{
  "mode": "benchmark-scaling-sweep",
  "reports": [
    {
      "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": 6,
      "repeats": 2,
      "best_time_seconds": 1.1892000202351483e-05,
      "mean_time_seconds": 1.788350004972017e-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": 1.237537672871711e-15,
        "relative_residual_norm": 6.614917107302102e-16,
        "solution_norm": 0.1927685597819864,
        "condition_number_2": 19.1956693580892
      },
      "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": [
          0.6407771211247505,
          -1.3268610014984081,
          -0.7375728169394938,
          2.2347516314106337,
          0.6193793615754618,
          -1.3853069641515074
        ],
        "resources": {
          "estimate_kind": "proxy",
          "degree": 5,
          "coefficient_count": 6,
          "qsp_phase_count": 6,
          "signal_operator_calls": 5,
          "inverse_signal_operator_calls": 5,
          "matrix_dimension": 6,
          "encoding_qubits": 3,
          "total_qubits": 4,
          "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": [
            0.6407771211247505,
            -1.3268610014984081,
            -0.7375728169394938,
            2.2347516314106337,
            0.6193793615754618,
            -1.3853069641515074
          ],
          "polynomial_degree": 5,
          "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": 1.0000000000000004,
          "bounded_margin": -4.440892098500626e-16,
          "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."
      ]
    },
    {
      "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": "qsvt.benchmarks.conjugate_gradient_solve",
      "problem": "positive-definite-linear-system",
      "matrix_dimension": 6,
      "repeats": 2,
      "best_time_seconds": 0.00011610699993980234,
      "mean_time_seconds": 0.00012892599988845177,
      "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": {
        "iterations": 1,
        "converged": true,
        "residual_norm": 3.101181028300686e-15,
        "relative_residual_norm": 1.6576509860377815e-15,
        "tolerance": 1e-10,
        "condition_number_2": 19.195669358089173,
        "matvec_count": 1
      },
      "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": [
          0.6407771211247505,
          -1.3268610014984081,
          -0.7375728169394938,
          2.2347516314106337,
          0.6193793615754618,
          -1.3853069641515074
        ],
        "resources": {
          "estimate_kind": "proxy",
          "degree": 5,
          "coefficient_count": 6,
          "qsp_phase_count": 6,
          "signal_operator_calls": 5,
          "inverse_signal_operator_calls": 5,
          "matrix_dimension": 6,
          "encoding_qubits": 3,
          "total_qubits": 4,
          "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": [
            0.6407771211247505,
            -1.3268610014984081,
            -0.7375728169394938,
            2.2347516314106337,
            0.6193793615754618,
            -1.3853069641515074
          ],
          "polynomial_degree": 5,
          "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": 1.0000000000000004,
          "bounded_margin": -4.440892098500626e-16,
          "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": [
        "CG is a relevant sparse positive-definite baseline; this implementation uses dense NumPy matvecs for reproducibility."
      ]
    },
    {
      "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": 10,
      "repeats": 2,
      "best_time_seconds": 1.3455000043904874e-05,
      "mean_time_seconds": 1.874949998637021e-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": 4.287674996678596e-15,
        "relative_residual_norm": 1.8282707615838322e-15,
        "solution_norm": 0.2392410037779549,
        "condition_number_2": 48.37415007870825
      },
      "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": [
          0.6099658704315425,
          -2.460791933093626,
          -1.930746952558497,
          12.862958259307264,
          7.103138949778324,
          -33.5172158271262,
          -9.881011467051344,
          38.05015498626214,
          4.5942725341137916,
          -15.439486550635765
        ],
        "resources": {
          "estimate_kind": "proxy",
          "degree": 9,
          "coefficient_count": 10,
          "qsp_phase_count": 10,
          "signal_operator_calls": 9,
          "inverse_signal_operator_calls": 9,
          "matrix_dimension": 10,
          "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": [
            0.6099658704315425,
            -2.460791933093626,
            -1.930746952558497,
            12.862958259307264,
            7.103138949778324,
            -33.5172158271262,
            -9.881011467051344,
            38.05015498626214,
            4.5942725341137916,
            -15.439486550635765
          ],
          "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": 1.0000000000000018,
          "bounded_margin": -1.7763568394002505e-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."
