{
  "slug": "2026-10-13-autonomous-quantum-repair",
  "scope": "T134 finite Lindblad models of unknown-state repair and finite ancilla reset.\n\nEffective 3-data-qubit conditional jumps match the algebraic repetition-code\nmodel (Reiter et al., 2017 Eqs.3-9); parameters/contrasts are chosen here.\nThe explicit 4-level ancilla is our model, not the microscopic ion/cavity device.\nOnly X noise is corrected; Z controls and leaked logical labels are separate.\nTime unit 1/kappa; no joule/real-device efficiency is inferred.\n",
  "single_error": [
    {
      "channel": "coherent_repair",
      "Gamma_t": 0,
      "Fe": 0.9999999999999998,
      "classical_Z_success": 1.0,
      "code_population": 0.0,
      "ancilla_excited_population": 0.0,
      "choi_min_eigenvalue": 0.0
    },
    {
      "channel": "coherent_repair",
      "Gamma_t": 0.2,
      "Fe": 0.9999999999999998,
      "classical_Z_success": 1.0,
      "code_population": 0.18126924692201815,
      "ancilla_excited_population": 0.0,
      "choi_min_eigenvalue": 0.0
    },
    {
      "channel": "coherent_repair",
      "Gamma_t": 1,
      "Fe": 0.9999999999999997,
      "classical_Z_success": 0.9999999999999998,
      "code_population": 0.6321205588285576,
      "ancilla_excited_population": 0.0,
      "choi_min_eigenvalue": 0.0
    },
    {
      "channel": "coherent_repair",
      "Gamma_t": 3,
      "Fe": 0.9999999999999997,
      "classical_Z_success": 0.9999999999999998,
      "code_population": 0.9502129316321358,
      "ancilla_excited_population": 0.0,
      "choi_min_eigenvalue": 0.0
    },
    {
      "channel": "coherent_repair",
      "Gamma_t": 10,
      "Fe": 0.9999999999999997,
      "classical_Z_success": 0.9999999999999998,
      "code_population": 0.9999546000702373,
      "ancilla_excited_population": 0.0,
      "choi_min_eigenvalue": 0.0
    },
    {
      "channel": "logical_label_leak",
      "Gamma_t": 0,
      "Fe": 0.9999999999999998,
      "classical_Z_success": 1.0,
      "code_population": 0.0,
      "ancilla_excited_population": 0.0,
      "choi_min_eigenvalue": 0.0
    },
    {
      "channel": "logical_label_leak",
      "Gamma_t": 0.2,
      "Fe": 0.9093653765389906,
      "classical_Z_success": 1.0,
      "code_population": 0.18126924692201815,
      "ancilla_excited_population": 0.0,
      "choi_min_eigenvalue": 0.0
    },
    {
      "channel": "logical_label_leak",
      "Gamma_t": 1,
      "Fe": 0.683939720585721,
      "classical_Z_success": 0.9999999999999998,
      "code_population": 0.6321205588285576,
      "ancilla_excited_population": 0.0,
      "choi_min_eigenvalue": 0.0
    },
    {
      "channel": "logical_label_leak",
      "Gamma_t": 3,
      "Fe": 0.5248935341839318,
      "classical_Z_success": 0.9999999999999998,
      "code_population": 0.9502129316321358,
      "ancilla_excited_population": 0.0,
      "choi_min_eigenvalue": 0.0
    },
    {
      "channel": "logical_label_leak",
      "Gamma_t": 10,
      "Fe": 0.500022699964881,
      "classical_Z_success": 0.9999999999999998,
      "code_population": 0.9999546000702373,
      "ancilla_excited_population": 0.0,
      "choi_min_eigenvalue": 0.0
    }
  ],
  "known_state_reset": [
    {
      "Gamma_t": 0,
      "known_ground_state_fidelity": 1.0,
      "unknown_state_Fe": 0.9999999999999997
    },
    {
      "Gamma_t": 0.2,
      "known_ground_state_fidelity": 1.0,
      "unknown_state_Fe": 0.9071013972874749
    },
    {
      "Gamma_t": 1,
      "known_ground_state_fidelity": 1.0,
      "unknown_state_Fe": 0.6452351901491771
    },
    {
      "Gamma_t": 3,
      "known_ground_state_fidelity": 1.0,
      "unknown_state_Fe": 0.3740118471661808
    },
    {
      "Gamma_t": 10,
      "known_ground_state_fidelity": 1.0,
      "unknown_state_Fe": 0.25338032348198325
    }
  ],
  "continuous": [
    {
      "Gamma_over_kappa": 0.0,
      "condition": "ideal",
      "kappa_t": 1.0,
      "Z_rate_per_data_qubit": 0,
      "Fe": 0.6008817743832928,
