{
  "title": "150-Qubit Hardware-Native Ising Optimization Study",
  "date": "2026-07-23",
  "backend": "ibm_fez",
  "processor_qubits": 156,
  "active_physical_qubits": 150,
  "problem": {
    "variables": 150,
    "search_space": "2^150",
    "search_space_approx": "1.427e45",
    "weighted_xor_constraints": 167,
    "total_weight": 873
  },
  "classical_exact": {
    "solver": "scipy.optimize.milp / HiGHS",
    "optimal_weight": 865,
    "total_weight": 873,
    "fraction": 0.9908361970217641,
    "mip_gap": 0.0,
    "wall_seconds": 3.2867870409972966
  },
  "hardware_depth_curve": [
    {
      "p": 1,
      "job_id": "d9gke4bsbqfc73eoovq0",
      "quantum_seconds": 24,
      "pubs": 10,
      "shots_per_pub": 8192,
      "shots": 81920,
      "two_qubit_gates": 334,
      "compiled_depth": 381,
      "mean_approximation_ratio": 0.6733289209266619,
      "best_sample_approximation_ratio": 0.8473988439306358
    },
    {
      "p": 2,
      "job_id": "d9gk9kjsbqfc73eoops0",
      "quantum_seconds": 57,
      "pubs": 50,
      "shots_per_pub": 4096,
      "shots": 204800,
      "two_qubit_gates": 668,
      "compiled_depth": 406,
      "mean_approximation_ratio": 0.6903317490065028,
      "best_sample_approximation_ratio": 0.8208092485549133
    },
    {
      "p": 3,
      "job_id": "d9gkajl0k0jc738gsv80",
      "quantum_seconds": 57,
      "pubs": 50,
      "shots_per_pub": 4096,
      "shots": 204800,
      "two_qubit_gates": 1002,
      "compiled_depth": 431,
      "mean_approximation_ratio": 0.7048139450867053,
      "best_sample_approximation_ratio": 0.8439306358381503
    },
    {
      "p": 4,
      "job_id": "d9gkj98gk0ls73f1mspg",
      "quantum_seconds": 57,
      "pubs": 50,
      "shots_per_pub": 4096,
      "shots": 204800,
      "two_qubit_gates": 1336,
      "compiled_depth": 456,
      "mean_approximation_ratio": 0.7262520321531792,
      "best_sample_approximation_ratio": 0.8578034682080925
    },
    {
      "p": 5,
      "job_id": "d9gkle3sbqfc73eop9tg",
      "quantum_seconds": 58,
      "pubs": 50,
      "shots_per_pub": 4096,
      "shots": 204800,
      "two_qubit_gates": 1670,
      "compiled_depth": 481,
      "mean_approximation_ratio": 0.7356699331647398,
      "best_sample_approximation_ratio": 0.892485549132948
    },
    {
      "p": 6,
      "job_id": "d9gknv4honhs73abouig",
      "quantum_seconds": 58,
      "pubs": 50,
      "shots_per_pub": 4096,
      "shots": 204800,
      "two_qubit_gates": 2004,
      "compiled_depth": 506,
      "mean_approximation_ratio": 0.739049516799133,
      "best_sample_approximation_ratio": 0.8774566473988439
    },
    {
      "p": 7,
      "job_id": "d9gkq3ogk0ls73f1n5tg",
      "quantum_seconds": 58,
      "pubs": 50,
      "shots_per_pub": 4096,
      "shots": 204800,
      "two_qubit_gates": 2338,
      "compiled_depth": 531,
      "mean_approximation_ratio": 0.736153416275289,
      "best_sample_approximation_ratio": 0.8647398843930636
    },
    {
      "p": 8,
      "job_id": "d9gkrnjsbqfc73eopi3g",
      "quantum_seconds": 58,
      "pubs": 50,
      "shots_per_pub": 4096,
      "shots": 204800,
      "two_qubit_gates": 2672,
      "compiled_depth": 556,
      "mean_approximation_ratio": 0.7354015195989885,
      "best_sample_approximation_ratio": 0.8797687861271676
    }
  ],
  "mitigation_ablation": [
    {
      "mode": "raw",
      "job_id": "d9gke4bsbqfc73eoovq0",
      "quantum_seconds": 24,
      "pubs": 10,
      "shots": 81920,
      "mean_approximation_ratio": 0.6733289209266619,
      "best_sample_approximation_ratio": 0.8473988439306358
    },
    {
      "mode": "dd_only",
      "job_id": "d9gkekggk0ls73f1mlsg",
      "quantum_seconds": 24,
      "pubs": 10,
      "shots": 81920,
      "mean_approximation_ratio": 0.6792395654579119,
      "best_sample_approximation_ratio": 0.8520231213872832
    },
    {
      "mode": "twirling_only",
      "job_id": "d9gkf4t0k0jc738gt5hg",
      "quantum_seconds": 25,
      "pubs": 10,
      "shots": 81920,
      "mean_approximation_ratio": 0.6653075042901012,
      "best_sample_approximation_ratio": 0.823121387283237
    },
    {
      "mode": "dd_plus_twirling",
      "job_id": "d9gkg04honhs73aboj8g",
      "quantum_seconds": 25,
      "pubs": 10,
      "shots": 81920,
      "mean_approximation_ratio": 0.5556691287707731,
      "best_sample_approximation_ratio": 0.7549132947976879
    }
  ],
  "jobs": [
    {
      "role": "original_smoke",
      "job_id": "d9gjobkhonhs73abnl3g",
      "quantum_seconds": 3,
      "pubs": 3,
      "shots": 3072
    },
    {
      "role": "p1_parameter_grid",
      "job_id": "d9gk5gchonhs73abo5ag",