      ]
    },
    {
      "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": "qsvt.benchmarks.conjugate_gradient_solve",
      "problem": "positive-definite-linear-system",
      "matrix_dimension": 10,
      "repeats": 2,
      "best_time_seconds": 0.00012582499994095997,
      "mean_time_seconds": 0.00014266100015447591,
      "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": {
        "iterations": 1,
        "converged": true,
        "residual_norm": 1.131964797668267e-14,
        "relative_residual_norm": 4.826714115044162e-15,
        "tolerance": 1e-10,
        "condition_number_2": 48.37415007870815,
        "matvec_count": 1
      },
      "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": [
          0.6099658704315425,
          -2.460791933093626,
          -1.930746952558497,
          12.862958259307264,
          7.103138949778324,
          -33.5172158271262,
          -9.881011467051344,
          38.05015498626214,
          4.5942725341137916,
          -15.439486550635765
        ],
        "resources": {
          "estimate_kind": "proxy",
          "degree": 9,
          "coefficient_count": 10,
          "qsp_phase_count": 10,
          "signal_operator_calls": 9,
          "inverse_signal_operator_calls": 9,
          "matrix_dimension": 10,
          "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": [
            0.6099658704315425,
            -2.460791933093626,
            -1.930746952558497,
            12.862958259307264,
            7.103138949778324,
            -33.5172158271262,
            -9.881011467051344,
            38.05015498626214,
            4.5942725341137916,
            -15.439486550635765
          ],
          "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": 1.0000000000000018,
          "bounded_margin": -1.7763568394002505e-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": [
        "CG is a relevant sparse positive-definite baseline; this implementation uses dense NumPy matvecs for reproducibility."
      ]
    },
    {
      "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": 14,
      "repeats": 2,
      "best_time_seconds": 1.6030000097089214e-05,
      "mean_time_seconds": 2.0863500139967073e-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": 8.268413461230521e-15,
        "relative_residual_norm": 3.019197711663549e-15,
        "solution_norm": 0.27849601869194196,
        "condition_number_2": 90.5231309677748
      },
      "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": [
          0.5492264987764421,
          -2.674156253262369,
          -1.3006615014856018,
          14.693434824804458,
          4.84335317062601,
          -38.97364855152707,
          -6.775113479829505,
          44.64827680848878,
          3.160256859552598,
          -18.21684528086386
        ],
        "resources": {
          "estimate_kind": "proxy",
          "degree": 9,
          "coefficient_count": 10,
          "qsp_phase_count": 10,
          "signal_operator_calls": 9,
          "inverse_signal_operator_calls": 9,
          "matrix_dimension": 14,
          "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": [
            0.5492264987764421,
            -2.674156253262369,
            -1.3006615014856018,
            14.693434824804458,
            4.84335317062601,
            -38.97364855152707,
            -6.775113479829505,
            44.64827680848878,
            3.160256859552598,
            -18.21684528086386
          ],
          "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."
      ]
    },
    {
      "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": "qsvt.benchmarks.conjugate_gradient_solve",
      "problem": "positive-definite-linear-system",
      "matrix_dimension": 14,
      "repeats": 2,
      "best_time_seconds": 0.00013932000001659617,
      "mean_time_seconds": 0.001477076499895702,
      "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": {
        "iterations": 1,
        "converged": true,
        "residual_norm": 1.612849727161784e-14,
        "relative_residual_norm": 5.889294516217078e-15,
        "tolerance": 1e-10,
        "condition_number_2": 90.52313096777365,
        "matvec_count": 1
      },
      "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": [
          0.5492264987764421,
          -2.674156253262369,
          -1.3006615014856018,
          14.693434824804458,
          4.84335317062601,
          -38.97364855152707,
          -6.775113479829505,
          44.64827680848878,
          3.160256859552598,
          -18.21684528086386
        ],
        "resources": {
          "estimate_kind": "proxy",
          "degree": 9,
          "coefficient_count": 10,
          "qsp_phase_count": 10,
          "signal_operator_calls": 9,
          "inverse_signal_operator_calls": 9,
          "matrix_dimension": 14,
          "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": [
            0.5492264987764421,
            -2.674156253262369,
            -1.3006615014856018,
            14.693434824804458,
            4.84335317062601,
            -38.97364855152707,
            -6.775113479829505,
            44.64827680848878,
            3.160256859552598,
            -18.21684528086386
          ],
          "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": [
        "CG is a relevant sparse positive-definite baseline; this implementation uses dense NumPy matvecs for reproducibility."
      ]
    }
  ]
}