offline_deterministic": true,
        "references": {
          "bundle_hash": "42234f4fd9d09c4d8102e6dc8d5f703c5ec76e567a4a89e630381577a0768e05",
          "calibration_snapshot_hash": null,
          "compiled_program_hash": null,
          "discretized_program_hash": null,
          "execution_package_id": null,
          "final_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
          "initial_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
          "metadata": {
            "graph_hash": "7f1df6f7e79a08131273f5367d8b40cf1a5fab604b12a94df8efb2411a53452c"
          },
          "plan_hash": "4388febf8e9092f0d5a1bdee8ba9658cd610618a595779025d6019da97dad681",
          "program_hash": "3ae12596e75deff789e526006cd6fad95bd8363cc46c441de4e19eaecd54aa05",
          "schema_version": "0.1",
          "target_snapshot_hash": null
        },
        "register_snapshots": [
          {
            "active_atom_ids": [
              "q0",
              "q1"
            ],
            "active_site_count": 2,
            "active_site_ids": [
              "q0",
              "q1"
            ],
            "lifecycle_stage": "planned",
            "physical_site_count": 2,
            "physical_site_ids": [
              "q0",
              "q1"
            ],
            "previous_snapshot_hash": null,
            "snapshot_hash": "571e481d25fc0fb0e4962bcb62d4b574c81cc965cb8e3b4fc69565faa8be68ec",
            "snapshot_id": "register.planned",
            "status_counts": {
              "defect": 0,
              "filled": 2,
              "loading_failed": 0,
              "vacant": 0
            }
          }
        ],
        "run_trace": {
          "events": [
            {
              "event_time": "logical:0x0.0p+0",
              "message": "Completed digital state transition.",
              "metadata": {
                "state_transition": {
                  "block_id": "block.0000.prepare",
                  "input_logical_time": 0.0,
                  "input_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
                  "kernel": "ExactDensityMatrixKernel.digital",
                  "metadata": {
                    "logical_order": [
                      "q0",
                      "q1"
                    ],
                    "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
                    "payload_id": "payload.0.block.0000.prepare.digital",
                    "solver_evidence": {
                      "absolute_tolerance": null,
                      "accepted_steps": 0,
                      "final_time": 0.0,
                      "function_evaluations": null,
                      "initial_time": 0.0,
                      "integrator_requested": "fixed_step_krylov",
                      "integrator_selected": "not_applicable",
                      "max_step_size": null,
                      "metadata": {
                        "consumer": "ExactDensityMatrixKernel.digital"
                      },
                      "min_step_size": null,
                      "rejected_steps": null,
                      "rejected_steps_available": false,
                      "relative_tolerance": null,
                      "schema_version": "0.1",
                      "segment_count": 0,
                      "termination_reason": "not_applicable",
                      "time_unit": "us",
                      "tolerance_applied": false
                    }
                  },
                  "order_index": 0,
                  "output_logical_time": 0.0,
                  "output_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
                  "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
                  "program_kind": "digital",
                  "schema_version": "0.1",
                  "solver_evidence_hash": "dfca8e955ca173fed5f1dce4f8b20a513e634a38ff28f78dddce9fcdaa7803dd",
                  "time_unit": "us",
                  "transition_id": "transition.0.block.0000.prepare"
                }
              },
              "schema_version": "0.1",
              "stage": "running",
              "status": "ok"
            },
            {
              "event_time": "logical:0x1.3333333333333p-1",
              "message": "Completed analog state transition.",
              "metadata": {
                "state_transition": {
                  "block_id": "block.0001.evolve",
                  "input_logical_time": 0.0,
                  "input_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
                  "kernel": "ExactDensityMatrixKernel.analog",
                  "metadata": {
                    "logical_order": [
                      "q0",
                      "q1"
                    ],
                    "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
                    "payload_id": "payload.1.block.0001.evolve.analog",
                    "solver_evidence": {
                      "absolute_tolerance": null,
                      "accepted_steps": 32,
                      "final_time": 0.6,
                      "function_evaluations": null,
                      "initial_time": 0.0,
                      "integrator_requested": "fixed_step_krylov",
                      "integrator_selected": "fixed_step_krylov",
                      "max_step_size": 0.01875,
                      "metadata": {
                        "hermiticity_error_before_stabilization": 4.2841699744536696e-16,
                        "minimum_eigenvalue_before_stabilization": 0.016080082047543128,
                        "output_dtype": "complex128",
                        "positivity_evidence_available": true,
                        "solver": "strang_krylov_lindblad",
                        "stabilization_applied": true,
                        "trace_before_stabilization": {
                          "imag": -2.870804933781793e-18,
                          "real": 0.9999999999999972
                        }
                      },
                      "min_step_size": 0.01875,
                      "rejected_steps": null,
                      "rejected_steps_available": false,
                      "relative_tolerance": null,
                      "schema_version": "0.1",
                      "segment_count": 32,
                      "termination_reason": "completed",
                      "time_unit": "us",
                      "tolerance_applied": false
                    }
                  },
                  "order_index": 1,
                  "output_logical_time": 0.6,
                  "output_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
                  "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
                  "program_kind": "analog",
                  "schema_version": "0.1",
                  "solver_evidence_hash": "b87033a62649f443f68ae025e7d6d4ca57efd42e54be9728595a3bf363bf4e3f",
                  "time_unit": "us",
                  "transition_id": "transition.1.block.0001.evolve"
                }
              },
              "schema_version": "0.1",
              "stage": "running",
              "status": "ok"
            },
            {
              "event_time": "logical:0x1.3333333333333p-1",
              "message": "Completed digital state transition.",
              "metadata": {
                "state_transition": {
                  "block_id": "block.0002.readout_rotation",
                  "input_logical_time": 0.6,
                  "input_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
                  "kernel": "ExactDensityMatrixKernel.digital",
                  "metadata": {
                    "logical_order": [
                      "q0",
                      "q1"
                    ],
                    "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
                    "payload_id": "payload.2.block.0002.readout_rotation.digital",
                    "solver_evidence": {
                      "absolute_tolerance": null,
                      "accepted_steps": 0,
                      "final_time": 0.6,
                      "function_evaluations": null,
                      "initial_time": 0.6,
                      "integrator_requested": "fixed_step_krylov",
                      "integrator_selected": "not_applicable",
                      "max_step_size": null,
                      "metadata": {
                        "consumer": "ExactDensityMatrixKernel.digital"
                      },
                      "min_step_size": null,
                      "rejected_steps": null,
                      "rejected_steps_available": false,
                      "relative_tolerance": null,
                      "schema_version": "0.1",
                      "segment_count": 0,
                      "termination_reason": "not_applicable",
                      "time_unit": "us",
                      "tolerance_applied": false
                    }
                  },
                  "order_index": 2,
                  "output_logical_time": 0.6,
                  "output_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
                  "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
                  "program_kind": "digital",
                  "schema_version": "0.1",
                  "solver_evidence_hash": "8c6537a374163b7170874874c97426a424799f42a8be28e169dce0bf916296f1",
                  "time_unit": "us",
                  "transition_id": "transition.2.block.0002.readout_rotation"
                }
              },
              "schema_version": "0.1",
              "stage": "running",
              "status": "ok"
            },
            {
              "event_time": "logical:0x1.3333333333333p-1",
              "message": "Terminal noisy sampling completed.",
              "metadata": {
                "final_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
                "measurement_key": "result",
                "seed": 4883,
                "shots": 128
              },
              "schema_version": "0.1",
              "stage": "completed",
              "status": "ok"
            }
          ],
          "metadata": {
            "execution_mode": "local_hybrid_density_matrix"
          },
          "references": {
            "bundle_hash": "42234f4fd9d09c4d8102e6dc8d5f703c5ec76e567a4a89e630381577a0768e05",
            "calibration_snapshot_hash": null,
            "compiled_program_hash": null,
            "discretized_program_hash": null,
            "execution_package_id": null,
            "final_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "initial_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
            "metadata": {
              "graph_hash": "7f1df6f7e79a08131273f5367d8b40cf1a5fab604b12a94df8efb2411a53452c"
            },
            "plan_hash": "4388febf8e9092f0d5a1bdee8ba9658cd610618a595779025d6019da97dad681",
            "program_hash": "3ae12596e75deff789e526006cd6fad95bd8363cc46c441de4e19eaecd54aa05",
            "schema_version": "0.1",
            "target_snapshot_hash": null
          },
          "schema_version": "0.1",
          "trace_id": "trace.local_bundle.local_plan.project.noisy.hybrid.physical_noise"
        },
        "selected_simulator": "ExactDensityNoiseEngine",
        "simulation_execution_config": {
          "absolute_tolerance": 1e-11,
          "device": "cpu",
          "dtype": "complex128",
          "execution_scope": "job",
          "integrator_requested": "fixed_step_krylov",
          "integrator_selected": "fixed_step_krylov",
          "method": "density_matrix",
          "relative_tolerance": 1e-09,
          "schema_version": "0.1",
          "seed": 4883,
          "seed_semantics": "effective_seed",
          "solver_evidence_hash": "ef94260e54386e61fba4be5fe71dd918dd8b4fe0e55d432adf91e8b7ac110708",
          "step_semantics": "fixed_time_slices",
          "steps": 32,
          "tolerance_applied": false,
          "trajectories": null,
          "worker_semantics": "kernel_concurrency",
          "workers": 1
        },
        "simulation_plan": {
          "atol": 1e-11,
          "budget_bytes": 20615843020,
          "candidates": [
            {
              "estimate": {
                "dtype": "complex128",
                "estimated_peak_bytes": 9792,
                "hilbert_dimension": 4,
                "itemsize_bytes": 16,
                "logical_sites": 2,
                "method": "state_vector",
                "operator_bytes": 128,
                "result_buffer_bytes": 4096,
                "sampling_bytes": 4096,
                "schema_version": "cascaqit.simulation.planning.v1",
                "state_bytes": 64,
                "state_dimension": 4,
                "trajectories": 1,
                "worker_copy_bytes": 0,
                "workers": 1,
                "workspace_bytes": 1408
              },
              "method": "state_vector",
              "reason_codes": [
                "SIMULATION_METHOD_REQUIRES_IDEAL_MODEL"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "rejected"
            },
            {
              "estimate": null,
              "method": "subspace",
              "reason_codes": [
                "SIMULATION_METHOD_REQUIRES_IDEAL_MODEL"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "rejected"
            },
            {
              "estimate": {
                "dtype": "complex128",
                "estimated_peak_bytes": 9728,
                "hilbert_dimension": 4,
                "itemsize_bytes": 16,
                "logical_sites": 2,
                "method": "density_matrix",
                "operator_bytes": 512,
                "result_buffer_bytes": 4096,
                "sampling_bytes": 4096,
                "schema_version": "cascaqit.simulation.planning.v1",
                "state_bytes": 256,
                "state_dimension": 16,
                "trajectories": 1,
                "worker_copy_bytes": 0,
                "workers": 1,
                "workspace_bytes": 768
              },
              "method": "density_matrix",
              "reason_codes": [
                "SIMULATION_METHOD_ELIGIBLE",
                "SIMULATION_METHOD_SELECTED"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "selected"
            },
            {
              "estimate": {
                "dtype": "complex128",
                "estimated_peak_bytes": 368768,
                "hilbert_dimension": 4,
                "itemsize_bytes": 16,
                "logical_sites": 2,
                "method": "trajectory",
                "operator_bytes": 128,
                "result_buffer_bytes": 4096,
                "sampling_bytes": 4096,
                "schema_version": "cascaqit.simulation.planning.v1",
                "state_bytes": 16384,
                "state_dimension": 1024,
                "trajectories": 256,
                "worker_copy_bytes": 229376,
                "workers": 15,
                "workspace_bytes": 114688
              },
              "method": "trajectory",
              "reason_codes": [
                "SIMULATION_METHOD_ELIGIBLE"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "eligible"
            }
          ],
          "device": "cpu",
          "dtype": "complex128",
          "estimate": {
            "dtype": "complex128",
            "estimated_peak_bytes": 9728,
            "hilbert_dimension": 4,
            "itemsize_bytes": 16,
            "logical_sites": 2,
            "method": "density_matrix",
            "operator_bytes": 512,
            "result_buffer_bytes": 4096,
            "sampling_bytes": 4096,
            "schema_version": "cascaqit.simulation.planning.v1",
            "state_bytes": 256,
            "state_dimension": 16,
            "trajectories": 1,
            "worker_copy_bytes": 0,
            "workers": 1,
            "workspace_bytes": 768
          },
          "hilbert_dimension": 4,
          "host_hash": "fc340411ec9c1fe45ae7d312ce900fdaeaa5935813f6c5c169cb18b81d90aea1",
          "integrator_requested": "fixed_step_krylov",
          "integrator_selected": "fixed_step_krylov",
          "logical_sites": 2,
          "max_steps": 32,
          "metadata": {
            "array_backend": "numpy",
            "blockade_dimension": null,
            "host_snapshot_source": "platform.effective_resource_probe",
            "max_wall_time_seconds": null,
            "memory_fraction": 0.8,
            "network_accessed": false,
            "numpy_version": "2.0.2",
            "requires_trajectory": false,
            "scipy_version": "1.17.1",
            "target_statistical_error": null,
            "time_integration_required": true,
            "workers_cpu_limit": 15,
            "workers_requested": "auto"
          },
          "method_requested": "density_matrix",
          "method_selected": "density_matrix",
          "noisy": true,
          "options_hash": "1af863a3a5012a150859839dd3a1e91c106688749067f8317825bd54a038f8fd",
          "plan_id": "simulation_plan.hybrid.2.density_matrix.fixed_step_krylov",
          "program_kind": "hybrid",
          "rtol": 1e-09,
          "schema_version": "cascaqit.simulation.planning.v1",
          "seed": 4883,
          "state_representation": "density_matrix",
          "trajectories": 256,
          "truthfulness": "planning_only",
          "workers": 1
        },
        "simulation_plan_hash": "c5bbbd578ec9d58e124ec797146081320f88ec73b601082523fbe71813ff1539",
        "simulation_plan_truthfulness": "planning_only",
        "simulation_resource_estimate": {
          "dtype": "complex128",
          "estimated_peak_bytes": 9728,
          "hilbert_dimension": 4,
          "itemsize_bytes": 16,
          "logical_sites": 2,
          "method": "density_matrix",
          "operator_bytes": 512,
          "result_buffer_bytes": 4096,
          "sampling_bytes": 4096,
          "schema_version": "cascaqit.simulation.planning.v1",
          "state_bytes": 256,
          "state_dimension": 16,
          "trajectories": 1,
          "worker_copy_bytes": 0,
          "workers": 1,
          "workspace_bytes": 768
        },
        "simulation_resource_usage": {
          "actual_peak_rss_bytes": 143736832,
          "baseline_peak_rss_bytes": 143736832,
          "estimate_error_fraction": null,
          "estimate_within_tolerance": null,
          "estimated_peak_bytes": 9728,
          "incremental_peak_rss_bytes": 0,
          "measurement_scope": "job",
          "measurement_status": "baseline_dominated",
          "rss_semantics": "process_high_water_mark",
          "schema_version": "0.1",
          "wall_time_seconds": 0.03289974993094802
        },
        "simulation_solver_evidence": {
          "absolute_tolerance": null,
          "accepted_steps": 32,
          "final_time": 0.6,
          "function_evaluations": null,
          "initial_time": 0.0,
          "integrator_requested": "fixed_step_krylov",
          "integrator_selected": "fixed_step_krylov",
          "max_step_size": 0.01875,
          "metadata": {
            "aggregation_scope": "physical_density_hybrid_blocks",
            "component_count": 1,