      "quantum_seconds": 30,
      "pubs": 100,
      "shots": 102400
    },
    {
      "role": "initial_mitigated_confirmation",
      "job_id": "d9gk64ogk0ls73f1mar0",
      "quantum_seconds": 14,
      "pubs": 10,
      "shots": 40960
    },
    {
      "role": "p2_depth",
      "job_id": "d9gk9kjsbqfc73eoops0",
      "quantum_seconds": 57,
      "pubs": 50,
      "shots": 204800
    },
    {
      "role": "p3_depth",
      "job_id": "d9gkajl0k0jc738gsv80",
      "quantum_seconds": 57,
      "pubs": 50,
      "shots": 204800
    },
    {
      "role": "p4_depth",
      "job_id": "d9gkj98gk0ls73f1mspg",
      "quantum_seconds": 57,
      "pubs": 50,
      "shots": 204800
    },
    {
      "role": "p5_depth",
      "job_id": "d9gkle3sbqfc73eop9tg",
      "quantum_seconds": 58,
      "pubs": 50,
      "shots": 204800
    },
    {
      "role": "p6_depth",
      "job_id": "d9gknv4honhs73abouig",
      "quantum_seconds": 58,
      "pubs": 50,
      "shots": 204800
    },
    {
      "role": "p7_depth",
      "job_id": "d9gkq3ogk0ls73f1n5tg",
      "quantum_seconds": 58,
      "pubs": 50,
      "shots": 204800
    },
    {
      "role": "p8_depth",
      "job_id": "d9gkrnjsbqfc73eopi3g",
      "quantum_seconds": 58,
      "pubs": 50,
      "shots": 204800
    },
    {
      "role": "ablation_raw",
      "job_id": "d9gke4bsbqfc73eoovq0",
      "quantum_seconds": 24,
      "pubs": 10,
      "shots": 81920
    },
    {
      "role": "ablation_dd_only",
      "job_id": "d9gkekggk0ls73f1mlsg",
      "quantum_seconds": 24,
      "pubs": 10,
      "shots": 81920
    },
    {
      "role": "ablation_twirling_only",
      "job_id": "d9gkf4t0k0jc738gt5hg",
      "quantum_seconds": 25,
      "pubs": 10,
      "shots": 81920
    },
    {
      "role": "ablation_dd_plus_twirling",
      "job_id": "d9gkg04honhs73aboj8g",
      "quantum_seconds": 25,
      "pubs": 10,
      "shots": 81920
    }
  ],
  "totals": {
    "jobs": 15,
    "qaoa_pubs": 544,
    "all_pubs": 547,
    "qaoa_shots": 2084864,
    "all_shots": 2087936,
    "quantum_seconds": 599,
    "allowance_seconds": 600,
    "remaining_seconds": 1
  },
  "findings": {
    "best_mean_depth": 6,
    "best_mean_approximation_ratio": 0.739049516799133,
    "best_sample_depth": 5,
    "best_sample_approximation_ratio": 0.892485549132948,
    "dd_only_delta_vs_raw": 0.005910644531250009,
    "twirling_only_delta_vs_raw": -0.008021416636560641,
    "combined_delta_vs_raw": -0.11765979215588873,
    "replicated_best_mean_depth": 6,
    "replicated_best_mean_approximation_ratio": 0.742274123095113,
    "replicated_best_sample_depth": 6,
    "replicated_best_sample_approximation_ratio": 0.915606936416185
  },
  "truth_boundary": {
    "hardware_execution_verified": true,
    "classical_exact_solution_verified": true,
    "quantum_acceleration_measured": false,
    "quantum_advantage_claimed": false,
    "note": "Classical HiGHS solved this instance exactly and remains the production winner."
  },
  "final_p5_p6_confirmation": {
    "job_id": "d9gl69t0k0jc738gu9mg",
    "usage": 51,
    "pubs": 44,
    "shots": 180224,
    "groups": {
      "p5": {
        "replicates": 22,
        "total_shots": 90112,
        "mean_approximation_ratio": 0.7366256353044535,
        "standard_deviation_across_replicates": 0.0007774597290066907,
        "standard_error": 0.00016575497116186523,
        "best_sample_approximation_ratio": 0.9109826589595376
      },
      "p6": {
        "replicates": 22,
        "total_shots": 90112,
        "mean_approximation_ratio": 0.742274123095113,
        "standard_deviation_across_replicates": 0.00071458200975097,
        "standard_error": 0.0001523493963737386,
        "best_sample_approximation_ratio": 0.915606936416185
      }
    }
  },
  "failed_workloads": [
    {
      "job_id": "d9glaishonhs73abprjg",
      "status": "ERROR",
      "usage": 0,
      "reason": "IBM error 1305: one-second max_execution_time was too small; no result and no billed usage."
    },
    {
      "job_id": "d9glbkshonhs73abpt5g",
      "status": "CANCELLED",
      "usage": 0,
      "reason": "150-qubit 128-shot control remained account-queued with one second left; cancelled unbilled."
    },
    {
      "job_id": "d9gli80gk0ls73f1oae0",
      "status": "CANCELLED",
      "usage": 0,
      "reason": "One-qubit 128-shot control on ibm_fez remained account-queued; cancelled unbilled."
    },
    {
      "job_id": "d9glklggk0ls73f1odu0",
      "status": "CANCELLED",
      "usage": 0,
      "reason": "One-qubit 128-shot control on ibm_kingston also remained account-queued; cancelled unbilled."
    }
  ]
}