{
  "mode": "classical-benchmark",
  "truth_contract": {
    "implementation_kind": "classical-baseline-with-optional-qsvt-proxy",
    "truth_status": "classical_timing_reference",
    "is_quantum_runtime_benchmark": false,
    "implemented_components": [
      "classical_dense_or_iterative_numpy_computation",
      "wall_clock_timing_for_the_classical_path",
      "residual_or_matrix_function_diagnostics",
      "optional_polynomial_resource_proxy"
    ],
    "validation_scope": "The timing fields measure only the classical baseline path in this Python/NumPy environment. Attached QSVT fields are polynomial proxies and are not quantum runtimes."
  },
  "algorithm": "numpy.linalg.solve",
  "problem": "dense-linear-system",
  "matrix_dimension": 12,
  "repeats": 3,
  "best_time_seconds": 1.6690999927959638e-05,
  "mean_time_seconds": 3.258733325613624e-05,
  "benchmark_environment": {
    "timing_kind": "python_wall_clock_microbenchmark",
    "timer": "time.perf_counter",
    "python_version": "3.13.12",
    "numpy_version": "2.4.5",
    "platform_system": "Linux",
    "platform_release": "6.8.0-1052-azure",
    "platform_machine": "x86_64",
    "processor": "x86_64",
    "stability_note": "Timing fields are environment-dependent snapshots. Use metrics and QSVT proxy fields for stable schema checks; regenerate timings deliberately for benchmark studies."
  },
  "metrics": {
    "residual_norm": 7.091807567026073e-15,
    "relative_residual_norm": 2.781635782377763e-15,
    "solution_norm": 0.25958018039669606,
    "condition_number_2": 67.82742906960378
  },
  "qsvt_proxy": {
    "mode": "resource-report",
    "estimate_kind": "proxy",
    "truth_contract": {
      "implementation_kind": "polynomial-resource-proxy",
      "truth_status": "proxy_only",
      "is_end_to_end_quantum_resource_estimate": false,
      "reported_components": [
        "polynomial_degree",
        "coefficient_count",
        "qsp_phase_count_proxy",
        "signal_operator_call_proxy",
        "matrix_register_width_when_dimension_is_supplied",
        "sampled_compatibility_checks"
      ],
      "conditional_qsvt_statement": "The proxy is relevant only after a valid block encoding, state-preparation model, and readout strategy have been specified.",
      "validation_scope": "The report compares polynomial-level quantities and sampled compatibility checks; it does not estimate wall-clock runtime."
    },
    "coeffs": [
      0.5740771268896445,
      -2.5894968944169845,
      -1.5692594163347968,
      13.970171231498076,
      5.815038459350933,
      -36.817911761175324,
      -8.116145515828556,
      42.041133485744254,
      3.7809199020638133,
      -17.119265505508988
    ],
    "resources": {
      "estimate_kind": "proxy",
      "degree": 9,
      "coefficient_count": 10,
      "qsp_phase_count": 10,
      "signal_operator_calls": 9,
      "inverse_signal_operator_calls": 9,
      "matrix_dimension": 12,
      "encoding_qubits": 4,
      "total_qubits": 5,
      "block_encoding": "dense-block-encoding",
      "notes": [
        "Proxy estimate based on polynomial degree; not a hardware resource model.",
        "Signal-call counts assume one forward and one inverse query per QSVT step.",
        "Encoding width includes unused basis states."
      ],
      "omitted_costs": [
        "block_encoding_construction",
        "state_preparation",
        "amplitude_amplification",
        "error_correction",
        "hardware_compilation"
      ],
      "requires_block_encoding": true,
      "requires_state_preparation": true,
      "fault_tolerant_estimate": false
    },
    "compatibility": {
      "mode": "qsvt-compatibility-report",
      "poly": [
        0.5740771268896445,
        -2.5894968944169845,
        -1.5692594163347968,
        13.970171231498076,
        5.815038459350933,
        -36.817911761175324,
        -8.116145515828556,
        42.041133485744254,
        3.7809199020638133,
        -17.119265505508988
      ],
      "polynomial_degree": 9,
      "coefficients_finite": true,
      "parity": "mixed",
      "has_definite_parity": false,
      "bounded_domain": [
        -1.0,
        1.0
      ],
      "bounded_num_points": 4001,
      "bound": 1.0,
      "max_abs_value": 1.0000000000000036,
      "bounded_margin": -3.552713678800501e-15,
      "is_bounded": true,
      "attempted_pennylane_synthesis": false,
      "pennylane_synthesis_succeeded": null,
      "reasons": [
        "mixed_parity"
      ],
      "compatible": false
    },
    "diagnostics": {},
    "requires_block_encoding": true,
    "requires_state_preparation": true,
    "fault_tolerant_estimate": false,
    "omitted_costs": [
      "block_encoding_construction",
      "state_preparation",
      "amplitude_amplification",
      "error_correction",
      "hardware_compilation"
    ],
    "limitations": [
      "No block-encoding construction cost is included.",
      "No state-preparation, amplitude-amplification, error-correction, or hardware compilation cost is included.",
      "Use the report for comparing small polynomial workflows, not for claiming end-to-end quantum runtime."
    ]
  },
  "notes": [
    "Dense direct solves are strong small-system baselines but scale cubically and do not exploit sparsity."
  ]
}