            "component_evidence_hashes": [
              "b87033a62649f443f68ae025e7d6d4ca57efd42e54be9728595a3bf363bf4e3f"
            ]
          },
          "min_step_size": 0.01875,
          "rejected_steps": null,
          "rejected_steps_available": false,
          "relative_tolerance": null,
          "schema_version": "0.1",
          "segment_count": 32,
          "termination_reason": "completed",
          "time_unit": "us",
          "tolerance_applied": false
        },
        "simulation_solver_evidence_hash": "ef94260e54386e61fba4be5fe71dd918dd8b4fe0e55d432adf91e8b7ac110708",
        "simulation_state": {
          "arrays": {
            "rho": {
              "content_hash": "6e3ff60d8eb326639015a4e1b4fe7d8db257751cc3bf160b0d7c7d54572ddced",
              "dtype": "complex128",
              "nbytes": 256,
              "returned_state_bytes": false,
              "shape": [
                4,
                4
              ]
            }
          },
          "basis": "logical_two_level",
          "logical_order": [
            "q0",
            "q1"
          ],
          "logical_time": 0.6,
          "metrics": {
            "minimum_eigenvalue": 0.016080082047543194,
            "purity": 0.5302271049763567,
            "trace": 1.0
          },
          "noise_context": {},
          "provenance": {
            "conversion": null,
            "metadata": {
              "dephasing_duration": 0.0,
              "dephasing_rate": 0.0,
              "operation_count": 1,
              "program_hash": "c439c000a20062942c65081686f9e97ff09b1930f870b6090c842f0a4b79d040"
            },
            "parent_state_hash": "0f00ee3c858716b93a944d7fcc02114b6b0bdb5ae272180533083453d4776c76",
            "producer": "ExactDensityMatrixKernel.digital",
            "schema_version": "cascaqit.simulation.array_state.v1",
            "step_index": 5
          },
          "returned_state_bytes": false,
          "schema_version": "cascaqit.simulation.array_state.v1",
          "stable_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
          "state_kind": "density_matrix",
          "time_unit": "us"
        },
        "simulation_truthfulness": "physical_state_evolution",
        "state_bytes_returned": false,
        "state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
        "state_transitions": [
          {
            "block_id": "block.0000.prepare",
            "input_logical_time": 0.0,
            "input_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
            "kernel": "ExactDensityMatrixKernel.digital",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
              "payload_id": "payload.0.block.0000.prepare.digital",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.0,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "ExactDensityMatrixKernel.digital"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 0,
            "output_logical_time": 0.0,
            "output_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
            "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "dfca8e955ca173fed5f1dce4f8b20a513e634a38ff28f78dddce9fcdaa7803dd",
            "time_unit": "us",
            "transition_id": "transition.0.block.0000.prepare"
          },
          {
            "block_id": "block.0001.evolve",
            "input_logical_time": 0.0,
            "input_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
            "kernel": "ExactDensityMatrixKernel.analog",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
              "payload_id": "payload.1.block.0001.evolve.analog",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 32,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "fixed_step_krylov",
                "max_step_size": 0.01875,
                "metadata": {
                  "hermiticity_error_before_stabilization": 4.2841699744536696e-16,
                  "minimum_eigenvalue_before_stabilization": 0.016080082047543128,
                  "output_dtype": "complex128",
                  "positivity_evidence_available": true,
                  "solver": "strang_krylov_lindblad",
                  "stabilization_applied": true,
                  "trace_before_stabilization": {
                    "imag": -2.870804933781793e-18,
                    "real": 0.9999999999999972
                  }
                },
                "min_step_size": 0.01875,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 32,
                "termination_reason": "completed",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 1,
            "output_logical_time": 0.6,
            "output_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
            "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
            "program_kind": "analog",
            "schema_version": "0.1",
            "solver_evidence_hash": "b87033a62649f443f68ae025e7d6d4ca57efd42e54be9728595a3bf363bf4e3f",
            "time_unit": "us",
            "transition_id": "transition.1.block.0001.evolve"
          },
          {
            "block_id": "block.0002.readout_rotation",
            "input_logical_time": 0.6,
            "input_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
            "kernel": "ExactDensityMatrixKernel.digital",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
              "payload_id": "payload.2.block.0002.readout_rotation.digital",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.6,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "ExactDensityMatrixKernel.digital"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 2,
            "output_logical_time": 0.6,
            "output_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "8c6537a374163b7170874874c97426a424799f42a8be28e169dce0bf916296f1",
            "time_unit": "us",
            "transition_id": "transition.2.block.0002.readout_rotation"
          }
        ]
      }
    },
    {
      "result_id": "result.local_bundle.local_plan.project.noisy.hybrid.physical_noise",
      "program_hash": "3ae12596e75deff789e526006cd6fad95bd8363cc46c441de4e19eaecd54aa05",
      "target_id": "local.simulator",
      "shots": 128,
      "counts": {
        "00": 45,
        "01": 34,
        "10": 36,
        "11": 13
      },
      "samples": [
        "01",
        "00",
        "11",
        "01",
        "00",
        "00",
        "00",
        "11",
        "00",
        "01",
        "00",
        "10",
        "00",
        "01",
        "10",
        "00",
        "00",
        "01",
        "11",
        "10",
        "00",
        "00",
        "00",
        "00",
        "01",
        "10",
        "00",
        "01",
        "00",
        "10",
        "10",
        "00",
        "11",
        "01",
        "11",
        "01",
        "01",
        "00",
        "11",
        "00",
        "01",
        "10",
        "10",
        "00",
        "00",
        "00",
        "00",
        "10",
        "01",
        "00",
        "01",
        "00",
        "00",
        "10",
        "10",
        "01",
        "00",
        "11",
        "10",
        "01",
        "01",
        "10",
        "10",
        "01",
        "11",
        "00",
        "00",
        "10",
        "01",
        "10",
        "11",
        "10",
        "01",
        "10",
        "00",
        "00",
        "01",
        "10",
        "00",
        "10",
        "00",
        "00",
        "10",
        "00",
        "00",
        "10",
        "10",
        "00",
        "10",
        "01",
        "10",
        "01",
        "01",
        "01",
        "10",
        "10",
        "10",
        "01",
        "01",
        "10",
        "00",
        "10",
        "01",
        "00",
        "10",
        "00",
        "01",
        "01",
        "10",
        "01",
        "00",
        "10",
        "00",
        "11",
        "11",
        "10",
        "00",
        "01",
        "01",
        "10",
        "01",
        "00",
        "11",
        "10",
        "01",
        "11",
        "00",
        "00"
      ],
      "probabilities": {
        "00": 0.4327894017200914,
        "01": 0.23601050347734526,
        "10": 0.2900376720088961,
        "11": 0.041162422793667296
      },
      "observables": {
        "minimum_eigenvalue": 0.016080082047543194,
        "purity": 0.5302271049763567,
        "trace": 1.0
      },
      "observable_batch": {
        "observable_set_hash": "dbdcda5c7aa312b23da7566b6bc7da5ac7b572b561161122735a2aeef6c5bbcc",
        "items": [
          {
            "observable": {
              "name": "Z(q0)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.33759981039487336,
            "variance": 0.8860263680213456,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q1)",
              "terms": [
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.44565414745797494,
            "variance": 0.8013923808535055,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q0)*Z(q1)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                },
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": -0.052096350972482636,
            "variance": 0.9972859702153519,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          }
        ],
        "schema_version": "cascaqit.observables.v1"
      },
      "bit_ordering": {
        "convention": "logical_order",
        "logical_order": "q0,q1"
      },
      "occupation_encoding": {
        "ground": 0,
        "rydberg": 1
      },
      "diagnostics": [
        {
          "diagnostic_id": "simulation.noise.physical.completed",
          "stage": "simulation",
          "severity": "info",
          "code": "PHYSICAL_NOISE_SIMULATION_COMPLETED",
          "message": "Canonical physical noise simulation completed.",
          "schema_version": "0.1",
          "object_path": "result",
          "suggestion": null,
          "metadata": {
            "channel_count": 2,
            "method": "density_matrix"
          }
        }
      ],
      "schema_version": "0.1",
      "metadata": {
        "backend_called": true,
        "backend_id": "local.simulator",
        "block_state_chain": [
          {
            "block_id": "block.0000.prepare",
            "input_logical_time": 0.0,
            "input_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
            "kernel": "ExactDensityMatrixKernel.digital",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
              "payload_id": "payload.0.block.0000.prepare.digital",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.0,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "ExactDensityMatrixKernel.digital"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 0,
            "output_logical_time": 0.0,
            "output_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
            "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "dfca8e955ca173fed5f1dce4f8b20a513e634a38ff28f78dddce9fcdaa7803dd",
            "time_unit": "us",
            "transition_id": "transition.0.block.0000.prepare"
          },
          {
            "block_id": "block.0001.evolve",
            "input_logical_time": 0.0,
            "input_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
            "kernel": "ExactDensityMatrixKernel.analog",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
              "payload_id": "payload.1.block.0001.evolve.analog",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 32,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "fixed_step_krylov",
                "max_step_size": 0.01875,
                "metadata": {
                  "hermiticity_error_before_stabilization": 4.2841699744536696e-16,
                  "minimum_eigenvalue_before_stabilization": 0.016080082047543128,
                  "output_dtype": "complex128",
                  "positivity_evidence_available": true,
                  "solver": "strang_krylov_lindblad",
                  "stabilization_applied": true,
                  "trace_before_stabilization": {
                    "imag": -2.870804933781793e-18,
                    "real": 0.9999999999999972
                  }
                },
                "min_step_size": 0.01875,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 32,
                "termination_reason": "completed",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 1,
            "output_logical_time": 0.6,
            "output_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
            "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
            "program_kind": "analog",
            "schema_version": "0.1",
            "solver_evidence_hash": "b87033a62649f443f68ae025e7d6d4ca57efd42e54be9728595a3bf363bf4e3f",
            "time_unit": "us",
            "transition_id": "transition.1.block.0001.evolve"
          },
          {
            "block_id": "block.0002.readout_rotation",
            "input_logical_time": 0.6,
            "input_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
            "kernel": "ExactDensityMatrixKernel.digital",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
              "payload_id": "payload.2.block.0002.readout_rotation.digital",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.6,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "ExactDensityMatrixKernel.digital"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 2,
            "output_logical_time": 0.6,
            "output_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "8c6537a374163b7170874874c97426a424799f42a8be28e169dce0bf916296f1",
            "time_unit": "us",
            "transition_id": "transition.2.block.0002.readout_rotation"
          }
        ],
        "control_report_evidence": [
          {
            "block_id": "block.0001.evolve",
            "diagnostic_count": 4,
            "diagnostics": [
              {
                "code": "CONTROL_CONCURRENCY_SUPPORTED",
                "diagnostic_id": "control.control_concurrency_supported.rydberg.local",
                "message": "Control concurrency is within the declared group limit.",
                "metadata": {
                  "actual_max_concurrency": 1,
                  "group_id": "rydberg.local",
                  "max_concurrent_operations": 2,
                  "operation_ids": [
                    "operation.local_detuning.0"
                  ]
                },
                "object_path": "control_schedule.operations",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              },
              {
                "code": "CONTROL_BANDWIDTH_SUPPORTED",
                "diagnostic_id": "control.control_bandwidth_supported.operation.local_detuning.0",
                "message": "Waveform knot-spacing bandwidth bound is within the Target limit.",
                "metadata": {
                  "bandwidth_limit": 2.0,
                  "bandwidth_unit": "MHz",
                  "channel_id": "rydberg.detuning.local",
                  "estimate_semantics": "nyquist_bound_from_minimum_knot_spacing",
                  "estimated_bandwidth": 0.0,
                  "operation_id": "operation.local_detuning.0"
                },
                "object_path": "hamiltonian.terms.local_detuning_terms[0].waveform",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              },
              {
                "code": "CONTROL_SLEW_SUPPORTED",
                "diagnostic_id": "control.control_slew_supported.operation.local_detuning.0",
                "message": "Waveform segment slew is within the Target limit.",
                "metadata": {
                  "actual_max_slew_rate": 0.0,
                  "channel_id": "rydberg.detuning.local",
                  "estimate_semantics": "maximum_actual_waveform_segment_derivative",
                  "max_slew_rate": 30.0,
                  "operation_id": "operation.local_detuning.0",
                  "slew_rate_unit": "rad/us^2"
                },
                "object_path": "hamiltonian.terms.local_detuning_terms[0].waveform",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              },
              {
                "code": "CONTROL_CROSSTALK_NO_OVERLAP",
                "diagnostic_id": "control.control_crosstalk_no_overlap.crosstalk.rydberg.rabi.local.rydberg.rabi.global",
                "message": "Crosstalk-constrained channels do not overlap.",
                "metadata": {
                  "actual_overlap_duration": 0.0,
                  "channel_ids": [
                    "rydberg.rabi.local",
                    "rydberg.rabi.global"
                  ],
                  "constraint_id": "crosstalk.rydberg.rabi.local.rydberg.rabi.global",
                  "max_overlap_duration": null,
                  "overlap_policy": "calibration_required",
                  "time_unit": "us"
                },
                "object_path": "control_schedule.operations",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              }
            ],
            "has_errors": false,
            "production_channel_allocation_performed": false,
            "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
            "schedule": {
              "control_system_hash": "fbbc3937e5187ca6bb0a3f00e176187027581e3382a83ee377e7115bffd5a87a",
              "diagnostics": [],
              "metadata": {
                "production_channel_allocation_performed": false,
                "projection": "program_ir_control_terms",
                "time_origin": 0.0,
                "time_unit": "us"
              },
              "operations": [
                {
                  "channel_id": "rydberg.detuning.global",
                  "end_time": 0.6,
                  "metadata": {
                    "production_assigned": false,
                    "program_path": "hamiltonian.terms.detuning",
                    "time_unit": "us",
                    "value_unit": "rad/us",
                    "waveform_kind": "constant"
                  },
                  "operation_id": "operation.global_detuning",
                  "operation_kind": "global_detuning",
                  "schema_version": "0.1",
                  "source_hash": "19b3cbf48a848eccf4b459d549c9603d70c02b450b81211bb93c55010a4339ab",
                  "start_time": 0.0,
                  "target_site_ids": [
                    "q0",
                    "q1"
                  ],
                  "waveform_hash": "19b3cbf48a848eccf4b459d549c9603d70c02b450b81211bb93c55010a4339ab"
                },
                {
                  "channel_id": "rydberg.rabi.global",
                  "end_time": 0.6,
                  "metadata": {
                    "production_assigned": false,
                    "program_path": "hamiltonian.terms.rabi",
                    "time_unit": "us",
                    "value_unit": "rad/us",
                    "waveform_kind": "constant"
                  },
                  "operation_id": "operation.global_rabi",
                  "operation_kind": "global_rabi",
                  "schema_version": "0.1",
                  "source_hash": "ad464599d866805baa0f7753cf0d4ce853b1688908e85f1baa172d7740efa2da",
                  "start_time": 0.0,
