{
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        "probability": 7.458340731199692e-155
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      "public_strategy": "diagonal_phase_certificate",
      "qubits": 512,
      "query": "basis_probability_pattern",
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      "source_url": "https://github.com/pnnl/QASMBench",
      "state_space_basis_states": "2^512",
      "suite": "QASMBench / MQT Bench",
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    {
      "absolute_error": 1.695830344760954e-167,
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        "log10_16gb_ratio": 299.223816,
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        "over_16gb_dense_limit": true
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      "exact": true,
      "expected": {
        "abs": 7.458340731200207e-155,
        "imag": 0.0,
        "real": 7.458340731200207e-155
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      "family": "1D phase mixer",
      "gate_count": 3071,
      "hardware": {
        "machine": "arm64",
        "platform": "macOS-26.4-arm64-arm-64bit",
        "processor": "arm",
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      "materialized_states": 0,
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        "real": 7.458340731198511e-155
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      "public_strategy": "chain_phase_certificate",
      "qubits": 1024,
      "query": "basis_amplitude_zero",
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        "basis_state_sha256": "6e340b9cffb37a989ca544e6bb780a2c78901d3fb33738768511a30617afa01d"
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      "source_url": "https://www.scholars.northwestern.edu/en/publications/supermarq-a-scalable-quantum-benchmark-suite",
      "state_space_basis_states": "2^1024",
      "suite": "SuperMarQ-style application circuit",
      "visited_nodes": 4094
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    {
      "absolute_error": 4.547473508864641e-13,
      "dense_statevector_memory": {
        "complex128_bytes_formula": "2^2052 bytes",
        "log10_16gb_ratio": 607.478531,
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        "over_16gb_dense_limit": true
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      "exact": true,
      "expected": {
        "log2_probability": -2048.0,
        "probability": 0.0
      },
      "family": "Parameterized product rotations",
      "gate_count": 6144,
      "hardware": {
        "machine": "arm64",
        "platform": "macOS-26.4-arm64-arm-64bit",
        "processor": "arm",
        "python": "3.9.6"
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      "id": "qedc_product_rotations_2048",
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      "metric": "probability",
      "observed": {
        "log2_probability": -2048.0000000000005,
        "probability": 0.0
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      "public_strategy": "separable_product_certificate",
      "qubits": 2048,
      "query": "basis_probability_periodic",
      "query_details": {
        "basis_label": "pattern",
        "basis_state_bit_length": 2047,
        "basis_state_sha256": "f68f851dd0a76d418720eba5f027dacab2c885b1107cb6d740b9acebcf179283"
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      "runtime_s": 0.0358445,
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      "source_url": "https://quantumconsortium.org/publication/quantum-algorithm-exploration-using-application-oriented-performance-benchmarks/",
      "state_space_basis_states": "2^2048",
      "suite": "QED-C application-oriented",
      "visited_nodes": 8192
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    {
      "absolute_error": 8.71842416900956e-18,
      "dense_statevector_memory": {
        "complex128_bytes_formula": "2^260 bytes",
        "log10_16gb_ratio": 68.032779,
        "log10_bytes": 78.267799,
        "over_16gb_dense_limit": true
      },
      "exact": true,
      "expected": {
        "abs": 6.730765058463587e-18,
        "imag": 4.9996392230497455e-19,
        "real": 6.712170613790129e-18
      },
      "family": "Dense symmetric phase mixer",
      "gate_count": 33152,
      "hardware": {
        "machine": "arm64",
        "platform": "macOS-26.4-arm64-arm-64bit",
        "processor": "arm",
        "python": "3.9.6"
      },
      "id": "mqt_symmetric_phase_256",
      "materialized_states": 0,
      "metric": "amplitude",
      "observed": {
        "abs": 7.651578248720627e-18,
        "imag": 7.500072105413969e-18,
        "real": 1.5151132333544895e-18
      },
      "public_strategy": "symmetric_orbit_certificate",
      "qubits": 256,
      "query": "basis_amplitude_alternating",
      "query_details": {
        "basis_label": "pattern",
        "basis_state_bit_length": 256,
        "basis_state_sha256": "e0e77a507412b120f6ede61f62295b1a7b2ff19d3dcc8f7253e51663470c888e"
      },
      "runtime_s": 0.31628825,
      "scope": "targeted_exact_observable",
      "source_url": "https://github.com/munich-quantum-toolkit/bench",
      "state_space_basis_states": "2^256",
      "suite": "MQT Bench / SuperMarQ-style",
      "visited_nodes": 49793
    },
    {
      "absolute_error": 2.220446049250313e-16,
      "dense_statevector_memory": {
        "complex128_bytes_formula": "2^4100 bytes",
        "log10_16gb_ratio": 1223.987962,
        "log10_bytes": 1234.222982,
        "over_16gb_dense_limit": true
      },
      "exact": true,
      "expected": {
        "abs": 1.0,
        "imag": 0.0,
        "real": 1.0
      },
      "family": "GHZ Pauli observable",
      "gate_count": 4096,
      "hardware": {
        "machine": "arm64",
        "platform": "macOS-26.4-arm64-arm-64bit",
        "processor": "arm",
        "python": "3.9.6"
      },
      "id": "supermarq_ghz_4096_x_observable",
      "materialized_states": 0,
      "metric": "observable",
      "observed": {
        "abs": 0.9999999999999998,
        "imag": 0.0,
        "real": 0.9999999999999998
      },
      "public_strategy": "structured_entanglement_certificate",
      "qubits": 4096,
      "query": "pauli_x_all",
      "query_details": {
        "observable": "all-X"
      },
      "runtime_s": 0.022773875,
      "scope": "targeted_exact_observable",
      "source_url": "https://www.scholars.northwestern.edu/en/publications/supermarq-a-scalable-quantum-benchmark-suite",
      "state_space_basis_states": "2^4096",
      "suite": "SuperMarQ",
      "visited_nodes": 4096
    }
  ],
  "claim_scope": "query-native-targeted-exactness",
  "disclaimer": "This campaign validates compact exact execution answers for named structured and bounded-contraction circuits. It is not a claim that arbitrary dense output distributions can be materialized at these widths.",
  "generated_at": "deterministic-local",
  "sources": {
    "mqt_bench": "https://github.com/munich-quantum-toolkit/bench",
    "qasmbench": "https://github.com/pnnl/QASMBench",
    "qedc": "https://quantumconsortium.org/publication/application-oriented-performance-benchmarks-for-quantum-computing/",
    "qedc_exploration": "https://quantumconsortium.org/publication/quantum-algorithm-exploration-using-application-oriented-performance-benchmarks/",
    "supermarq": "https://www.scholars.northwestern.edu/en/publications/supermarq-a-scalable-quantum-benchmark-suite"
  },
  "summary": {
    "exact_cases": 11,
    "max_dense_statevector_log10_bytes": 1234.222982,
    "max_gate_count": 131328,
    "max_qubits": 4096,
    "runtime_s": 58.006441,
    "total_cases": 11,
    "zero_materialization_cases": 11
  }
}