{"abstract":"A register whose amplitudes are about 1e-8 is normalized into a confident distribution instead of reporting \"zero-state\".","category":"Quantum circuit simulation","checks":7,"contract":"Input [n, amps, qubits]; amps are 2**n [re, im] pairs (qubit 0 = LSB), possibly unnormalized. Return the marginal outcome distribution over the listed qubits as {bitstring: probability} where the first listed qubit is the rightmost character, probabilities are normalized by the total squared norm, rounded to 6 decimals after summation, and zero entries are omitted. Errors: \"bad-length\", \"duplicate-qubit\", \"bad-qubit\", \"zero-state\" (total squared norm <= 1e-12).","contract_signature":"x","evaluation_group":"w2-quantum_circuit_simulation-marginal-distribution","failed_approach":"The attempted repair uses a far looser 1e-6 tolerance, rejecting small but legitimate states.","family":"w2-quantum_circuit_simulation-marginal-distribution-zero-state-threshold","id":"FA-90901","implementations":{"attempt":{"sha256":"f7689a22723fde1759d4493669843ecc7108674f56ed220022679ff8aa1ae5c5","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    n, amps, qubits = x\n    if len(amps) != 1 << n:\n        return 'bad-length'\n    if len(set(qubits)) != len(qubits):\n        return 'duplicate-qubit'\n    if any(q < 0 or q >= n for q in qubits):\n        return 'bad-qubit'\n    total = sum(re * re + im * im for re, im in amps)\n    if total <= 1e-6:\n        return 'zero-state'\n    acc = {}\n    for idx, (a, b) in enumerate(amps):\n        p = a * a + b * b\n        if p == 0:\n            continue\n        key = ''.join('1' if idx >> q & 1 else '0' for q in reversed(qubits))\n        acc[key] = acc.get(key, 0.0) + p\n    out = {}\n    for key in sorted(acc):\n        v = round(acc[key] / total, 6)\n        if v > 0:\n            out[key] = v\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression: near zero state', [1, [[1e-08, 0], [0, 1e-08]], [0]], 'zero-state'], ['repair check: tiny but valid state', [1, [[0.0001, 0], [0, 0.0002]], [0]], {'0': 0.2, '1': 0.8}], ['control: bell state on both qubits', [2, [[0.707107, 0], [0, 0], [0, 0], [0.707107, 0]], [0, 1]], {'00': 0.5, '11': 0.5}], ['control: reversed qubit list', [2, [[0, 0], [1, 0], [0, 0], [0, 0]], [1, 0]], {'10': 1.0}], ['control: single qubit marginal of |01>', [2, [[0, 0], [1, 0], [0, 0], [0, 0]], [1]], {'0': 1.0}], ['control: out of range qubit equals n', [2, [[1, 0], [0, 0], [0, 0], [0, 0]], [2]], 'bad-qubit'], ['repair check: small valid state', [1, [[0.0005, 0], [0, 0.0005]], [0]], {'0': 0.5, '1': 0.5}]], [['regression: near zero state', [1, [[1e-08, 0], [0, 1e-08]], [0]], 'zero-state'], ['repair check: tiny but valid state', [1, [[0.0001, 0], [0, 0.0002]], [0]], {'0': 0.2, '1': 0.8}], ['control: negative qubit index', [2, [[1, 0], [0, 0], [0, 0], [0, 0]], [-1]], 'bad-qubit'], ['control: duplicate qubits', [2, [[0.6, 0], [0, 0.8], [0, 0], [0, 0]], [0, 0]], 'duplicate-qubit'], ['control: wrong amplitude count', [2, [[1, 0], [0, 0]], [0]], 'bad-length'], ['control: all-zero state', [1, [[0, 0], [0, 0]], [0]], 'zero-state'], ['repair check: small valid state', [1, [[0.0005, 0], [0, 0.0005]], [0]], {'0': 0.5, '1': 0.5}]], [['regression: near zero state', [1, [[1e-08, 0], [0, 1e-08]], [0]], 'zero-state'], ['repair check: tiny but valid state', [1, [[0.0001, 0], [0, 0.0002]], [0]], {'0': 0.2, '1': 0.8}], ['control: unnormalized pair', [1, [[3, 0], [0, 4]], [0]], {'0': 0.36, '1': 0.64}], ['control: random state 0', [2, [[0.0, 0.0], [0.282, -0.043], [-0.278, 0.017], [0.0, 0.0]], [0, 1]], {'01': 0.511954, '10': 0.488046}], ['control: random state 1', [2, [[0.129, 0.125], [0.0, 0.0], [0.0, 0.0], [0.0, 0.0]], [1, 0]], {'00': 1.0}], ['control: random state 