                  "target_site_ids": [
                    "q0",
                    "q1"
                  ],
                  "waveform_hash": "ad464599d866805baa0f7753cf0d4ce853b1688908e85f1baa172d7740efa2da"
                },
                {
                  "channel_id": "rydberg.detuning.local",
                  "end_time": 0.6,
                  "metadata": {
                    "production_assigned": false,
                    "program_path": "hamiltonian.terms.local_detuning_terms[0].waveform",
                    "time_unit": "us",
                    "value_unit": "rad/us",
                    "waveform_kind": "constant"
                  },
                  "operation_id": "operation.local_detuning.0",
                  "operation_kind": "local_detuning",
                  "schema_version": "0.1",
                  "source_hash": "5cf7b4b36d89a2948d9ee6b9b1974f74b74438df6df8aeaaafad175c714c34ed",
                  "start_time": 0.0,
                  "target_site_ids": [
                    "q0",
                    "q1"
                  ],
                  "waveform_hash": "e1caa1faf062ab87977975eab5ad7eb6366c3974acdadba829e14493602d0665"
                }
              ],
              "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
              "schedule_id": "schedule.program.control",
              "schema_version": "0.1"
            },
            "target_id": "mock.neutral_atom.local_ahs.v0_1"
          }
        ],
        "execution_package_created": false,
        "network_accessed": false,
        "noise_model_hash": "448a2c0332c24677c533b6381aa06e6ab1f1057ebbee842aae4160508d83713c",
        "noise_report": {
          "applied_channel_types": [
            "dephasing",
            "readout"
          ],
          "measurement_application_count": 1,
          "method": "density_matrix",
          "noise_model_hash": "448a2c0332c24677c533b6381aa06e6ab1f1057ebbee842aae4160508d83713c",
          "noise_model_id": "phase.readout",
          "physical_application_count": 1,
          "records": [
            {
              "channel_id": "noise.dephasing",
              "channel_type": "dephasing",
              "injection_point": "analog_evolution",
              "input_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
              "metadata": {
                "model": "lindblad_phase_flip",
                "parameters": {
                  "rate": 0.8
                },
                "schedule_ref": null
              },
              "output_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
              "targets": [
                "q0",
                "q1"
              ],
              "truthfulness": "physical_state_evolution"
            },
            {
              "channel_id": "noise.readout",
              "channel_type": "readout",
              "injection_point": "terminal_measurement",
              "input_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
              "metadata": {
                "counts_modified": true,
                "model": "asymmetric_confusion",
                "parameters": {
                  "p01": 0.08,
                  "p10": 0.12
                }
              },
              "output_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
              "targets": [
                "q0",
                "q1"
              ],
              "truthfulness": "measurement_model_only"
            }
          ],
          "truthfulness": "physical_state_evolution"
        },
        "noise_report_hash": "7ca997c6cfefc571460c84e5d226798ca0fafece5d9502f5e3b39913ddb9d993",
        "offline_deterministic": true,
        "references": {
          "bundle_hash": "49bf06e86bd96e992244a38daea8a830f278ddf182a63cdfd7a6605f84006ed7",
          "calibration_snapshot_hash": null,
          "compiled_program_hash": null,
          "discretized_program_hash": null,
          "execution_package_id": null,
          "final_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
          "initial_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
          "metadata": {
            "graph_hash": "7f1df6f7e79a08131273f5367d8b40cf1a5fab604b12a94df8efb2411a53452c"
          },
          "plan_hash": "4388febf8e9092f0d5a1bdee8ba9658cd610618a595779025d6019da97dad681",
          "program_hash": "3ae12596e75deff789e526006cd6fad95bd8363cc46c441de4e19eaecd54aa05",
          "schema_version": "0.1",
          "target_snapshot_hash": null
        },
        "register_snapshots": [
          {
            "active_atom_ids": [
              "q0",
              "q1"
            ],
            "active_site_count": 2,
            "active_site_ids": [
              "q0",
              "q1"
            ],
            "lifecycle_stage": "planned",
            "physical_site_count": 2,
            "physical_site_ids": [
              "q0",
              "q1"
            ],
            "previous_snapshot_hash": null,
            "snapshot_hash": "571e481d25fc0fb0e4962bcb62d4b574c81cc965cb8e3b4fc69565faa8be68ec",
            "snapshot_id": "register.planned",
            "status_counts": {
              "defect": 0,
              "filled": 2,
              "loading_failed": 0,
              "vacant": 0
            }
          }
        ],
        "run_trace": {
          "events": [
            {
              "event_time": "logical:0x0.0p+0",
              "message": "Completed digital state transition.",
              "metadata": {
                "state_transition": {
                  "block_id": "block.0000.prepare",
                  "input_logical_time": 0.0,
                  "input_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
                  "kernel": "ExactDensityMatrixKernel.digital",
                  "metadata": {
                    "logical_order": [
                      "q0",
                      "q1"
                    ],
                    "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
                    "payload_id": "payload.0.block.0000.prepare.digital",
                    "solver_evidence": {
                      "absolute_tolerance": null,
                      "accepted_steps": 0,
                      "final_time": 0.0,
                      "function_evaluations": null,
                      "initial_time": 0.0,
                      "integrator_requested": "fixed_step_krylov",
                      "integrator_selected": "not_applicable",
                      "max_step_size": null,
                      "metadata": {
                        "consumer": "ExactDensityMatrixKernel.digital"
                      },
                      "min_step_size": null,
                      "rejected_steps": null,
                      "rejected_steps_available": false,
                      "relative_tolerance": null,
                      "schema_version": "0.1",
                      "segment_count": 0,
                      "termination_reason": "not_applicable",
                      "time_unit": "us",
                      "tolerance_applied": false
                    }
                  },
                  "order_index": 0,
                  "output_logical_time": 0.0,
                  "output_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
                  "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
                  "program_kind": "digital",
                  "schema_version": "0.1",
                  "solver_evidence_hash": "dfca8e955ca173fed5f1dce4f8b20a513e634a38ff28f78dddce9fcdaa7803dd",
                  "time_unit": "us",
                  "transition_id": "transition.0.block.0000.prepare"
                }
              },
              "schema_version": "0.1",
              "stage": "running",
              "status": "ok"
            },
            {
              "event_time": "logical:0x1.3333333333333p-1",
              "message": "Completed analog state transition.",
              "metadata": {
                "state_transition": {
                  "block_id": "block.0001.evolve",
                  "input_logical_time": 0.0,
                  "input_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
                  "kernel": "ExactDensityMatrixKernel.analog",
                  "metadata": {
                    "logical_order": [
                      "q0",
                      "q1"
                    ],
                    "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
                    "payload_id": "payload.1.block.0001.evolve.analog",
                    "solver_evidence": {
                      "absolute_tolerance": null,
                      "accepted_steps": 32,
                      "final_time": 0.6,
                      "function_evaluations": null,
                      "initial_time": 0.0,
                      "integrator_requested": "fixed_step_krylov",
                      "integrator_selected": "fixed_step_krylov",
                      "max_step_size": 0.01875,
                      "metadata": {
                        "hermiticity_error_before_stabilization": 4.2841699744536696e-16,
                        "minimum_eigenvalue_before_stabilization": 0.016080082047543128,
                        "output_dtype": "complex128",
                        "positivity_evidence_available": true,
                        "solver": "strang_krylov_lindblad",
                        "stabilization_applied": true,
                        "trace_before_stabilization": {
                          "imag": -2.870804933781793e-18,
                          "real": 0.9999999999999972
                        }
                      },
                      "min_step_size": 0.01875,
                      "rejected_steps": null,
                      "rejected_steps_available": false,
                      "relative_tolerance": null,
                      "schema_version": "0.1",
                      "segment_count": 32,
                      "termination_reason": "completed",
                      "time_unit": "us",
                      "tolerance_applied": false
                    }
                  },
                  "order_index": 1,
                  "output_logical_time": 0.6,
                  "output_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
                  "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
                  "program_kind": "analog",
                  "schema_version": "0.1",
                  "solver_evidence_hash": "b87033a62649f443f68ae025e7d6d4ca57efd42e54be9728595a3bf363bf4e3f",
                  "time_unit": "us",
                  "transition_id": "transition.1.block.0001.evolve"
                }
              },
              "schema_version": "0.1",
              "stage": "running",
              "status": "ok"
            },
            {
              "event_time": "logical:0x1.3333333333333p-1",
              "message": "Completed digital state transition.",
              "metadata": {
                "state_transition": {
                  "block_id": "block.0002.readout_rotation",
                  "input_logical_time": 0.6,
                  "input_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
                  "kernel": "ExactDensityMatrixKernel.digital",
                  "metadata": {
                    "logical_order": [
                      "q0",
                      "q1"
                    ],
                    "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
                    "payload_id": "payload.2.block.0002.readout_rotation.digital",
                    "solver_evidence": {
                      "absolute_tolerance": null,
                      "accepted_steps": 0,
                      "final_time": 0.6,
                      "function_evaluations": null,
                      "initial_time": 0.6,
                      "integrator_requested": "fixed_step_krylov",
                      "integrator_selected": "not_applicable",
                      "max_step_size": null,
                      "metadata": {
                        "consumer": "ExactDensityMatrixKernel.digital"
                      },
                      "min_step_size": null,
                      "rejected_steps": null,
                      "rejected_steps_available": false,
                      "relative_tolerance": null,
                      "schema_version": "0.1",
                      "segment_count": 0,
                      "termination_reason": "not_applicable",
                      "time_unit": "us",
                      "tolerance_applied": false
                    }
                  },
                  "order_index": 2,
                  "output_logical_time": 0.6,
                  "output_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
                  "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
                  "program_kind": "digital",
                  "schema_version": "0.1",
                  "solver_evidence_hash": "8c6537a374163b7170874874c97426a424799f42a8be28e169dce0bf916296f1",
                  "time_unit": "us",
                  "transition_id": "transition.2.block.0002.readout_rotation"
                }
              },
              "schema_version": "0.1",
              "stage": "running",
              "status": "ok"
            },
            {
              "event_time": "logical:0x1.3333333333333p-1",
              "message": "Terminal noisy sampling completed.",
              "metadata": {
                "final_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
                "measurement_key": "result",
                "seed": 4881,
                "shots": 128
              },
              "schema_version": "0.1",
              "stage": "completed",
              "status": "ok"
            }
          ],
          "metadata": {
            "execution_mode": "local_hybrid_density_matrix"
          },
          "references": {
            "bundle_hash": "49bf06e86bd96e992244a38daea8a830f278ddf182a63cdfd7a6605f84006ed7",
            "calibration_snapshot_hash": null,
            "compiled_program_hash": null,
            "discretized_program_hash": null,
            "execution_package_id": null,
            "final_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "initial_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
            "metadata": {
              "graph_hash": "7f1df6f7e79a08131273f5367d8b40cf1a5fab604b12a94df8efb2411a53452c"
            },
            "plan_hash": "4388febf8e9092f0d5a1bdee8ba9658cd610618a595779025d6019da97dad681",
            "program_hash": "3ae12596e75deff789e526006cd6fad95bd8363cc46c441de4e19eaecd54aa05",
            "schema_version": "0.1",
            "target_snapshot_hash": null
          },
          "schema_version": "0.1",
          "trace_id": "trace.local_bundle.local_plan.project.noisy.hybrid.physical_noise"
        },
        "selected_simulator": "ExactDensityNoiseEngine",
        "simulation_execution_config": {
          "absolute_tolerance": 1e-11,
          "device": "cpu",
          "dtype": "complex128",
          "execution_scope": "job",
          "integrator_requested": "fixed_step_krylov",
          "integrator_selected": "fixed_step_krylov",
          "method": "density_matrix",
          "relative_tolerance": 1e-09,
          "schema_version": "0.1",
          "seed": 4881,
          "seed_semantics": "effective_seed",
          "solver_evidence_hash": "ef94260e54386e61fba4be5fe71dd918dd8b4fe0e55d432adf91e8b7ac110708",
          "step_semantics": "fixed_time_slices",
          "steps": 32,
          "tolerance_applied": false,
          "trajectories": null,
          "worker_semantics": "kernel_concurrency",
          "workers": 1
        },
        "simulation_plan": {
          "atol": 1e-11,
          "budget_bytes": 20615843020,
          "candidates": [
            {
              "estimate": {
                "dtype": "complex128",
                "estimated_peak_bytes": 9792,
                "hilbert_dimension": 4,
                "itemsize_bytes": 16,
                "logical_sites": 2,
                "method": "state_vector",
                "operator_bytes": 128,
                "result_buffer_bytes": 4096,
                "sampling_bytes": 4096,
                "schema_version": "cascaqit.simulation.planning.v1",
                "state_bytes": 64,
                "state_dimension": 4,
                "trajectories": 1,
                "worker_copy_bytes": 0,
                "workers": 1,
                "workspace_bytes": 1408
              },
              "method": "state_vector",
              "reason_codes": [
                "SIMULATION_METHOD_REQUIRES_IDEAL_MODEL"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "rejected"
            },
            {
              "estimate": null,
              "method": "subspace",
              "reason_codes": [
                "SIMULATION_METHOD_REQUIRES_IDEAL_MODEL"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "rejected"
            },
            {
              "estimate": {
                "dtype": "complex128",
                "estimated_peak_bytes": 9728,
                "hilbert_dimension": 4,
                "itemsize_bytes": 16,
                "logical_sites": 2,
                "method": "density_matrix",
                "operator_bytes": 512,
                "result_buffer_bytes": 4096,
                "sampling_bytes": 4096,
                "schema_version": "cascaqit.simulation.planning.v1",
                "state_bytes": 256,
                "state_dimension": 16,
                "trajectories": 1,
                "worker_copy_bytes": 0,
                "workers": 1,
                "workspace_bytes": 768
              },
              "method": "density_matrix",
              "reason_codes": [
                "SIMULATION_METHOD_ELIGIBLE",
                "SIMULATION_METHOD_SELECTED"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "selected"
            },
            {
              "estimate": {
                "dtype": "complex128",
                "estimated_peak_bytes": 368768,
                "hilbert_dimension": 4,
                "itemsize_bytes": 16,
                "logical_sites": 2,
                "method": "trajectory",
                "operator_bytes": 128,
                "result_buffer_bytes": 4096,
                "sampling_bytes": 4096,
                "schema_version": "cascaqit.simulation.planning.v1",
                "state_bytes": 16384,
                "state_dimension": 1024,
                "trajectories": 256,
                "worker_copy_bytes": 229376,
                "workers": 15,
                "workspace_bytes": 114688
              },
              "method": "trajectory",
              "reason_codes": [
                "SIMULATION_METHOD_ELIGIBLE"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "eligible"
            }
          ],
          "device": "cpu",
          "dtype": "complex128",
          "estimate": {
            "dtype": "complex128",
            "estimated_peak_bytes": 9728,
            "hilbert_dimension": 4,
            "itemsize_bytes": 16,
            "logical_sites": 2,
            "method": "density_matrix",
            "operator_bytes": 512,