      "classical_Z_success": 0.6008817743832929,
      "code_population": 0.26373672916655067,
      "ancilla_excited_population": 0.0,
      "choi_min_eigenvalue": 0.0
    },
    {
      "Gamma_over_kappa": 0.5,
      "condition": "ideal",
      "kappa_t": 1.0,
      "Z_rate_per_data_qubit": 0,
      "Fe": 0.6138185786295914,
      "classical_Z_success": 0.6138185786295915,
      "code_population": 0.3407393310254948,
      "ancilla_excited_population": 0.0,
      "choi_min_eigenvalue": 0.0
    },
    {
      "Gamma_over_kappa": 0.5,
      "condition": "logical_label_leak",
      "kappa_t": 1.0,
      "Z_rate_per_data_qubit": 0,
      "Fe": 0.5421298571528238,
      "classical_Z_success": 0.6138185786295915,
      "code_population": 0.3407393310254948,
      "ancilla_excited_population": 0.0,
      "choi_min_eigenvalue": 0.04770785197215238
    },
    {
      "Gamma_over_kappa": 0.5,
      "condition": "control_Z_noise",
      "kappa_t": 1.0,
      "Z_rate_per_data_qubit": 0.0015,
      "Fe": 0.6110687876462475,
      "classical_Z_success": 0.6138185786295919,
      "code_population": 0.3407393310254949,
      "ancilla_excited_population": 0.0,
      "choi_min_eigenvalue": 0.0017300196302141857
    },
    {
      "Gamma_over_kappa": 1.0,
      "condition": "ideal",
      "kappa_t": 1.0,
      "Z_rate_per_data_qubit": 0,
      "Fe": 0.6259211650573719,
      "classical_Z_success": 0.625921165057372,
      "code_population": 0.4040427681994513,
      "ancilla_excited_population": 0.0,
      "choi_min_eigenvalue": -9.064409496785168e-17
    },
    {
      "Gamma_over_kappa": 1.0,
      "condition": "logical_label_leak",
      "kappa_t": 1.0,
      "Z_rate_per_data_qubit": 0,
      "Fe": 0.5014319410031234,
      "classical_Z_success": 0.625921165057372,
      "code_population": 0.4040427681994513,
      "ancilla_excited_population": 0.0,
      "choi_min_eigenvalue": 0.07968916554725557
    },
    {
      "Gamma_over_kappa": 1.0,
      "condition": "control_Z_noise",
      "kappa_t": 1.0,
      "Z_rate_per_data_qubit": 0.003,
      "Fe": 0.6203382713525154,
      "classical_Z_success": 0.6259211650573724,
      "code_population": 0.4040427681994513,
      "ancilla_excited_population": 0.0,
      "choi_min_eigenvalue": 0.00333659011599316
    },
    {
      "Gamma_over_kappa": 2.0,
      "condition": "ideal",
      "kappa_t": 1.0,
      "Z_rate_per_data_qubit": 0,
      "Fe": 0.6479427475601982,
      "classical_Z_success": 0.6479427475601983,
      "code_population": 0.5012393760883331,
      "ancilla_excited_population": 0.0,
      "choi_min_eigenvalue": -8.212472233381969e-18
    },
    {
      "Gamma_over_kappa": 2.0,
      "condition": "logical_label_leak",
      "kappa_t": 1.0,
      "Z_rate_per_data_qubit": 0,
      "Fe": 0.4535187794748431,
      "classical_Z_success": 0.6479427475601983,
      "code_population": 0.5012393760883331,
      "ancilla_excited_population": 0.0,
      "choi_min_eigenvalue": 0.11498274182347722
    },
    {
      "Gamma_over_kappa": 2.0,
      "condition": "control_Z_noise",
      "kappa_t": 1.0,
      "Z_rate_per_data_qubit": 0.006,
      "Fe": 0.6364872148634642,
      "classical_Z_success": 0.6479427475601975,
      "code_population": 0.5012393760883325,
      "ancilla_excited_population": 0.0,
      "choi_min_eigenvalue": 0.006224320561704448
    },
    {
      "Gamma_over_kappa": 5.0,
      "condition": "ideal",
      "kappa_t": 1.0,
      "Z_rate_per_data_qubit": 0,
      "Fe": 0.7006612340838614,
      "classical_Z_success": 0.7006612340838616,
      "code_population": 0.666707803268029,
      "ancilla_excited_population": 0.0,
      "choi_min_eigenvalue": -1.1138936111480063e-17
    },
    {
      "Gamma_over_kappa": 5.0,
      "condition": "logical_label_leak",
      "kappa_t": 1.0,
      "Z_rate_per_data_qubit": 0,
      "Fe": 0.4157533096290189,
      "classical_Z_success": 0.7006612340838616,
      "code_population": 0.666707803268029,
      "ancilla_excited_population": 0.0,