2', [1, [[0.541, -0.923], [-0.479, -0.646]], [0]], {'0': 0.638959, '1': 0.361041}], ['repair check: small valid state', [1, [[0.0005, 0], [0, 0.0005]], [0]], {'0': 0.5, '1': 0.5}]], [['regression: near zero state', [1, [[1e-08, 0], [0, 1e-08]], [0]], 'zero-state'], ['repair check: tiny but valid state', [1, [[0.0001, 0], [0, 0.0002]], [0]], {'0': 0.2, '1': 0.8}], ['control: random state 3', [2, [[0.379, 0.308], [-0.129, -0.524], [0.79, -0.299], [-0.403, -0.327]], [0, 1]], {'00': 0.157683, '01': 0.192532, '10': 0.471717, '11': 0.178068}], ['control: random state 4', [1, [[-0.217, 0.525], [-0.308, -0.181]], [0]], {'0': 0.716602, '1': 0.283398}], ['control: random state 5', [2, [[0.175, -0.97], [0.914, 0.939], [-0.22, 0.959], [-0.79, 0.837]], [1]], {'0': 0.539737, '1': 0.460263}], ['control: random state 6', [3, [[-0.119, 0.092], [0.264, -0.223], [-0.189, 0.034], [-0.22, -0.267], [-0.291, -0.092], [0.09, -0.02], [0.062, -0.284], [-0.239, 0.039]], [2]], {'0': 0.54953, '1': 0.45047}], ['repair check: small valid state', [1, [[0.0005, 0], [0, 0.0005]], [0]], {'0': 0.5, '1': 0.5}]], [['regression: near zero state', [1, [[1e-08, 0], [0, 1e-08]], [0]], 'zero-state'], ['repair check: tiny but valid state', [1, [[0.0001, 0], [0, 0.0002]], [0]], {'0': 0.2, '1': 0.8}], ['control: random state 7', [1, [[0.725, -0.825], [-0.233, -0.266]], [0]], {'0': 0.906073, '1': 0.093927}], ['control: random state 8', [2, [[0.258, -0.148], [-0.044, -0.154], [0.09, 0.21], [0.28, 0.265]], [0]], {'0': 0.446643, '1': 0.553357}], ['control: random state 9', [1, [[-0.25, -0.175], [0.0, 0.0]], [0]], {'0': 1.0}], ['control: random state 10', [3, [[-0.064, 0.212], [0.264, -0.114], [-0.15, -0.24], [0.031, 0.141], [0.037, -0.002], [0.023, -0.229], [0.193, -0.153], [0.251, 0.097]], [0, 1, 2]], {'000': 0.116738, '001': 0.196846, '010': 0.190676, '011': 0.049614, '100': 0.003268, '101': 0.126094, '110': 0.144395, '111': 0.17237}], ['repair check: small valid state', [1, [[0.0005, 0], [0, 0.0005]], [0]], {'0': 0.5, '1': 0.5}]]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"6938092f0d2df2035f4ac6637757e5b15cfce9d07535bdf1cec34d09aaa774cf","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    n, amps, qubits = x\n    if len(amps) != 1 << n:\n        return 'bad-length'\n    if len(set(qubits)) != len(qubits):\n        return 'duplicate-qubit'\n    if any(q < 0 or q >= n for q in qubits):\n        return 'bad-qubit'\n    total = sum(re * re + im * im for re, im in amps)\n    if total == 0:\n        return 'zero-state'\n    acc = {}\n    for idx, (a, b) in enumerate(amps):\n        p = a * a + b * b\n        if p == 0:\n            continue\n        key = ''.join('1' if idx >> q & 1 else '0' for q in reversed(qubits))\n        acc[key] = acc.get(key, 0.0) + p\n    out = {}\n    for key in sorted(acc):\n        v = round(acc[key] / total, 6)\n        if v > 0:\n            out[key] = v\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression: near zero state', [1, [[1e-08, 0], [0, 1e-08]], [0]], 'zero-state'], ['repair check: tiny but valid state', [1, [[0.0001, 0], [0, 0.0002]], [0]], {'0': 0.2, '1': 0.8}], ['control: bell state on both qubits', [2, [[0.707107, 0], [0, 0], [0, 0], [0.707107, 0]], [0, 1]], {'00': 0.5, '11': 0.5}], ['control: reversed qubit list', [2, [[0, 0], [1, 0], [0, 0], [0, 0]], [1, 0]], {'10': 1.0}], ['control: single qubit marginal of |01>', [2, [[0, 0], [1, 0], [0, 0], [0, 0]], [1]], {'0': 1.0}], ['control: out of range qubit equals n', [2, [[1, 0], [0, 0], [0, 0], [0, 0]], [2]], 'bad-qubit'], ['repair check: small valid state', [1, [[0.0005, 0], [0, 0.0005]], [0]], {'0': 0.5, '1': 0.5}]], [['regression: near zero state', [1, [[1e-08, 0], [0, 1e-08]], [0]], 'zero-state'], ['repair check: tiny but valid state', [1, [[0.0001, 0], [0, 