            "result_buffer_bytes": 4096,
            "sampling_bytes": 4096,
            "schema_version": "cascaqit.simulation.planning.v1",
            "state_bytes": 256,
            "state_dimension": 16,
            "trajectories": 1,
            "worker_copy_bytes": 0,
            "workers": 1,
            "workspace_bytes": 768
          },
          "hilbert_dimension": 4,
          "host_hash": "fc340411ec9c1fe45ae7d312ce900fdaeaa5935813f6c5c169cb18b81d90aea1",
          "integrator_requested": "fixed_step_krylov",
          "integrator_selected": "fixed_step_krylov",
          "logical_sites": 2,
          "max_steps": 32,
          "metadata": {
            "array_backend": "numpy",
            "blockade_dimension": null,
            "host_snapshot_source": "platform.effective_resource_probe",
            "max_wall_time_seconds": null,
            "memory_fraction": 0.8,
            "network_accessed": false,
            "numpy_version": "2.0.2",
            "requires_trajectory": false,
            "scipy_version": "1.17.1",
            "target_statistical_error": null,
            "time_integration_required": true,
            "workers_cpu_limit": 15,
            "workers_requested": "auto"
          },
          "method_requested": "density_matrix",
          "method_selected": "density_matrix",
          "noisy": true,
          "options_hash": "2a941fe55d2238532ebd3114677c2cbbf495f4dfb815cb1a7caf566a75ffa99f",
          "plan_id": "simulation_plan.hybrid.2.density_matrix.fixed_step_krylov",
          "program_kind": "hybrid",
          "rtol": 1e-09,
          "schema_version": "cascaqit.simulation.planning.v1",
          "seed": 4881,
          "state_representation": "density_matrix",
          "trajectories": 256,
          "truthfulness": "planning_only",
          "workers": 1
        },
        "simulation_plan_hash": "ebb59f2ca97625a39f64ab5f58854cb4655e72e400495fa82a4e7e10ee92c493",
        "simulation_plan_truthfulness": "planning_only",
        "simulation_resource_estimate": {
          "dtype": "complex128",
          "estimated_peak_bytes": 9728,
          "hilbert_dimension": 4,
          "itemsize_bytes": 16,
          "logical_sites": 2,
          "method": "density_matrix",
          "operator_bytes": 512,
          "result_buffer_bytes": 4096,
          "sampling_bytes": 4096,
          "schema_version": "cascaqit.simulation.planning.v1",
          "state_bytes": 256,
          "state_dimension": 16,
          "trajectories": 1,
          "worker_copy_bytes": 0,
          "workers": 1,
          "workspace_bytes": 768
        },
        "simulation_resource_usage": {
          "actual_peak_rss_bytes": 143736832,
          "baseline_peak_rss_bytes": 143736832,
          "estimate_error_fraction": null,
          "estimate_within_tolerance": null,
          "estimated_peak_bytes": 9728,
          "incremental_peak_rss_bytes": 0,
          "measurement_scope": "job",
          "measurement_status": "baseline_dominated",
          "rss_semantics": "process_high_water_mark",
          "schema_version": "0.1",
          "wall_time_seconds": 0.025362666929140687
        },
        "simulation_solver_evidence": {
          "absolute_tolerance": null,
          "accepted_steps": 32,
          "final_time": 0.6,
          "function_evaluations": null,
          "initial_time": 0.0,
          "integrator_requested": "fixed_step_krylov",
          "integrator_selected": "fixed_step_krylov",
          "max_step_size": 0.01875,
          "metadata": {
            "aggregation_scope": "physical_density_hybrid_blocks",
            "component_count": 1,
            "component_evidence_hashes": [
              "b87033a62649f443f68ae025e7d6d4ca57efd42e54be9728595a3bf363bf4e3f"
            ]
          },
          "min_step_size": 0.01875,
          "rejected_steps": null,
          "rejected_steps_available": false,
          "relative_tolerance": null,
          "schema_version": "0.1",
          "segment_count": 32,
          "termination_reason": "completed",
          "time_unit": "us",
          "tolerance_applied": false
        },
        "simulation_solver_evidence_hash": "ef94260e54386e61fba4be5fe71dd918dd8b4fe0e55d432adf91e8b7ac110708",
        "simulation_state": {
          "arrays": {
            "rho": {
              "content_hash": "6e3ff60d8eb326639015a4e1b4fe7d8db257751cc3bf160b0d7c7d54572ddced",
              "dtype": "complex128",
              "nbytes": 256,
              "returned_state_bytes": false,
              "shape": [
                4,
                4
              ]
            }
          },
          "basis": "logical_two_level",
          "logical_order": [
            "q0",
            "q1"
          ],
          "logical_time": 0.6,
          "metrics": {
            "minimum_eigenvalue": 0.016080082047543194,
            "purity": 0.5302271049763567,
            "trace": 1.0
          },
          "noise_context": {},
          "provenance": {
            "conversion": null,
            "metadata": {
              "dephasing_duration": 0.0,
              "dephasing_rate": 0.0,
              "operation_count": 1,
              "program_hash": "c439c000a20062942c65081686f9e97ff09b1930f870b6090c842f0a4b79d040"
            },
            "parent_state_hash": "0f00ee3c858716b93a944d7fcc02114b6b0bdb5ae272180533083453d4776c76",
            "producer": "ExactDensityMatrixKernel.digital",
            "schema_version": "cascaqit.simulation.array_state.v1",
            "step_index": 5
          },
          "returned_state_bytes": false,
          "schema_version": "cascaqit.simulation.array_state.v1",
          "stable_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
          "state_kind": "density_matrix",
          "time_unit": "us"
        },
        "simulation_truthfulness": "physical_state_evolution",
        "state_bytes_returned": false,
        "state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
        "state_transitions": [
          {
            "block_id": "block.0000.prepare",
            "input_logical_time": 0.0,
            "input_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
            "kernel": "ExactDensityMatrixKernel.digital",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
              "payload_id": "payload.0.block.0000.prepare.digital",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.0,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "ExactDensityMatrixKernel.digital"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 0,
            "output_logical_time": 0.0,
            "output_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
            "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "dfca8e955ca173fed5f1dce4f8b20a513e634a38ff28f78dddce9fcdaa7803dd",
            "time_unit": "us",
            "transition_id": "transition.0.block.0000.prepare"
          },
          {
            "block_id": "block.0001.evolve",
            "input_logical_time": 0.0,
            "input_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
            "kernel": "ExactDensityMatrixKernel.analog",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
              "payload_id": "payload.1.block.0001.evolve.analog",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 32,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "fixed_step_krylov",
                "max_step_size": 0.01875,
                "metadata": {
                  "hermiticity_error_before_stabilization": 4.2841699744536696e-16,
                  "minimum_eigenvalue_before_stabilization": 0.016080082047543128,
                  "output_dtype": "complex128",
                  "positivity_evidence_available": true,
                  "solver": "strang_krylov_lindblad",
                  "stabilization_applied": true,
                  "trace_before_stabilization": {
                    "imag": -2.870804933781793e-18,
                    "real": 0.9999999999999972
                  }
                },
                "min_step_size": 0.01875,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 32,
                "termination_reason": "completed",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 1,
            "output_logical_time": 0.6,
            "output_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
            "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
            "program_kind": "analog",
            "schema_version": "0.1",
            "solver_evidence_hash": "b87033a62649f443f68ae025e7d6d4ca57efd42e54be9728595a3bf363bf4e3f",
            "time_unit": "us",
            "transition_id": "transition.1.block.0001.evolve"
          },
          {
            "block_id": "block.0002.readout_rotation",
            "input_logical_time": 0.6,
            "input_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
            "kernel": "ExactDensityMatrixKernel.digital",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
              "payload_id": "payload.2.block.0002.readout_rotation.digital",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.6,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "ExactDensityMatrixKernel.digital"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 2,
            "output_logical_time": 0.6,
            "output_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "8c6537a374163b7170874874c97426a424799f42a8be28e169dce0bf916296f1",
            "time_unit": "us",
            "transition_id": "transition.2.block.0002.readout_rotation"
          }
        ]
      }
    },
    {
      "result_id": "result.local_bundle.local_plan.project.noisy.hybrid.physical_noise",
      "program_hash": "3ae12596e75deff789e526006cd6fad95bd8363cc46c441de4e19eaecd54aa05",
      "target_id": "local.simulator",
      "shots": 128,
      "counts": {
        "00": 42,
        "01": 39,
        "10": 38,
        "11": 9
      },
      "samples": [
        "10",
        "10",
        "10",
        "10",
        "00",
        "10",
        "01",
        "10",
        "01",
        "00",
        "01",
        "11",
        "00",
        "10",
        "00",
        "00",
        "00",
        "10",
        "00",
        "00",
        "11",
        "01",
        "00",
        "01",
        "01",
        "10",
        "01",
        "00",
        "00",
        "01",
        "01",
        "11",
        "00",
        "10",
        "01",
        "01",
        "01",
        "10",
        "10",
        "00",
        "11",
        "01",
        "10",
        "01",
        "00",
        "00",
        "01",
        "00",
        "10",
        "10",
        "10",
        "01",
        "11",
        "00",
        "01",
        "00",
        "01",
        "10",
        "10",
        "10",
        "10",
        "10",
        "01",
        "01",
        "00",
        "10",
        "01",
        "00",
        "10",
        "10",
        "11",
        "10",
        "10",
        "00",
        "00",
        "10",
        "11",
        "01",
        "10",
        "00",
        "01",
        "01",
        "01",
        "00",
        "01",
        "00",
        "10",
        "01",
        "00",
        "01",
        "00",
        "10",
        "01",
        "10",
        "10",
        "10",
        "01",
        "11",
        "10",
        "00",
        "00",
        "01",
        "10",
        "00",
        "00",
        "01",
        "00",
        "01",
        "01",
        "01",
        "00",
        "01",
        "01",
        "00",
        "11",
        "00",
        "01",
        "10",
        "00",
        "00",
        "10",
        "00",
        "01",
        "00",
        "00",
        "00",
        "00",
        "10"
      ],
      "probabilities": {
        "00": 0.4327894017200914,
        "01": 0.23601050347734526,
        "10": 0.2900376720088961,
        "11": 0.041162422793667296
      },
      "observables": {
        "minimum_eigenvalue": 0.016080082047543194,
        "purity": 0.5302271049763567,
        "trace": 1.0
      },
      "observable_batch": {
        "observable_set_hash": "dbdcda5c7aa312b23da7566b6bc7da5ac7b572b561161122735a2aeef6c5bbcc",
        "items": [
          {
            "observable": {
              "name": "Z(q0)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.33759981039487336,
            "variance": 0.8860263680213456,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q1)",
              "terms": [
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.44565414745797494,
            "variance": 0.8013923808535055,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q0)*Z(q1)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                },
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": -0.052096350972482636,
            "variance": 0.9972859702153519,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          }
        ],
        "schema_version": "cascaqit.observables.v1"
      },
      "bit_ordering": {
        "convention": "logical_order",
        "logical_order": "q0,q1"
      },
      "occupation_encoding": {
        "ground": 0,
        "rydberg": 1
      },
      "diagnostics": [
        {
          "diagnostic_id": "simulation.noise.physical.completed",
          "stage": "simulation",
          "severity": "info",
          "code": "PHYSICAL_NOISE_SIMULATION_COMPLETED",
          "message": "Canonical physical noise simulation completed.",
          "schema_version": "0.1",
          "object_path": "result",
          "suggestion": null,
          "metadata": {
            "channel_count": 2,
            "method": "density_matrix"
          }
        }
      ],
      "schema_version": "0.1",
      "metadata": {
        "backend_called": true,
        "backend_id": "local.simulator",
        "block_state_chain": [
          {
            "block_id": "block.0000.prepare",
            "input_logical_time": 0.0,
            "input_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
            "kernel": "ExactDensityMatrixKernel.digital",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
              "payload_id": "payload.0.block.0000.prepare.digital",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.0,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "ExactDensityMatrixKernel.digital"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 0,
            "output_logical_time": 0.0,
            "output_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
            "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "dfca8e955ca173fed5f1dce4f8b20a513e634a38ff28f78dddce9fcdaa7803dd",
            "time_unit": "us",
            "transition_id": "transition.0.block.0000.prepare"
          },
          {
            "block_id": "block.0001.evolve",
            "input_logical_time": 0.0,
            "input_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
            "kernel": "ExactDensityMatrixKernel.analog",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
              "payload_id": "payload.1.block.0001.evolve.analog",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 32,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "fixed_step_krylov",
                "max_step_size": 0.01875,
                "metadata": {
                  "hermiticity_error_before_stabilization": 4.2841699744536696e-16,
                  "minimum_eigenvalue_before_stabilization": 0.016080082047543128,
                  "output_dtype": "complex128",
                  "positivity_evidence_available": true,
                  "solver": "strang_krylov_lindblad",
                  "stabilization_applied": true,
                  "trace_before_stabilization": {
                    "imag": -2.870804933781793e-18,
                    "real": 0.9999999999999972
                  }
                },
                "min_step_size": 0.01875,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 32,
                "termination_reason": "completed",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 1,
            "output_logical_time": 0.6,
            "output_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
            "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
            "program_kind": "analog",
            "schema_version": "0.1",
            "solver_evidence_hash": "b87033a62649f443f68ae025e7d6d4ca57efd42e54be9728595a3bf363bf4e3f",
            "time_unit": "us",
            "transition_id": "transition.1.block.0001.evolve"
          },
          {
            "block_id": "block.0002.readout_rotation",
            "input_logical_time": 0.6,
            "input_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
            "kernel": "ExactDensityMatrixKernel.digital",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
              "payload_id": "payload.2.block.0002.readout_rotation.digital",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.6,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "ExactDensityMatrixKernel.digital"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 2,
            "output_logical_time": 0.6,
            "output_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "8c6537a374163b7170874874c97426a424799f42a8be28e169dce0bf916296f1",
            "time_unit": "us",
            "transition_id": "transition.2.block.0002.readout_rotation"
          }
        ],
        "control_report_evidence": [
          {
            "block_id": "block.0001.evolve",
            "diagnostic_count": 4,
            "diagnostics": [
              {
                "code": "CONTROL_CONCURRENCY_SUPPORTED",
                "diagnostic_id": "control.control_concurrency_supported.rydberg.local",
                "message": "Control concurrency is within the declared group limit.",
                "metadata": {
                  "actual_max_concurrency": 1,
                  "group_id": "rydberg.local",
                  "max_concurrent_operations": 2,
                  "operation_ids": [
                    "operation.local_detuning.0"
                  ]
                },
                "object_path": "control_schedule.operations",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              },
              {
                "code": "CONTROL_BANDWIDTH_SUPPORTED",
                "diagnostic_id": "control.control_bandwidth_supported.operation.local_detuning.0",
                "message": "Waveform knot-spacing bandwidth bound is within the Target limit.",
                "metadata": {
                  "bandwidth_limit": 2.0,
                  "bandwidth_unit": "MHz",
                  "channel_id": "rydberg.detuning.local",
                  "estimate_semantics": "nyquist_bound_from_minimum_knot_spacing",
                  "estimated_bandwidth": 0.0,
                  "operation_id": "operation.local_detuning.0"
                },
                "object_path": "hamiltonian.terms.local_detuning_terms[0].waveform",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              },
              {
                "code": "CONTROL_SLEW_SUPPORTED",
                "diagnostic_id": "control.control_slew_supported.operation.local_detuning.0",
                "message": "Waveform segment slew is within the Target limit.",
                "metadata": {