      "choi_min_eigenvalue": 0.13397096899477842
    },
    {
      "Gamma_over_kappa": 5.0,
      "condition": "control_Z_noise",
      "kappa_t": 1.0,
      "Z_rate_per_data_qubit": 0.015,
      "Fe": 0.6705086931118638,
      "classical_Z_success": 0.7006612340838625,
      "code_population": 0.6667078032680296,
      "ancilla_excited_population": 0.0,
      "choi_min_eigenvalue": 0.012881866392387753
    },
    {
      "Gamma_over_kappa": 10.0,
      "condition": "ideal",
      "kappa_t": 1.0,
      "Z_rate_per_data_qubit": 0,
      "Fe": 0.7603744628290569,
      "classical_Z_success": 0.7603744628290569,
      "code_population": 0.7857144638990117,
      "ancilla_excited_population": 0.0,
      "choi_min_eigenvalue": -1.0030993936809612e-16
    },
    {
      "Gamma_over_kappa": 10.0,
      "condition": "logical_label_leak",
      "kappa_t": 1.0,
      "Z_rate_per_data_qubit": 0,
      "Fe": 0.4228157694043241,
      "classical_Z_success": 0.7603744628290569,
      "code_population": 0.7857144638990117,
      "ancilla_excited_population": 0.0,
      "choi_min_eigenvalue": 0.11600396989562106
    },
    {
      "Gamma_over_kappa": 10.0,
      "condition": "control_Z_noise",
      "kappa_t": 1.0,
      "Z_rate_per_data_qubit": 0.03,
      "Fe": 0.6977463005740068,
      "classical_Z_success": 0.7603744628290552,
      "code_population": 0.7857144638990099,
      "ancilla_excited_population": 0.0,
      "choi_min_eigenvalue": 0.01973673203931474
    },
    {
      "Gamma_over_kappa": 30.0,
      "condition": "ideal",
      "kappa_t": 1.0,
      "Z_rate_per_data_qubit": 0,
      "Fe": 0.8667340820305636,
      "classical_Z_success": 0.8667340820305633,
      "code_population": 0.911764705882351,
      "ancilla_excited_population": 0.0,
      "choi_min_eigenvalue": -2.3684009397777895e-16
    },
    {
      "Gamma_over_kappa": 30.0,
      "condition": "logical_label_leak",
      "kappa_t": 1.0,
      "Z_rate_per_data_qubit": 0,
      "Fe": 0.46353645365281293,
      "classical_Z_success": 0.8667340820305633,
      "code_population": 0.911764705882351,
      "ancilla_excited_population": 0.0,
      "choi_min_eigenvalue": 0.06626446133899541
    },
    {
      "Gamma_over_kappa": 30.0,
      "condition": "control_Z_noise",
      "kappa_t": 1.0,
      "Z_rate_per_data_qubit": 0.09,
      "Fe": 0.6859109268034256,
      "classical_Z_success": 0.8667340820305653,
      "code_population": 0.9117647058823531,
      "ancilla_excited_population": 0.0,
      "choi_min_eigenvalue": 0.02780271858586557
    },
    {
      "Gamma_over_kappa": 100.0,
      "condition": "ideal",
      "kappa_t": 1.0,
      "Z_rate_per_data_qubit": 0,
      "Fe": 0.9478300914653077,
      "classical_Z_success": 0.947830091465308,
      "code_population": 0.9711538461538498,
      "ancilla_excited_population": 0.0,
      "choi_min_eigenvalue": -3.1808811602678724e-17
    },
    {
      "Gamma_over_kappa": 100.0,
      "condition": "logical_label_leak",
      "kappa_t": 1.0,
      "Z_rate_per_data_qubit": 0,
      "Fe": 0.5003284910062482,
      "classical_Z_success": 0.947830091465308,
      "code_population": 0.9711538461538498,
      "ancilla_excited_population": 0.0,
      "choi_min_eigenvalue": 0.026054052145115476
    },
    {
      "Gamma_over_kappa": 100.0,
      "condition": "control_Z_noise",
      "kappa_t": 1.0,
      "Z_rate_per_data_qubit": 0.3,
      "Fe": 0.552252675903747,
      "classical_Z_success": 0.9478300914653128,
      "code_population": 0.9711538461538545,
      "ancilla_excited_population": 0.0,
      "choi_min_eigenvalue": 0.02177314032764436
    }
  ],
  "ancilla": [
    {
      "g_over_kappa": 5.0,
      "gamma_over_kappa": 0.0,
      "kappa_t": 1.0,
      "effective_Gamma_over_kappa": null,
      "effective_model_Fe": null,
      "expected_reset_events_trapezoid_51_points": 0.0,
      "Fe": 0.638051231839486,
      "classical_Z_success": 0.638051231839486,
      "code_population": 0.35691902324339986,