0.0002]], [0]], {'0': 0.2, '1': 0.8}], ['control: negative qubit index', [2, [[1, 0], [0, 0], [0, 0], [0, 0]], [-1]], 'bad-qubit'], ['control: duplicate qubits', [2, [[0.6, 0], [0, 0.8], [0, 0], [0, 0]], [0, 0]], 'duplicate-qubit'], ['control: wrong amplitude count', [2, [[1, 0], [0, 0]], [0]], 'bad-length'], ['control: all-zero state', [1, [[0, 0], [0, 0]], [0]], 'zero-state'], ['repair check: small valid state', [1, [[0.0005, 0], [0, 0.0005]], [0]], {'0': 0.5, '1': 0.5}]], [['regression: near zero state', [1, [[1e-08, 0], [0, 1e-08]], [0]], 'zero-state'], ['repair check: tiny but valid state', [1, [[0.0001, 0], [0, 0.0002]], [0]], {'0': 0.2, '1': 0.8}], ['control: unnormalized pair', [1, [[3, 0], [0, 4]], [0]], {'0': 0.36, '1': 0.64}], ['control: random state 0', [2, [[0.0, 0.0], [0.282, -0.043], [-0.278, 0.017], [0.0, 0.0]], [0, 1]], {'01': 0.511954, '10': 0.488046}], ['control: random state 1', [2, [[0.129, 0.125], [0.0, 0.0], [0.0, 0.0], [0.0, 0.0]], [1, 0]], {'00': 1.0}], ['control: random state 2', [1, [[0.541, -0.923], [-0.479, -0.646]], [0]], {'0': 0.638959, '1': 0.361041}], ['repair check: small valid state', [1, [[0.0005, 0], [0, 0.0005]], [0]], {'0': 0.5, '1': 0.5}]], [['regression: near zero state', [1, [[1e-08, 0], [0, 1e-08]], [0]], 'zero-state'], ['repair check: tiny but valid state', [1, [[0.0001, 0], [0, 0.0002]], [0]], {'0': 0.2, '1': 0.8}], ['control: random state 3', [2, [[0.379, 0.308], [-0.129, -0.524], [0.79, -0.299], [-0.403, -0.327]], [0, 1]], {'00': 0.157683, '01': 0.192532, '10': 0.471717, '11': 0.178068}], ['control: random state 4', [1, [[-0.217, 0.525], [-0.308, -0.181]], [0]], {'0': 0.716602, '1': 0.283398}], ['control: random state 5', [2, [[0.175, -0.97], [0.914, 0.939], [-0.22, 0.959], [-0.79, 0.837]], [1]], {'0': 0.539737, '1': 0.460263}], ['control: random state 6', [3, [[-0.119, 0.092], [0.264, -0.223], [-0.189, 0.034], [-0.22, -0.267], [-0.291, -0.092], [0.09, -0.02], [0.062, -0.284], [-0.239, 0.039]], [2]], {'0': 0.54953, '1': 0.45047}], ['repair check: small valid state', [1, [[0.0005, 0], [0, 0.0005]], [0]], {'0': 0.5, '1': 0.5}]], [['regression: near zero state', [1, [[1e-08, 0], [0, 1e-08]], [0]], 'zero-state'], ['repair check: tiny but valid state', [1, [[0.0001, 0], [0, 0.0002]], [0]], {'0': 0.2, '1': 0.8}], ['control: random state 7', [1, [[0.725, -0.825], [-0.233, -0.266]], [0]], {'0': 0.906073, '1': 0.093927}], ['control: random state 8', [2, [[0.258, -0.148], [-0.044, -0.154], [0.09, 0.21], [0.28, 0.265]], [0]], {'0': 0.446643, '1': 0.553357}], ['control: random state 9', [1, [[-0.25, -0.175], [0.0, 0.0]], [0]], {'0': 1.0}], ['control: random state 10', [3, [[-0.064, 0.212], [0.264, -0.114], [-0.15, -0.24], [0.031, 0.141], [0.037, -0.002], [0.023, -0.229], [0.193, -0.153], [0.251, 0.097]], [0, 1, 2]], {'000': 0.116738, '001': 0.196846, '010': 0.190676, '011': 0.049614, '100': 0.003268, '101': 0.126094, '110': 0.144395, '111': 0.17237}], ['repair check: small valid state', [1, [[0.0005, 0], [0, 0.0005]], [0]], {'0': 0.5, '1': 0.5}]]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"A deterministic bounded teaching model with a stipulated toy contract; amplitudes are rounded to fixed decimals for strict JSON output. It is not a production quantum SDK and claims no standards conformance. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"w2-quantum_circuit_simulation-marginal-distribution-zero-state-threshold","generated_at":"2026-09-29T14:51:30.991296+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Marginal readout distributions are what users compare against hardware counts; ordering or normalization slips mislabel every histogram.","root_cause":"The empty-state guard compares the squared norm to exactly 0.0 rather than the 1e-12 tolerance.","sha256":"3f472d224bfd99c92bb6a73a3620019c44f4c12ebbd0504f6329750ee3c82e66","title":"Marginal treats near-zero norm with exact equality · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":36.881,"exit_code":1,"observations":[{"actual":"zero-state","check":"regression: near zero state","expected":"zero-state","passed":true},{"actual":"zero-state","check":"repair check: tiny but valid state","expected":{"0":0.2,"1":0.8},"passed":false},{"actual":{"00":0.5,"11":0.5},"check":"control: bell state on both qubits","expected":{"00":0.5,"11":0.5},"passed":true},{"actual":{"10":1.0},"check":"control: reversed qubit list","expected":{"10":1.0},"passed":true},{"actual":{"0":1.0},"check":"control: single qubit marginal of |01>","expected":{"0":1.0},"passed":true},{"actual":"bad-qubit","check":"control: out of range qubit equals n","expected":"bad-qubit","passed":true},{"actual":"zero-state","check":"repair check: small valid state","expected":{"0":0.5,"1":0.5},"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: near zero state\", \"actual\": \"zero-state\", \"expected\": \"zero-state\", \"passed\": true}, {\"check\": \"repair check: tiny but valid state\", \"actual\": \"zero-state\", \"expected\": {\"0\": 0.2, \"1\": 0.8}, \"passed\": false}, {\"check\": \"control: bell state on both qubits\", \"actual\": {\"00\": 0.5, \"11\": 0.5}, \"expected\": {\"00\": 0.5, \"11\": 0.5}, \"passed\": true}, {\"check\": \"control: reversed qubit list\", \"actual\": {\"10\": 1.0}, \"expected\": {\"10\": 1.0}, \"passed\": true}, {\"check\": \"control: single qubit marginal of |01>\", \"actual\": {\"0\": 1.0}, \"expected\": {\"0\": 1.0}, \"passed\": true}, {\"check\": \"control: out of range qubit equals n\", \"actual\": \"bad-qubit\", \"expected\": \"bad-qubit\", \"passed\": true}, {\"check\": \"repair check: small valid state\", \"actual\": \"zero-state\", \"expected\": {\"0\": 0.5, \"1\": 0.5}, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":40.291,"exit_code":1,"observations":[{"actual":{"0":0.5,"1":0.5},"check":"regression: near zero state","expected":"zero-state","passed":false},{"actual":{"0":0.2,"1":0.8},"check":"repair check: tiny but valid state","expected":{"0":0.2,"1":0.8},"passed":true},{"actual":{"00":0.5,"11":0.5},"check":"control: bell state on both qubits","expected":{"00":0.5,"11":0.5},"passed":true},{"actual":{"10":1.0},"check":"control: reversed qubit list","expected":{"10":1.0},"passed":true},{"actual":{"0":1.0},"check":"control: single qubit marginal of |01>","expected":{"0":1.0},"passed":true},{"actual":"bad-qubit","check":"control: out of range qubit equals n","expected":"bad-qubit","passed":true},{"actual":{"0":0.5,"1":0.5},"check":"repair check: small valid state","expected":{"0":0.5,"1":0.5},"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: near zero state\", \"actual\": {\"0\": 0.5, \"1\": 0.5}, \"expected\": \"zero-state\", \"passed\": false}, {\"check\": \"repair check: tiny but valid state\", \"actual\": {\"0\": 0.2, \"1\": 0.8}, \"expected\": {\"0\": 0.2, \"1\": 0.8}, \"passed\": true}, {\"check\": \"control: bell state on both qubits\", \"actual\": {\"00\": 0.5, \"11\": 0.5}, \"expected\": {\"00\": 0.5, \"11\": 0.5}, \"passed\": true}, {\"check\": \"control: reversed qubit list\", \"actual\": {\"10\": 1.0}, \"expected\": {\"10\": 1.0}, \"passed\": true}, {\"check\": \"control: single qubit marginal of |01>\", \"actual\": {\"0\": 1.0}, \"expected\": {\"0\": 1.0}, \"passed\": true}, {\"check\": \"control: out of range qubit equals n\", \"actual\": \"bad-qubit\", \"expected\": \"bad-qubit\", \"passed\": true}, {\"check\": \"repair check: small valid state\", \"actual\": {\"0\": 0.5, \"1\": 0.5}, \"expected\": {\"0\": 0.5, \"1\": 0.5}, \"passed\": true}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}