                  "actual_max_slew_rate": 0.0,
                  "channel_id": "rydberg.detuning.local",
                  "estimate_semantics": "maximum_actual_waveform_segment_derivative",
                  "max_slew_rate": 30.0,
                  "operation_id": "operation.local_detuning.0",
                  "slew_rate_unit": "rad/us^2"
                },
                "object_path": "hamiltonian.terms.local_detuning_terms[0].waveform",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              },
              {
                "code": "CONTROL_CROSSTALK_NO_OVERLAP",
                "diagnostic_id": "control.control_crosstalk_no_overlap.crosstalk.rydberg.rabi.local.rydberg.rabi.global",
                "message": "Crosstalk-constrained channels do not overlap.",
                "metadata": {
                  "actual_overlap_duration": 0.0,
                  "channel_ids": [
                    "rydberg.rabi.local",
                    "rydberg.rabi.global"
                  ],
                  "constraint_id": "crosstalk.rydberg.rabi.local.rydberg.rabi.global",
                  "max_overlap_duration": null,
                  "overlap_policy": "calibration_required",
                  "time_unit": "us"
                },
                "object_path": "control_schedule.operations",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              }
            ],
            "has_errors": false,
            "production_channel_allocation_performed": false,
            "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
            "schedule": {
              "control_system_hash": "fbbc3937e5187ca6bb0a3f00e176187027581e3382a83ee377e7115bffd5a87a",
              "diagnostics": [],
              "metadata": {
                "production_channel_allocation_performed": false,
                "projection": "program_ir_control_terms",
                "time_origin": 0.0,
                "time_unit": "us"
              },
              "operations": [
                {
                  "channel_id": "rydberg.detuning.global",
                  "end_time": 0.6,
                  "metadata": {
                    "production_assigned": false,
                    "program_path": "hamiltonian.terms.detuning",
                    "time_unit": "us",
                    "value_unit": "rad/us",
                    "waveform_kind": "constant"
                  },
                  "operation_id": "operation.global_detuning",
                  "operation_kind": "global_detuning",
                  "schema_version": "0.1",
                  "source_hash": "19b3cbf48a848eccf4b459d549c9603d70c02b450b81211bb93c55010a4339ab",
                  "start_time": 0.0,
                  "target_site_ids": [
                    "q0",
                    "q1"
                  ],
                  "waveform_hash": "19b3cbf48a848eccf4b459d549c9603d70c02b450b81211bb93c55010a4339ab"
                },
                {
                  "channel_id": "rydberg.rabi.global",
                  "end_time": 0.6,
                  "metadata": {
                    "production_assigned": false,
                    "program_path": "hamiltonian.terms.rabi",
                    "time_unit": "us",
                    "value_unit": "rad/us",
                    "waveform_kind": "constant"
                  },
                  "operation_id": "operation.global_rabi",
                  "operation_kind": "global_rabi",
                  "schema_version": "0.1",
                  "source_hash": "ad464599d866805baa0f7753cf0d4ce853b1688908e85f1baa172d7740efa2da",
                  "start_time": 0.0,
                  "target_site_ids": [
                    "q0",
                    "q1"
                  ],
                  "waveform_hash": "ad464599d866805baa0f7753cf0d4ce853b1688908e85f1baa172d7740efa2da"
                },
                {
                  "channel_id": "rydberg.detuning.local",
                  "end_time": 0.6,
                  "metadata": {
                    "production_assigned": false,
                    "program_path": "hamiltonian.terms.local_detuning_terms[0].waveform",
                    "time_unit": "us",
                    "value_unit": "rad/us",
                    "waveform_kind": "constant"
                  },
                  "operation_id": "operation.local_detuning.0",
                  "operation_kind": "local_detuning",
                  "schema_version": "0.1",
                  "source_hash": "5cf7b4b36d89a2948d9ee6b9b1974f74b74438df6df8aeaaafad175c714c34ed",
                  "start_time": 0.0,
                  "target_site_ids": [
                    "q0",
                    "q1"
                  ],
                  "waveform_hash": "e1caa1faf062ab87977975eab5ad7eb6366c3974acdadba829e14493602d0665"
                }
              ],
              "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
              "schedule_id": "schedule.program.control",
              "schema_version": "0.1"
            },
            "target_id": "mock.neutral_atom.local_ahs.v0_1"
          }
        ],
        "execution_package_created": false,
        "network_accessed": false,
        "noise_model_hash": "448a2c0332c24677c533b6381aa06e6ab1f1057ebbee842aae4160508d83713c",
        "noise_report": {
          "applied_channel_types": [
            "dephasing",
            "readout"
          ],
          "measurement_application_count": 1,
          "method": "density_matrix",
          "noise_model_hash": "448a2c0332c24677c533b6381aa06e6ab1f1057ebbee842aae4160508d83713c",
          "noise_model_id": "phase.readout",
          "physical_application_count": 1,
          "records": [
            {
              "channel_id": "noise.dephasing",
              "channel_type": "dephasing",
              "injection_point": "analog_evolution",
              "input_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
              "metadata": {
                "model": "lindblad_phase_flip",
                "parameters": {
                  "rate": 0.8
                },
                "schedule_ref": null
              },
              "output_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
              "targets": [
                "q0",
                "q1"
              ],
              "truthfulness": "physical_state_evolution"
            },
            {
              "channel_id": "noise.readout",
              "channel_type": "readout",
              "injection_point": "terminal_measurement",
              "input_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
              "metadata": {
                "counts_modified": true,
                "model": "asymmetric_confusion",
                "parameters": {
                  "p01": 0.08,
                  "p10": 0.12
                }
              },
              "output_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
              "targets": [
                "q0",
                "q1"
              ],
              "truthfulness": "measurement_model_only"
            }
          ],
          "truthfulness": "physical_state_evolution"
        },
        "noise_report_hash": "7ca997c6cfefc571460c84e5d226798ca0fafece5d9502f5e3b39913ddb9d993",
        "offline_deterministic": true,
        "references": {
          "bundle_hash": "bdc9f85447b0a582c5a90d39865e409738f6d81124016bf3a3295c6d0a94f9b4",
          "calibration_snapshot_hash": null,
          "compiled_program_hash": null,
          "discretized_program_hash": null,
          "execution_package_id": null,
          "final_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
          "initial_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
          "metadata": {
            "graph_hash": "7f1df6f7e79a08131273f5367d8b40cf1a5fab604b12a94df8efb2411a53452c"
          },
          "plan_hash": "4388febf8e9092f0d5a1bdee8ba9658cd610618a595779025d6019da97dad681",
          "program_hash": "3ae12596e75deff789e526006cd6fad95bd8363cc46c441de4e19eaecd54aa05",
          "schema_version": "0.1",
          "target_snapshot_hash": null
        },
        "register_snapshots": [
          {
            "active_atom_ids": [
              "q0",
              "q1"
            ],
            "active_site_count": 2,
            "active_site_ids": [
              "q0",
              "q1"
            ],
            "lifecycle_stage": "planned",
            "physical_site_count": 2,
            "physical_site_ids": [
              "q0",
              "q1"
            ],
            "previous_snapshot_hash": null,
            "snapshot_hash": "571e481d25fc0fb0e4962bcb62d4b574c81cc965cb8e3b4fc69565faa8be68ec",
            "snapshot_id": "register.planned",
            "status_counts": {
              "defect": 0,
              "filled": 2,
              "loading_failed": 0,
              "vacant": 0
            }
          }
        ],
        "run_trace": {
          "events": [
            {
              "event_time": "logical:0x0.0p+0",
              "message": "Completed digital state transition.",
              "metadata": {
                "state_transition": {
                  "block_id": "block.0000.prepare",
                  "input_logical_time": 0.0,
                  "input_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
                  "kernel": "ExactDensityMatrixKernel.digital",
                  "metadata": {
                    "logical_order": [
                      "q0",
                      "q1"
                    ],
                    "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
                    "payload_id": "payload.0.block.0000.prepare.digital",
                    "solver_evidence": {
                      "absolute_tolerance": null,
                      "accepted_steps": 0,
                      "final_time": 0.0,
                      "function_evaluations": null,
                      "initial_time": 0.0,
                      "integrator_requested": "fixed_step_krylov",
                      "integrator_selected": "not_applicable",
                      "max_step_size": null,
                      "metadata": {
                        "consumer": "ExactDensityMatrixKernel.digital"
                      },
                      "min_step_size": null,
                      "rejected_steps": null,
                      "rejected_steps_available": false,
                      "relative_tolerance": null,
                      "schema_version": "0.1",
                      "segment_count": 0,
                      "termination_reason": "not_applicable",
                      "time_unit": "us",
                      "tolerance_applied": false
                    }
                  },
                  "order_index": 0,
                  "output_logical_time": 0.0,
                  "output_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
                  "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
                  "program_kind": "digital",
                  "schema_version": "0.1",
                  "solver_evidence_hash": "dfca8e955ca173fed5f1dce4f8b20a513e634a38ff28f78dddce9fcdaa7803dd",
                  "time_unit": "us",
                  "transition_id": "transition.0.block.0000.prepare"
                }
              },
              "schema_version": "0.1",
              "stage": "running",
              "status": "ok"
            },
            {
              "event_time": "logical:0x1.3333333333333p-1",
              "message": "Completed analog state transition.",
              "metadata": {
                "state_transition": {
                  "block_id": "block.0001.evolve",
                  "input_logical_time": 0.0,
                  "input_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
                  "kernel": "ExactDensityMatrixKernel.analog",
                  "metadata": {
                    "logical_order": [
                      "q0",
                      "q1"
                    ],
                    "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
                    "payload_id": "payload.1.block.0001.evolve.analog",
                    "solver_evidence": {
                      "absolute_tolerance": null,
                      "accepted_steps": 32,
                      "final_time": 0.6,
                      "function_evaluations": null,
                      "initial_time": 0.0,
                      "integrator_requested": "fixed_step_krylov",
                      "integrator_selected": "fixed_step_krylov",
                      "max_step_size": 0.01875,
                      "metadata": {
                        "hermiticity_error_before_stabilization": 4.2841699744536696e-16,
                        "minimum_eigenvalue_before_stabilization": 0.016080082047543128,
                        "output_dtype": "complex128",
                        "positivity_evidence_available": true,
                        "solver": "strang_krylov_lindblad",
                        "stabilization_applied": true,
                        "trace_before_stabilization": {
                          "imag": -2.870804933781793e-18,
                          "real": 0.9999999999999972
                        }
                      },
                      "min_step_size": 0.01875,
                      "rejected_steps": null,
                      "rejected_steps_available": false,
                      "relative_tolerance": null,
                      "schema_version": "0.1",
                      "segment_count": 32,
                      "termination_reason": "completed",
                      "time_unit": "us",
                      "tolerance_applied": false
                    }
                  },
                  "order_index": 1,
                  "output_logical_time": 0.6,
                  "output_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
                  "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
                  "program_kind": "analog",
                  "schema_version": "0.1",
                  "solver_evidence_hash": "b87033a62649f443f68ae025e7d6d4ca57efd42e54be9728595a3bf363bf4e3f",
                  "time_unit": "us",
                  "transition_id": "transition.1.block.0001.evolve"
                }
              },
              "schema_version": "0.1",
              "stage": "running",
              "status": "ok"
            },
            {
              "event_time": "logical:0x1.3333333333333p-1",
              "message": "Completed digital state transition.",
              "metadata": {
                "state_transition": {
                  "block_id": "block.0002.readout_rotation",
                  "input_logical_time": 0.6,
                  "input_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
                  "kernel": "ExactDensityMatrixKernel.digital",
                  "metadata": {
                    "logical_order": [
                      "q0",
                      "q1"
                    ],
                    "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
                    "payload_id": "payload.2.block.0002.readout_rotation.digital",
                    "solver_evidence": {
                      "absolute_tolerance": null,
                      "accepted_steps": 0,
                      "final_time": 0.6,
                      "function_evaluations": null,
                      "initial_time": 0.6,
                      "integrator_requested": "fixed_step_krylov",
                      "integrator_selected": "not_applicable",
                      "max_step_size": null,
                      "metadata": {
                        "consumer": "ExactDensityMatrixKernel.digital"
                      },
                      "min_step_size": null,
                      "rejected_steps": null,
                      "rejected_steps_available": false,
                      "relative_tolerance": null,
                      "schema_version": "0.1",
                      "segment_count": 0,
                      "termination_reason": "not_applicable",
                      "time_unit": "us",
                      "tolerance_applied": false
                    }
                  },
                  "order_index": 2,
                  "output_logical_time": 0.6,
                  "output_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
                  "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
                  "program_kind": "digital",
                  "schema_version": "0.1",
                  "solver_evidence_hash": "8c6537a374163b7170874874c97426a424799f42a8be28e169dce0bf916296f1",
                  "time_unit": "us",
                  "transition_id": "transition.2.block.0002.readout_rotation"
                }
              },
              "schema_version": "0.1",
              "stage": "running",
              "status": "ok"
            },
            {
              "event_time": "logical:0x1.3333333333333p-1",
              "message": "Terminal noisy sampling completed.",
              "metadata": {
                "final_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
                "measurement_key": "result",
                "seed": 4882,
                "shots": 128
              },
              "schema_version": "0.1",
              "stage": "completed",
              "status": "ok"
            }
          ],
          "metadata": {
            "execution_mode": "local_hybrid_density_matrix"
          },
          "references": {
            "bundle_hash": "bdc9f85447b0a582c5a90d39865e409738f6d81124016bf3a3295c6d0a94f9b4",
            "calibration_snapshot_hash": null,
            "compiled_program_hash": null,
            "discretized_program_hash": null,
            "execution_package_id": null,
            "final_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "initial_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
            "metadata": {
              "graph_hash": "7f1df6f7e79a08131273f5367d8b40cf1a5fab604b12a94df8efb2411a53452c"
            },
            "plan_hash": "4388febf8e9092f0d5a1bdee8ba9658cd610618a595779025d6019da97dad681",
            "program_hash": "3ae12596e75deff789e526006cd6fad95bd8363cc46c441de4e19eaecd54aa05",
            "schema_version": "0.1",
            "target_snapshot_hash": null
          },
          "schema_version": "0.1",
          "trace_id": "trace.local_bundle.local_plan.project.noisy.hybrid.physical_noise"
        },
        "selected_simulator": "ExactDensityNoiseEngine",
        "simulation_execution_config": {
          "absolute_tolerance": 1e-11,
          "device": "cpu",
          "dtype": "complex128",
          "execution_scope": "job",
          "integrator_requested": "fixed_step_krylov",
          "integrator_selected": "fixed_step_krylov",
          "method": "density_matrix",
          "relative_tolerance": 1e-09,
          "schema_version": "0.1",
          "seed": 4882,
          "seed_semantics": "effective_seed",
          "solver_evidence_hash": "ef94260e54386e61fba4be5fe71dd918dd8b4fe0e55d432adf91e8b7ac110708",
          "step_semantics": "fixed_time_slices",
          "steps": 32,
          "tolerance_applied": false,
          "trajectories": null,