      "ancilla_excited_population": 0.6360800342201849,
      "choi_min_eigenvalue": -3.541895842393206e-17
    },
    {
      "g_over_kappa": 5.0,
      "gamma_over_kappa": 0.2,
      "kappa_t": 1.0,
      "effective_Gamma_over_kappa": 500.0,
      "effective_model_Fe": null,
      "expected_reset_events_trapezoid_51_points": 0.07579205441019782,
      "Fe": 0.6414451501883063,
      "classical_Z_success": 0.6414451501883064,
      "code_population": 0.37698783765231214,
      "ancilla_excited_population": 0.6101593134201069,
      "choi_min_eigenvalue": -2.5812987797920937e-17
    },
    {
      "g_over_kappa": 5.0,
      "gamma_over_kappa": 1.0,
      "kappa_t": 1.0,
      "effective_Gamma_over_kappa": 100.0,
      "effective_model_Fe": null,
      "expected_reset_events_trapezoid_51_points": 0.3327519965347605,
      "Fe": 0.6531402386186583,
      "classical_Z_success": 0.6531402386186584,
      "code_population": 0.4439386078095904,
      "ancilla_excited_population": 0.5200738473699216,
      "choi_min_eigenvalue": -1.769458549603266e-16
    },
    {
      "g_over_kappa": 5.0,
      "gamma_over_kappa": 3.0,
      "kappa_t": 1.0,
      "effective_Gamma_over_kappa": 33.333333333333336,
      "effective_model_Fe": null,
      "expected_reset_events_trapezoid_51_points": 0.7431737502996708,
      "Fe": 0.6721053196797225,
      "classical_Z_success": 0.6721053196797226,
      "code_population": 0.5460857885775929,
      "ancilla_excited_population": 0.36429871410746806,
      "choi_min_eigenvalue": -2.3924013361677684e-18
    },
    {
      "g_over_kappa": 5.0,
      "gamma_over_kappa": 10.0,
      "kappa_t": 1.0,
      "effective_Gamma_over_kappa": 10.0,
      "effective_model_Fe": null,
      "expected_reset_events_trapezoid_51_points": 1.1251442976366586,
      "Fe": 0.6851006862255206,
      "classical_Z_success": 0.6851006862255207,
      "code_population": 0.6237721153117537,
      "ancilla_excited_population": 0.1491918761476069,
      "choi_min_eigenvalue": -2.3289747799920544e-17
    },
    {
      "g_over_kappa": 5.0,
      "gamma_over_kappa": 30.0,
      "kappa_t": 1.0,
      "effective_Gamma_over_kappa": 3.3333333333333335,
      "effective_model_Fe": 0.673517292903632,
      "expected_reset_events_trapezoid_51_points": 0.9198696091658887,
      "Fe": 0.6589968907950948,
      "classical_Z_success": 0.6589968907950947,
      "code_population": 0.5432445074989176,
      "ancilla_excited_population": 0.039053422219644474,
      "choi_min_eigenvalue": -1.6653345369377348e-16
    },
    {
      "g_over_kappa": 5.0,
      "gamma_over_kappa": 100.0,
      "kappa_t": 1.0,
      "effective_Gamma_over_kappa": 1.0,
      "effective_model_Fe": 0.6259211650573719,
      "expected_reset_events_trapezoid_51_points": 0.4400497258888033,
      "Fe": 0.6244498561148574,
      "classical_Z_success": 0.6244498561148573,
      "code_population": 0.3961446120224109,
      "ancilla_excited_population": 0.005643679755951586,
      "choi_min_eigenvalue": -1.5962509891027338e-16
    },
    {
      "g_over_kappa": 5.0,
      "gamma_over_kappa": 300.0,
      "kappa_t": 1.0,
      "effective_Gamma_over_kappa": 0.3333333333333333,
      "effective_model_Fe": 0.609603459373711,
      "expected_reset_events_trapezoid_51_points": 0.17265576668278498,
      "Fe": 0.6094398758675456,
      "classical_Z_success": 0.6094398758675454,
      "code_population": 0.3156727747644069,
      "ancilla_excited_population": 0.0007443031367364091,
      "choi_min_eigenvalue": -2.376499135406335e-16
    }
  ],
  "inputs": {
    "kappa": 1,
    "duration": 1,
    "g": 5,
    "control_Z_rate": ".003 Gamma per data qubit",
    "final_readout": "ideal syndrome/Pauli recovery, always including all branches"
  },
  "limits": [
    "only X correction",
    "chosen effective jumps, not hardware resource-matched",
    "explicit 4-state ancilla is not the full experimental Hamiltonian",
    "no raw experiment data or author control code rerun"
  ]
}