          "worker_semantics": "kernel_concurrency",
          "workers": 1
        },
        "simulation_plan": {
          "atol": 1e-11,
          "budget_bytes": 20615843020,
          "candidates": [
            {
              "estimate": {
                "dtype": "complex128",
                "estimated_peak_bytes": 9792,
                "hilbert_dimension": 4,
                "itemsize_bytes": 16,
                "logical_sites": 2,
                "method": "state_vector",
                "operator_bytes": 128,
                "result_buffer_bytes": 4096,
                "sampling_bytes": 4096,
                "schema_version": "cascaqit.simulation.planning.v1",
                "state_bytes": 64,
                "state_dimension": 4,
                "trajectories": 1,
                "worker_copy_bytes": 0,
                "workers": 1,
                "workspace_bytes": 1408
              },
              "method": "state_vector",
              "reason_codes": [
                "SIMULATION_METHOD_REQUIRES_IDEAL_MODEL"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "rejected"
            },
            {
              "estimate": null,
              "method": "subspace",
              "reason_codes": [
                "SIMULATION_METHOD_REQUIRES_IDEAL_MODEL"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "rejected"
            },
            {
              "estimate": {
                "dtype": "complex128",
                "estimated_peak_bytes": 9728,
                "hilbert_dimension": 4,
                "itemsize_bytes": 16,
                "logical_sites": 2,
                "method": "density_matrix",
                "operator_bytes": 512,
                "result_buffer_bytes": 4096,
                "sampling_bytes": 4096,
                "schema_version": "cascaqit.simulation.planning.v1",
                "state_bytes": 256,
                "state_dimension": 16,
                "trajectories": 1,
                "worker_copy_bytes": 0,
                "workers": 1,
                "workspace_bytes": 768
              },
              "method": "density_matrix",
              "reason_codes": [
                "SIMULATION_METHOD_ELIGIBLE",
                "SIMULATION_METHOD_SELECTED"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "selected"
            },
            {
              "estimate": {
                "dtype": "complex128",
                "estimated_peak_bytes": 368768,
                "hilbert_dimension": 4,
                "itemsize_bytes": 16,
                "logical_sites": 2,
                "method": "trajectory",
                "operator_bytes": 128,
                "result_buffer_bytes": 4096,
                "sampling_bytes": 4096,
                "schema_version": "cascaqit.simulation.planning.v1",
                "state_bytes": 16384,
                "state_dimension": 1024,
                "trajectories": 256,
                "worker_copy_bytes": 229376,
                "workers": 15,
                "workspace_bytes": 114688
              },
              "method": "trajectory",
              "reason_codes": [
                "SIMULATION_METHOD_ELIGIBLE"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "eligible"
            }
          ],
          "device": "cpu",
          "dtype": "complex128",
          "estimate": {
            "dtype": "complex128",
            "estimated_peak_bytes": 9728,
            "hilbert_dimension": 4,
            "itemsize_bytes": 16,
            "logical_sites": 2,
            "method": "density_matrix",
            "operator_bytes": 512,
            "result_buffer_bytes": 4096,
            "sampling_bytes": 4096,
            "schema_version": "cascaqit.simulation.planning.v1",
            "state_bytes": 256,
            "state_dimension": 16,
            "trajectories": 1,
            "worker_copy_bytes": 0,
            "workers": 1,
            "workspace_bytes": 768
          },
          "hilbert_dimension": 4,
          "host_hash": "fc340411ec9c1fe45ae7d312ce900fdaeaa5935813f6c5c169cb18b81d90aea1",
          "integrator_requested": "fixed_step_krylov",
          "integrator_selected": "fixed_step_krylov",
          "logical_sites": 2,
          "max_steps": 32,
          "metadata": {
            "array_backend": "numpy",
            "blockade_dimension": null,
            "host_snapshot_source": "platform.effective_resource_probe",
            "max_wall_time_seconds": null,
            "memory_fraction": 0.8,
            "network_accessed": false,
            "numpy_version": "2.0.2",
            "requires_trajectory": false,
            "scipy_version": "1.17.1",
            "target_statistical_error": null,
            "time_integration_required": true,
            "workers_cpu_limit": 15,
            "workers_requested": "auto"
          },
          "method_requested": "density_matrix",
          "method_selected": "density_matrix",
          "noisy": true,
          "options_hash": "da08e4479dfebca841e152f623e8f6fedcb92e41b4999609317fd27be0fdd0f2",
          "plan_id": "simulation_plan.hybrid.2.density_matrix.fixed_step_krylov",
          "program_kind": "hybrid",
          "rtol": 1e-09,
          "schema_version": "cascaqit.simulation.planning.v1",
          "seed": 4882,
          "state_representation": "density_matrix",
          "trajectories": 256,
          "truthfulness": "planning_only",
          "workers": 1
        },
        "simulation_plan_hash": "63cde3827ecd111f55bd79cd26a4f6be3f2fbac6b2f1bb94497f87cc1aa21e58",
        "simulation_plan_truthfulness": "planning_only",
        "simulation_resource_estimate": {
          "dtype": "complex128",
          "estimated_peak_bytes": 9728,
          "hilbert_dimension": 4,
          "itemsize_bytes": 16,
          "logical_sites": 2,
          "method": "density_matrix",
          "operator_bytes": 512,
          "result_buffer_bytes": 4096,
          "sampling_bytes": 4096,
          "schema_version": "cascaqit.simulation.planning.v1",
          "state_bytes": 256,
          "state_dimension": 16,
          "trajectories": 1,
          "worker_copy_bytes": 0,
          "workers": 1,
          "workspace_bytes": 768
        },
        "simulation_resource_usage": {
          "actual_peak_rss_bytes": 143736832,
          "baseline_peak_rss_bytes": 143736832,
          "estimate_error_fraction": null,
          "estimate_within_tolerance": null,
          "estimated_peak_bytes": 9728,
          "incremental_peak_rss_bytes": 0,
          "measurement_scope": "job",
          "measurement_status": "baseline_dominated",
          "rss_semantics": "process_high_water_mark",
          "schema_version": "0.1",
          "wall_time_seconds": 0.02565762505400926
        },
        "simulation_solver_evidence": {
          "absolute_tolerance": null,
          "accepted_steps": 32,
          "final_time": 0.6,
          "function_evaluations": null,
          "initial_time": 0.0,
          "integrator_requested": "fixed_step_krylov",
          "integrator_selected": "fixed_step_krylov",
          "max_step_size": 0.01875,
          "metadata": {
            "aggregation_scope": "physical_density_hybrid_blocks",
            "component_count": 1,
            "component_evidence_hashes": [
              "b87033a62649f443f68ae025e7d6d4ca57efd42e54be9728595a3bf363bf4e3f"
            ]
          },
          "min_step_size": 0.01875,
          "rejected_steps": null,
          "rejected_steps_available": false,
          "relative_tolerance": null,
          "schema_version": "0.1",
          "segment_count": 32,
          "termination_reason": "completed",
          "time_unit": "us",
          "tolerance_applied": false
        },
        "simulation_solver_evidence_hash": "ef94260e54386e61fba4be5fe71dd918dd8b4fe0e55d432adf91e8b7ac110708",
        "simulation_state": {
          "arrays": {
            "rho": {
              "content_hash": "6e3ff60d8eb326639015a4e1b4fe7d8db257751cc3bf160b0d7c7d54572ddced",
              "dtype": "complex128",
              "nbytes": 256,
              "returned_state_bytes": false,
              "shape": [
                4,
                4
              ]
            }
          },
          "basis": "logical_two_level",
          "logical_order": [
            "q0",
            "q1"
          ],
          "logical_time": 0.6,
          "metrics": {
            "minimum_eigenvalue": 0.016080082047543194,
            "purity": 0.5302271049763567,
            "trace": 1.0
          },
          "noise_context": {},
          "provenance": {
            "conversion": null,
            "metadata": {
              "dephasing_duration": 0.0,
              "dephasing_rate": 0.0,
              "operation_count": 1,
              "program_hash": "c439c000a20062942c65081686f9e97ff09b1930f870b6090c842f0a4b79d040"
            },
            "parent_state_hash": "0f00ee3c858716b93a944d7fcc02114b6b0bdb5ae272180533083453d4776c76",
            "producer": "ExactDensityMatrixKernel.digital",
            "schema_version": "cascaqit.simulation.array_state.v1",
            "step_index": 5
          },
          "returned_state_bytes": false,
          "schema_version": "cascaqit.simulation.array_state.v1",
          "stable_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
          "state_kind": "density_matrix",
          "time_unit": "us"
        },
        "simulation_truthfulness": "physical_state_evolution",
        "state_bytes_returned": false,
        "state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
        "state_transitions": [
          {
            "block_id": "block.0000.prepare",
            "input_logical_time": 0.0,
            "input_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
            "kernel": "ExactDensityMatrixKernel.digital",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
              "payload_id": "payload.0.block.0000.prepare.digital",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.0,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "ExactDensityMatrixKernel.digital"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 0,
            "output_logical_time": 0.0,
            "output_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
            "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "dfca8e955ca173fed5f1dce4f8b20a513e634a38ff28f78dddce9fcdaa7803dd",
            "time_unit": "us",
            "transition_id": "transition.0.block.0000.prepare"
          },
          {
            "block_id": "block.0001.evolve",
            "input_logical_time": 0.0,
            "input_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
            "kernel": "ExactDensityMatrixKernel.analog",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
              "payload_id": "payload.1.block.0001.evolve.analog",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 32,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "fixed_step_krylov",
                "max_step_size": 0.01875,
                "metadata": {
                  "hermiticity_error_before_stabilization": 4.2841699744536696e-16,
                  "minimum_eigenvalue_before_stabilization": 0.016080082047543128,
                  "output_dtype": "complex128",
                  "positivity_evidence_available": true,
                  "solver": "strang_krylov_lindblad",
                  "stabilization_applied": true,
                  "trace_before_stabilization": {
                    "imag": -2.870804933781793e-18,
                    "real": 0.9999999999999972
                  }
                },
                "min_step_size": 0.01875,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 32,
                "termination_reason": "completed",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 1,
            "output_logical_time": 0.6,
            "output_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
            "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
            "program_kind": "analog",
            "schema_version": "0.1",
            "solver_evidence_hash": "b87033a62649f443f68ae025e7d6d4ca57efd42e54be9728595a3bf363bf4e3f",
            "time_unit": "us",
            "transition_id": "transition.1.block.0001.evolve"
          },
          {
            "block_id": "block.0002.readout_rotation",
            "input_logical_time": 0.6,
            "input_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
            "kernel": "ExactDensityMatrixKernel.digital",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
              "payload_id": "payload.2.block.0002.readout_rotation.digital",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.6,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "ExactDensityMatrixKernel.digital"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 2,
            "output_logical_time": 0.6,
            "output_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "8c6537a374163b7170874874c97426a424799f42a8be28e169dce0bf916296f1",
            "time_unit": "us",
            "transition_id": "transition.2.block.0002.readout_rotation"
          }
        ]
      }
    },
    {
      "result_id": "result.local_bundle.local_plan.project.noisy.hybrid.physical_noise",
      "program_hash": "3ae12596e75deff789e526006cd6fad95bd8363cc46c441de4e19eaecd54aa05",
      "target_id": "local.simulator",
      "shots": 128,
      "counts": {
        "00": 65,
        "01": 24,
        "10": 28,
        "11": 11
      },
      "samples": [
        "00",
        "01",
        "00",
        "00",
        "00",
        "00",
        "11",
        "00",
        "11",
        "10",
        "00",
        "10",
        "00",
        "00",
        "00",
        "10",
        "01",
        "00",
        "11",
        "00",
        "00",
        "01",
        "00",
        "00",
        "00",
        "10",
        "00",
        "00",
        "00",
        "00",
        "00",
        "10",
        "11",
        "00",
        "10",
        "10",
        "00",
        "00",
        "00",
        "00",
        "00",
        "01",
        "00",
        "10",
        "01",
        "10",
        "10",
        "10",
        "00",
        "00",
        "01",
        "00",
        "10",
        "01",
        "00",
        "11",
        "01",
        "11",
        "00",
        "01",
        "10",
        "01",
        "00",
        "00",
        "01",
        "10",
        "01",
        "00",
        "11",
        "10",
        "10",
        "00",
        "10",
        "01",
        "11",
        "00",
        "00",
        "00",
        "10",
        "00",
        "00",
        "00",
        "00",
        "10",
        "11",
        "00",
        "10",
        "00",
        "00",
        "01",
        "00",
        "00",
        "00",
        "01",
        "10",
        "00",
        "00",
        "01",
        "11",
        "01",
        "01",
        "00",
        "10",
        "10",
        "10",
        "10",
        "00",
        "00",
        "01",
        "00",
        "01",
        "00",
        "01",
        "10",
        "00",
        "01",
        "10",
        "01",
        "11",
        "01",
        "00",
        "10",
        "00",
        "00",
        "00",
        "00",
        "00",
        "00"
      ],
      "probabilities": {
        "00": 0.4327894017200914,
        "01": 0.23601050347734526,
        "10": 0.2900376720088961,
        "11": 0.041162422793667296
      },
      "observables": {
        "minimum_eigenvalue": 0.016080082047543194,
        "purity": 0.5302271049763567,
        "trace": 1.0
      },
      "observable_batch": {
        "observable_set_hash": "dbdcda5c7aa312b23da7566b6bc7da5ac7b572b561161122735a2aeef6c5bbcc",
        "items": [
          {
            "observable": {
              "name": "Z(q0)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.33759981039487336,
            "variance": 0.8860263680213456,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q1)",
              "terms": [
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": 0.44565414745797494,
            "variance": 0.8013923808535055,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          },
          {
            "observable": {
              "name": "Z(q0)*Z(q1)",
              "terms": [
                {
                  "target": "q0",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                },
                {
                  "target": "q1",
                  "basis": "Z",
                  "schema_version": "cascaqit.observables.v1"
                }
              ],
              "schema_version": "cascaqit.observables.v1"
            },
            "expectation": -0.052096350972482636,
            "variance": 0.9972859702153519,
            "standard_error": 0.0,
            "sample_count": null,
            "source_kind": "density_matrix",
            "source_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "estimator_kind": "exact_density",
            "schema_version": "cascaqit.observables.v1"
          }
        ],
        "schema_version": "cascaqit.observables.v1"
      },
      "bit_ordering": {
        "convention": "logical_order",
        "logical_order": "q0,q1"
      },
      "occupation_encoding": {
        "ground": 0,
        "rydberg": 1
      },
      "diagnostics": [
        {
          "diagnostic_id": "simulation.noise.physical.completed",
          "stage": "simulation",
          "severity": "info",
          "code": "PHYSICAL_NOISE_SIMULATION_COMPLETED",
          "message": "Canonical physical noise simulation completed.",
          "schema_version": "0.1",
          "object_path": "result",
          "suggestion": null,
          "metadata": {
            "channel_count": 2,
            "method": "density_matrix"
          }
        }
      ],
      "schema_version": "0.1",
      "metadata": {
        "backend_called": true,
        "backend_id": "local.simulator",
        "block_state_chain": [
          {
            "block_id": "block.0000.prepare",
            "input_logical_time": 0.0,
            "input_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
            "kernel": "ExactDensityMatrixKernel.digital",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
              "payload_id": "payload.0.block.0000.prepare.digital",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.0,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "ExactDensityMatrixKernel.digital"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 0,
            "output_logical_time": 0.0,
            "output_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
            "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "dfca8e955ca173fed5f1dce4f8b20a513e634a38ff28f78dddce9fcdaa7803dd",
            "time_unit": "us",
            "transition_id": "transition.0.block.0000.prepare"
          },
          {
            "block_id": "block.0001.evolve",
            "input_logical_time": 0.0,
            "input_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
            "kernel": "ExactDensityMatrixKernel.analog",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
              "payload_id": "payload.1.block.0001.evolve.analog",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 32,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "fixed_step_krylov",
                "max_step_size": 0.01875,
                "metadata": {
                  "hermiticity_error_before_stabilization": 4.2841699744536696e-16,
                  "minimum_eigenvalue_before_stabilization": 0.016080082047543128,
                  "output_dtype": "complex128",
                  "positivity_evidence_available": true,
                  "solver": "strang_krylov_lindblad",
                  "stabilization_applied": true,
                  "trace_before_stabilization": {
                    "imag": -2.870804933781793e-18,
                    "real": 0.9999999999999972
                  }
                },
                "min_step_size": 0.01875,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 32,
                "termination_reason": "completed",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 1,
            "output_logical_time": 0.6,
            "output_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
            "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
            "program_kind": "analog",
            "schema_version": "0.1",
            "solver_evidence_hash": "b87033a62649f443f68ae025e7d6d4ca57efd42e54be9728595a3bf363bf4e3f",
            "time_unit": "us",
            "transition_id": "transition.1.block.0001.evolve"
          },
          {
            "block_id": "block.0002.readout_rotation",
            "input_logical_time": 0.6,
            "input_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
            "kernel": "ExactDensityMatrixKernel.digital",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
              "payload_id": "payload.2.block.0002.readout_rotation.digital",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.6,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "ExactDensityMatrixKernel.digital"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 2,
            "output_logical_time": 0.6,
            "output_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "8c6537a374163b7170874874c97426a424799f42a8be28e169dce0bf916296f1",
            "time_unit": "us",
            "transition_id": "transition.2.block.0002.readout_rotation"
          }
        ],
        "control_report_evidence": [
          {
            "block_id": "block.0001.evolve",
            "diagnostic_count": 4,
            "diagnostics": [
              {
                "code": "CONTROL_CONCURRENCY_SUPPORTED",
                "diagnostic_id": "control.control_concurrency_supported.rydberg.local",
                "message": "Control concurrency is within the declared group limit.",
                "metadata": {
                  "actual_max_concurrency": 1,
                  "group_id": "rydberg.local",
                  "max_concurrent_operations": 2,
                  "operation_ids": [
                    "operation.local_detuning.0"
                  ]
                },
                "object_path": "control_schedule.operations",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              },
              {
                "code": "CONTROL_BANDWIDTH_SUPPORTED",
                "diagnostic_id": "control.control_bandwidth_supported.operation.local_detuning.0",
                "message": "Waveform knot-spacing bandwidth bound is within the Target limit.",
                "metadata": {
                  "bandwidth_limit": 2.0,
                  "bandwidth_unit": "MHz",
                  "channel_id": "rydberg.detuning.local",
                  "estimate_semantics": "nyquist_bound_from_minimum_knot_spacing",
                  "estimated_bandwidth": 0.0,
                  "operation_id": "operation.local_detuning.0"
                },
                "object_path": "hamiltonian.terms.local_detuning_terms[0].waveform",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              },
              {
                "code": "CONTROL_SLEW_SUPPORTED",
                "diagnostic_id": "control.control_slew_supported.operation.local_detuning.0",
                "message": "Waveform segment slew is within the Target limit.",
                "metadata": {
                  "actual_max_slew_rate": 0.0,
                  "channel_id": "rydberg.detuning.local",
                  "estimate_semantics": "maximum_actual_waveform_segment_derivative",
                  "max_slew_rate": 30.0,
                  "operation_id": "operation.local_detuning.0",
                  "slew_rate_unit": "rad/us^2"
                },
                "object_path": "hamiltonian.terms.local_detuning_terms[0].waveform",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              },
              {
                "code": "CONTROL_CROSSTALK_NO_OVERLAP",
                "diagnostic_id": "control.control_crosstalk_no_overlap.crosstalk.rydberg.rabi.local.rydberg.rabi.global",
                "message": "Crosstalk-constrained channels do not overlap.",
                "metadata": {
                  "actual_overlap_duration": 0.0,
                  "channel_ids": [
                    "rydberg.rabi.local",
                    "rydberg.rabi.global"
                  ],
                  "constraint_id": "crosstalk.rydberg.rabi.local.rydberg.rabi.global",
                  "max_overlap_duration": null,
                  "overlap_policy": "calibration_required",
                  "time_unit": "us"
                },
                "object_path": "control_schedule.operations",
                "schema_version": "0.1",
                "severity": "info",
                "stage": "validation",
                "suggestion": null
              }
            ],
            "has_errors": false,
            "production_channel_allocation_performed": false,
            "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
            "schedule": {
              "control_system_hash": "fbbc3937e5187ca6bb0a3f00e176187027581e3382a83ee377e7115bffd5a87a",
              "diagnostics": [],
              "metadata": {
                "production_channel_allocation_performed": false,
                "projection": "program_ir_control_terms",
                "time_origin": 0.0,
                "time_unit": "us"
              },
              "operations": [
                {
                  "channel_id": "rydberg.detuning.global",
                  "end_time": 0.6,
                  "metadata": {
                    "production_assigned": false,
                    "program_path": "hamiltonian.terms.detuning",
                    "time_unit": "us",
                    "value_unit": "rad/us",
                    "waveform_kind": "constant"
                  },
                  "operation_id": "operation.global_detuning",
                  "operation_kind": "global_detuning",
                  "schema_version": "0.1",
                  "source_hash": "19b3cbf48a848eccf4b459d549c9603d70c02b450b81211bb93c55010a4339ab",
                  "start_time": 0.0,
                  "target_site_ids": [
                    "q0",
                    "q1"
                  ],
                  "waveform_hash": "19b3cbf48a848eccf4b459d549c9603d70c02b450b81211bb93c55010a4339ab"
                },
                {
                  "channel_id": "rydberg.rabi.global",
                  "end_time": 0.6,
                  "metadata": {
                    "production_assigned": false,
                    "program_path": "hamiltonian.terms.rabi",
                    "time_unit": "us",
                    "value_unit": "rad/us",
                    "waveform_kind": "constant"
                  },
                  "operation_id": "operation.global_rabi",
                  "operation_kind": "global_rabi",
                  "schema_version": "0.1",
                  "source_hash": "ad464599d866805baa0f7753cf0d4ce853b1688908e85f1baa172d7740efa2da",
                  "start_time": 0.0,
                  "target_site_ids": [
                    "q0",
                    "q1"
                  ],
                  "waveform_hash": "ad464599d866805baa0f7753cf0d4ce853b1688908e85f1baa172d7740efa2da"
                },
                {
                  "channel_id": "rydberg.detuning.local",
                  "end_time": 0.6,
                  "metadata": {
                    "production_assigned": false,
                    "program_path": "hamiltonian.terms.local_detuning_terms[0].waveform",
                    "time_unit": "us",
                    "value_unit": "rad/us",
                    "waveform_kind": "constant"
                  },
                  "operation_id": "operation.local_detuning.0",
                  "operation_kind": "local_detuning",
                  "schema_version": "0.1",
                  "source_hash": "5cf7b4b36d89a2948d9ee6b9b1974f74b74438df6df8aeaaafad175c714c34ed",
                  "start_time": 0.0,
                  "target_site_ids": [
                    "q0",
                    "q1"
                  ],
                  "waveform_hash": "e1caa1faf062ab87977975eab5ad7eb6366c3974acdadba829e14493602d0665"
                }
              ],
              "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
              "schedule_id": "schedule.program.control",
              "schema_version": "0.1"
            },
            "target_id": "mock.neutral_atom.local_ahs.v0_1"
          }
        ],
        "execution_package_created": false,
        "network_accessed": false,
        "noise_model_hash": "448a2c0332c24677c533b6381aa06e6ab1f1057ebbee842aae4160508d83713c",
        "noise_report": {
          "applied_channel_types": [
            "dephasing",
            "readout"
          ],
          "measurement_application_count": 1,
          "method": "density_matrix",
          "noise_model_hash": "448a2c0332c24677c533b6381aa06e6ab1f1057ebbee842aae4160508d83713c",
          "noise_model_id": "phase.readout",
          "physical_application_count": 1,
          "records": [
            {
              "channel_id": "noise.dephasing",
              "channel_type": "dephasing",
              "injection_point": "analog_evolution",
              "input_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
              "metadata": {
                "model": "lindblad_phase_flip",
                "parameters": {
                  "rate": 0.8
                },
                "schedule_ref": null
              },
              "output_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
              "targets": [
                "q0",
                "q1"
              ],
              "truthfulness": "physical_state_evolution"
            },
            {
              "channel_id": "noise.readout",
              "channel_type": "readout",
              "injection_point": "terminal_measurement",
              "input_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
              "metadata": {
                "counts_modified": true,
                "model": "asymmetric_confusion",
                "parameters": {
                  "p01": 0.08,
                  "p10": 0.12
                }
              },
              "output_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
              "targets": [
                "q0",
                "q1"
              ],
              "truthfulness": "measurement_model_only"
            }
          ],
          "truthfulness": "physical_state_evolution"
        },
        "noise_report_hash": "7ca997c6cfefc571460c84e5d226798ca0fafece5d9502f5e3b39913ddb9d993",
        "offline_deterministic": true,
        "references": {
          "bundle_hash": "42234f4fd9d09c4d8102e6dc8d5f703c5ec76e567a4a89e630381577a0768e05",
          "calibration_snapshot_hash": null,
          "compiled_program_hash": null,
          "discretized_program_hash": null,
          "execution_package_id": null,
          "final_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
          "initial_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
          "metadata": {
            "graph_hash": "7f1df6f7e79a08131273f5367d8b40cf1a5fab604b12a94df8efb2411a53452c"
          },
          "plan_hash": "4388febf8e9092f0d5a1bdee8ba9658cd610618a595779025d6019da97dad681",
          "program_hash": "3ae12596e75deff789e526006cd6fad95bd8363cc46c441de4e19eaecd54aa05",
          "schema_version": "0.1",
          "target_snapshot_hash": null
        },
        "register_snapshots": [
          {
            "active_atom_ids": [
              "q0",
              "q1"
            ],
            "active_site_count": 2,
            "active_site_ids": [
              "q0",
              "q1"
            ],
            "lifecycle_stage": "planned",
            "physical_site_count": 2,
            "physical_site_ids": [
              "q0",
              "q1"
            ],
            "previous_snapshot_hash": null,
            "snapshot_hash": "571e481d25fc0fb0e4962bcb62d4b574c81cc965cb8e3b4fc69565faa8be68ec",
            "snapshot_id": "register.planned",
            "status_counts": {
              "defect": 0,
              "filled": 2,
              "loading_failed": 0,
              "vacant": 0
            }
          }
        ],
        "run_trace": {
          "events": [
            {
              "event_time": "logical:0x0.0p+0",
              "message": "Completed digital state transition.",
              "metadata": {
                "state_transition": {
                  "block_id": "block.0000.prepare",
                  "input_logical_time": 0.0,
                  "input_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
                  "kernel": "ExactDensityMatrixKernel.digital",
                  "metadata": {
                    "logical_order": [
                      "q0",
                      "q1"
                    ],
                    "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
                    "payload_id": "payload.0.block.0000.prepare.digital",
                    "solver_evidence": {
                      "absolute_tolerance": null,
                      "accepted_steps": 0,
                      "final_time": 0.0,
                      "function_evaluations": null,
                      "initial_time": 0.0,
                      "integrator_requested": "fixed_step_krylov",
                      "integrator_selected": "not_applicable",
                      "max_step_size": null,
                      "metadata": {
                        "consumer": "ExactDensityMatrixKernel.digital"
                      },
                      "min_step_size": null,
                      "rejected_steps": null,
                      "rejected_steps_available": false,
                      "relative_tolerance": null,
                      "schema_version": "0.1",
                      "segment_count": 0,
                      "termination_reason": "not_applicable",
                      "time_unit": "us",
                      "tolerance_applied": false
                    }
                  },
                  "order_index": 0,
                  "output_logical_time": 0.0,
                  "output_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
                  "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
                  "program_kind": "digital",
                  "schema_version": "0.1",
                  "solver_evidence_hash": "dfca8e955ca173fed5f1dce4f8b20a513e634a38ff28f78dddce9fcdaa7803dd",
                  "time_unit": "us",
                  "transition_id": "transition.0.block.0000.prepare"
                }
              },
              "schema_version": "0.1",
              "stage": "running",
              "status": "ok"
            },
            {
              "event_time": "logical:0x1.3333333333333p-1",
              "message": "Completed analog state transition.",
              "metadata": {
                "state_transition": {
                  "block_id": "block.0001.evolve",
                  "input_logical_time": 0.0,
                  "input_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
                  "kernel": "ExactDensityMatrixKernel.analog",
                  "metadata": {
                    "logical_order": [
                      "q0",
                      "q1"
                    ],
                    "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
                    "payload_id": "payload.1.block.0001.evolve.analog",
                    "solver_evidence": {
                      "absolute_tolerance": null,
                      "accepted_steps": 32,
                      "final_time": 0.6,
                      "function_evaluations": null,
                      "initial_time": 0.0,
                      "integrator_requested": "fixed_step_krylov",
                      "integrator_selected": "fixed_step_krylov",
                      "max_step_size": 0.01875,
                      "metadata": {
                        "hermiticity_error_before_stabilization": 4.2841699744536696e-16,
                        "minimum_eigenvalue_before_stabilization": 0.016080082047543128,
                        "output_dtype": "complex128",
                        "positivity_evidence_available": true,
                        "solver": "strang_krylov_lindblad",
                        "stabilization_applied": true,
                        "trace_before_stabilization": {
                          "imag": -2.870804933781793e-18,
                          "real": 0.9999999999999972
                        }
                      },
                      "min_step_size": 0.01875,
                      "rejected_steps": null,
                      "rejected_steps_available": false,
                      "relative_tolerance": null,
                      "schema_version": "0.1",
                      "segment_count": 32,
                      "termination_reason": "completed",
                      "time_unit": "us",
                      "tolerance_applied": false
                    }
                  },
                  "order_index": 1,
                  "output_logical_time": 0.6,
                  "output_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
                  "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
                  "program_kind": "analog",
                  "schema_version": "0.1",
                  "solver_evidence_hash": "b87033a62649f443f68ae025e7d6d4ca57efd42e54be9728595a3bf363bf4e3f",
                  "time_unit": "us",
                  "transition_id": "transition.1.block.0001.evolve"
                }
              },
              "schema_version": "0.1",
              "stage": "running",
              "status": "ok"
            },
            {
              "event_time": "logical:0x1.3333333333333p-1",
              "message": "Completed digital state transition.",
              "metadata": {
                "state_transition": {
                  "block_id": "block.0002.readout_rotation",
                  "input_logical_time": 0.6,
                  "input_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
                  "kernel": "ExactDensityMatrixKernel.digital",
                  "metadata": {
                    "logical_order": [
                      "q0",
                      "q1"
                    ],
                    "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
                    "payload_id": "payload.2.block.0002.readout_rotation.digital",
                    "solver_evidence": {
                      "absolute_tolerance": null,
                      "accepted_steps": 0,
                      "final_time": 0.6,
                      "function_evaluations": null,
                      "initial_time": 0.6,
                      "integrator_requested": "fixed_step_krylov",
                      "integrator_selected": "not_applicable",
                      "max_step_size": null,
                      "metadata": {
                        "consumer": "ExactDensityMatrixKernel.digital"
                      },
                      "min_step_size": null,
                      "rejected_steps": null,
                      "rejected_steps_available": false,
                      "relative_tolerance": null,
                      "schema_version": "0.1",
                      "segment_count": 0,
                      "termination_reason": "not_applicable",
                      "time_unit": "us",
                      "tolerance_applied": false
                    }
                  },
                  "order_index": 2,
                  "output_logical_time": 0.6,
                  "output_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
                  "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
                  "program_kind": "digital",
                  "schema_version": "0.1",
                  "solver_evidence_hash": "8c6537a374163b7170874874c97426a424799f42a8be28e169dce0bf916296f1",
                  "time_unit": "us",
                  "transition_id": "transition.2.block.0002.readout_rotation"
                }
              },
              "schema_version": "0.1",
              "stage": "running",
              "status": "ok"
            },
            {
              "event_time": "logical:0x1.3333333333333p-1",
              "message": "Terminal noisy sampling completed.",
              "metadata": {
                "final_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
                "measurement_key": "result",
                "seed": 4883,
                "shots": 128
              },
              "schema_version": "0.1",
              "stage": "completed",
              "status": "ok"
            }
          ],
          "metadata": {
            "execution_mode": "local_hybrid_density_matrix"
          },
          "references": {
            "bundle_hash": "42234f4fd9d09c4d8102e6dc8d5f703c5ec76e567a4a89e630381577a0768e05",
            "calibration_snapshot_hash": null,
            "compiled_program_hash": null,
            "discretized_program_hash": null,
            "execution_package_id": null,
            "final_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "initial_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
            "metadata": {
              "graph_hash": "7f1df6f7e79a08131273f5367d8b40cf1a5fab604b12a94df8efb2411a53452c"
            },
            "plan_hash": "4388febf8e9092f0d5a1bdee8ba9658cd610618a595779025d6019da97dad681",
            "program_hash": "3ae12596e75deff789e526006cd6fad95bd8363cc46c441de4e19eaecd54aa05",
            "schema_version": "0.1",
            "target_snapshot_hash": null
          },
          "schema_version": "0.1",
          "trace_id": "trace.local_bundle.local_plan.project.noisy.hybrid.physical_noise"
        },
        "selected_simulator": "ExactDensityNoiseEngine",
        "simulation_execution_config": {
          "absolute_tolerance": 1e-11,
          "device": "cpu",
          "dtype": "complex128",
          "execution_scope": "job",
          "integrator_requested": "fixed_step_krylov",
          "integrator_selected": "fixed_step_krylov",
          "method": "density_matrix",
          "relative_tolerance": 1e-09,
          "schema_version": "0.1",
          "seed": 4883,
          "seed_semantics": "effective_seed",
          "solver_evidence_hash": "ef94260e54386e61fba4be5fe71dd918dd8b4fe0e55d432adf91e8b7ac110708",
          "step_semantics": "fixed_time_slices",
          "steps": 32,
          "tolerance_applied": false,
          "trajectories": null,
          "worker_semantics": "kernel_concurrency",
          "workers": 1
        },
        "simulation_plan": {
          "atol": 1e-11,
          "budget_bytes": 20615843020,
          "candidates": [
            {
              "estimate": {
                "dtype": "complex128",
                "estimated_peak_bytes": 9792,
                "hilbert_dimension": 4,
                "itemsize_bytes": 16,
                "logical_sites": 2,
                "method": "state_vector",
                "operator_bytes": 128,
                "result_buffer_bytes": 4096,
                "sampling_bytes": 4096,
                "schema_version": "cascaqit.simulation.planning.v1",
                "state_bytes": 64,
                "state_dimension": 4,
                "trajectories": 1,
                "worker_copy_bytes": 0,
                "workers": 1,
                "workspace_bytes": 1408
              },
              "method": "state_vector",
              "reason_codes": [
                "SIMULATION_METHOD_REQUIRES_IDEAL_MODEL"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "rejected"
            },
            {
              "estimate": null,
              "method": "subspace",
              "reason_codes": [
                "SIMULATION_METHOD_REQUIRES_IDEAL_MODEL"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "rejected"
            },
            {
              "estimate": {
                "dtype": "complex128",
                "estimated_peak_bytes": 9728,
                "hilbert_dimension": 4,
                "itemsize_bytes": 16,
                "logical_sites": 2,
                "method": "density_matrix",
                "operator_bytes": 512,
                "result_buffer_bytes": 4096,
                "sampling_bytes": 4096,
                "schema_version": "cascaqit.simulation.planning.v1",
                "state_bytes": 256,
                "state_dimension": 16,
                "trajectories": 1,
                "worker_copy_bytes": 0,
                "workers": 1,
                "workspace_bytes": 768
              },
              "method": "density_matrix",
              "reason_codes": [
                "SIMULATION_METHOD_ELIGIBLE",
                "SIMULATION_METHOD_SELECTED"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "selected"
            },
            {
              "estimate": {
                "dtype": "complex128",
                "estimated_peak_bytes": 368768,
                "hilbert_dimension": 4,
                "itemsize_bytes": 16,
                "logical_sites": 2,
                "method": "trajectory",
                "operator_bytes": 128,
                "result_buffer_bytes": 4096,
                "sampling_bytes": 4096,
                "schema_version": "cascaqit.simulation.planning.v1",
                "state_bytes": 16384,
                "state_dimension": 1024,
                "trajectories": 256,
                "worker_copy_bytes": 229376,
                "workers": 15,
                "workspace_bytes": 114688
              },
              "method": "trajectory",
              "reason_codes": [
                "SIMULATION_METHOD_ELIGIBLE"
              ],
              "schema_version": "cascaqit.simulation.planning.v1",
              "status": "eligible"
            }
          ],
          "device": "cpu",
          "dtype": "complex128",
          "estimate": {
            "dtype": "complex128",
            "estimated_peak_bytes": 9728,
            "hilbert_dimension": 4,
            "itemsize_bytes": 16,
            "logical_sites": 2,
            "method": "density_matrix",
            "operator_bytes": 512,
            "result_buffer_bytes": 4096,
            "sampling_bytes": 4096,
            "schema_version": "cascaqit.simulation.planning.v1",
            "state_bytes": 256,
            "state_dimension": 16,
            "trajectories": 1,
            "worker_copy_bytes": 0,
            "workers": 1,
            "workspace_bytes": 768
          },
          "hilbert_dimension": 4,
          "host_hash": "fc340411ec9c1fe45ae7d312ce900fdaeaa5935813f6c5c169cb18b81d90aea1",
          "integrator_requested": "fixed_step_krylov",
          "integrator_selected": "fixed_step_krylov",
          "logical_sites": 2,
          "max_steps": 32,
          "metadata": {
            "array_backend": "numpy",
            "blockade_dimension": null,
            "host_snapshot_source": "platform.effective_resource_probe",
            "max_wall_time_seconds": null,
            "memory_fraction": 0.8,
            "network_accessed": false,
            "numpy_version": "2.0.2",
            "requires_trajectory": false,
            "scipy_version": "1.17.1",
            "target_statistical_error": null,
            "time_integration_required": true,
            "workers_cpu_limit": 15,
            "workers_requested": "auto"
          },
          "method_requested": "density_matrix",
          "method_selected": "density_matrix",
          "noisy": true,
          "options_hash": "1af863a3a5012a150859839dd3a1e91c106688749067f8317825bd54a038f8fd",
          "plan_id": "simulation_plan.hybrid.2.density_matrix.fixed_step_krylov",
          "program_kind": "hybrid",
          "rtol": 1e-09,
          "schema_version": "cascaqit.simulation.planning.v1",
          "seed": 4883,
          "state_representation": "density_matrix",
          "trajectories": 256,
          "truthfulness": "planning_only",
          "workers": 1
        },
        "simulation_plan_hash": "c5bbbd578ec9d58e124ec797146081320f88ec73b601082523fbe71813ff1539",
        "simulation_plan_truthfulness": "planning_only",
        "simulation_resource_estimate": {
          "dtype": "complex128",
          "estimated_peak_bytes": 9728,
          "hilbert_dimension": 4,
          "itemsize_bytes": 16,
          "logical_sites": 2,
          "method": "density_matrix",
          "operator_bytes": 512,
          "result_buffer_bytes": 4096,
          "sampling_bytes": 4096,
          "schema_version": "cascaqit.simulation.planning.v1",
          "state_bytes": 256,
          "state_dimension": 16,
          "trajectories": 1,
          "worker_copy_bytes": 0,
          "workers": 1,
          "workspace_bytes": 768
        },
        "simulation_resource_usage": {
          "actual_peak_rss_bytes": 143736832,
          "baseline_peak_rss_bytes": 143736832,
          "estimate_error_fraction": null,
          "estimate_within_tolerance": null,
          "estimated_peak_bytes": 9728,
          "incremental_peak_rss_bytes": 0,
          "measurement_scope": "job",
          "measurement_status": "baseline_dominated",
          "rss_semantics": "process_high_water_mark",
          "schema_version": "0.1",
          "wall_time_seconds": 0.02622237498871982
        },
        "simulation_solver_evidence": {
          "absolute_tolerance": null,
          "accepted_steps": 32,
          "final_time": 0.6,
          "function_evaluations": null,
          "initial_time": 0.0,
          "integrator_requested": "fixed_step_krylov",
          "integrator_selected": "fixed_step_krylov",
          "max_step_size": 0.01875,
          "metadata": {
            "aggregation_scope": "physical_density_hybrid_blocks",
            "component_count": 1,
            "component_evidence_hashes": [
              "b87033a62649f443f68ae025e7d6d4ca57efd42e54be9728595a3bf363bf4e3f"
            ]
          },
          "min_step_size": 0.01875,
          "rejected_steps": null,
          "rejected_steps_available": false,
          "relative_tolerance": null,
          "schema_version": "0.1",
          "segment_count": 32,
          "termination_reason": "completed",
          "time_unit": "us",
          "tolerance_applied": false
        },
        "simulation_solver_evidence_hash": "ef94260e54386e61fba4be5fe71dd918dd8b4fe0e55d432adf91e8b7ac110708",
        "simulation_state": {
          "arrays": {
            "rho": {
              "content_hash": "6e3ff60d8eb326639015a4e1b4fe7d8db257751cc3bf160b0d7c7d54572ddced",
              "dtype": "complex128",
              "nbytes": 256,
              "returned_state_bytes": false,
              "shape": [
                4,
                4
              ]
            }
          },
          "basis": "logical_two_level",
          "logical_order": [
            "q0",
            "q1"
          ],
          "logical_time": 0.6,
          "metrics": {
            "minimum_eigenvalue": 0.016080082047543194,
            "purity": 0.5302271049763567,
            "trace": 1.0
          },
          "noise_context": {},
          "provenance": {
            "conversion": null,
            "metadata": {
              "dephasing_duration": 0.0,
              "dephasing_rate": 0.0,
              "operation_count": 1,
              "program_hash": "c439c000a20062942c65081686f9e97ff09b1930f870b6090c842f0a4b79d040"
            },
            "parent_state_hash": "0f00ee3c858716b93a944d7fcc02114b6b0bdb5ae272180533083453d4776c76",
            "producer": "ExactDensityMatrixKernel.digital",
            "schema_version": "cascaqit.simulation.array_state.v1",
            "step_index": 5
          },
          "returned_state_bytes": false,
          "schema_version": "cascaqit.simulation.array_state.v1",
          "stable_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
          "state_kind": "density_matrix",
          "time_unit": "us"
        },
        "simulation_truthfulness": "physical_state_evolution",
        "state_bytes_returned": false,
        "state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
        "state_transitions": [
          {
            "block_id": "block.0000.prepare",
            "input_logical_time": 0.0,
            "input_state_hash": "33b7df1c2485373508f14bd0bed653c61c663bd78c929e2f66e60c9242bc5523",
            "kernel": "ExactDensityMatrixKernel.digital",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "17220d111c976b358bfe14c3e3a2ee80c22619d19fc1b109e822c46a0b8b5c8c",
              "payload_id": "payload.0.block.0000.prepare.digital",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.0,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "ExactDensityMatrixKernel.digital"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 0,
            "output_logical_time": 0.0,
            "output_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
            "program_hash": "8e56d221d334adfc2654c7f364fd6e806862f66af5701eae7149391673777ba1",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "dfca8e955ca173fed5f1dce4f8b20a513e634a38ff28f78dddce9fcdaa7803dd",
            "time_unit": "us",
            "transition_id": "transition.0.block.0000.prepare"
          },
          {
            "block_id": "block.0001.evolve",
            "input_logical_time": 0.0,
            "input_state_hash": "d3d57cd07ebe32f44121c8d57e7b694f525f43375e0aeb02e35c9ba23cf47104",
            "kernel": "ExactDensityMatrixKernel.analog",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "56311df6c86d526d821ec83b9e5d62d0a0e330e6c1016c650e8fba85fd7b5802",
              "payload_id": "payload.1.block.0001.evolve.analog",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 32,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.0,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "fixed_step_krylov",
                "max_step_size": 0.01875,
                "metadata": {
                  "hermiticity_error_before_stabilization": 4.2841699744536696e-16,
                  "minimum_eigenvalue_before_stabilization": 0.016080082047543128,
                  "output_dtype": "complex128",
                  "positivity_evidence_available": true,
                  "solver": "strang_krylov_lindblad",
                  "stabilization_applied": true,
                  "trace_before_stabilization": {
                    "imag": -2.870804933781793e-18,
                    "real": 0.9999999999999972
                  }
                },
                "min_step_size": 0.01875,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 32,
                "termination_reason": "completed",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 1,
            "output_logical_time": 0.6,
            "output_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
            "program_hash": "39639321a4b874a2f9516c3c91cba77bfefb73fb6c4ca72b5ff15daabe5a592b",
            "program_kind": "analog",
            "schema_version": "0.1",
            "solver_evidence_hash": "b87033a62649f443f68ae025e7d6d4ca57efd42e54be9728595a3bf363bf4e3f",
            "time_unit": "us",
            "transition_id": "transition.1.block.0001.evolve"
          },
          {
            "block_id": "block.0002.readout_rotation",
            "input_logical_time": 0.6,
            "input_state_hash": "80395c0b27fd7d20d562ec7f2e4bd1955ed4a72d7ac8f59a3de40043df2980dc",
            "kernel": "ExactDensityMatrixKernel.digital",
            "metadata": {
              "logical_order": [
                "q0",
                "q1"
              ],
              "payload_hash": "8fd9fc003e1e8efe0261d626398fb39d64eb112c263266070b7bb254c34e48a0",
              "payload_id": "payload.2.block.0002.readout_rotation.digital",
              "solver_evidence": {
                "absolute_tolerance": null,
                "accepted_steps": 0,
                "final_time": 0.6,
                "function_evaluations": null,
                "initial_time": 0.6,
                "integrator_requested": "fixed_step_krylov",
                "integrator_selected": "not_applicable",
                "max_step_size": null,
                "metadata": {
                  "consumer": "ExactDensityMatrixKernel.digital"
                },
                "min_step_size": null,
                "rejected_steps": null,
                "rejected_steps_available": false,
                "relative_tolerance": null,
                "schema_version": "0.1",
                "segment_count": 0,
                "termination_reason": "not_applicable",
                "time_unit": "us",
                "tolerance_applied": false
              }
            },
            "order_index": 2,
            "output_logical_time": 0.6,
            "output_state_hash": "dfed3388b2e593f62c0619e9163228a56c8eeca594a739b18e98f20f1b781242",
            "program_hash": "733f847b71fda52e773e29e700cf6c3ad5d99e44b8cdef2bd1cd031e67c821cf",
            "program_kind": "digital",
            "schema_version": "0.1",
            "solver_evidence_hash": "8c6537a374163b7170874874c97426a424799f42a8be28e169dce0bf916296f1",
            "time_unit": "us",
            "transition_id": "transition.2.block.0002.readout_rotation"
          }
        ]
      }
    }
  ],
  "artifacts": {
    "data": "artifacts/noisy-hybrid/comparison.json",
    "report_en": "artifacts/noisy-hybrid/hybrid-en.html",
    "report_zh": "artifacts/noisy-hybrid/hybrid-zh.html"
  }
}
