{"abstract":"H followed by S on |0> reports the stabilizer -Y instead of +Y.","category":"Quantum circuit simulation","checks":7,"contract":"Input [n, gates] with gates h, s, x, z ([\"g\", q]) and cx ([\"cx\", c, t]). Track the n stabilizer generators of |0...0> (initially Z on each qubit) under the Aaronson-Gottesman update rules and return them as signed strings such as \"+XX\", character q describing qubit q.","contract_signature":"x","evaluation_group":"w2-quantum_circuit_simulation-stabilizer-tableau","failed_approach":"The attempted repair toggles the sign whenever z is set, which ignores the x component.","family":"w2-quantum_circuit_simulation-stabilizer-tableau-phase-gate-update-order","id":"FA-90991","implementations":{"attempt":{"sha256":"9642ff7b75cdcb36ec3593ce44ceee1d1d8da9d3dd3ad8c4e790feb5fc49d59b","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(x):\n    n, gates = x\n    xs = [[0] * n for _ in range(n)]\n    zs = [[1 if i == j else 0 for j in range(n)] for i in range(n)]\n    rs = [0] * n\n    for g in gates:\n        op = g[0]\n        for row in range(n):\n            X, Z = xs[row], zs[row]\n            if op == 'h':\n                a = g[1]\n                rs[row] ^= X[a] & Z[a]\n                X[a], Z[a] = Z[a], X[a]\n            elif op == 's':\n                a = g[1]\n                rs[row] ^= Z[a]\n                Z[a] ^= X[a]\n            elif op == 'x':\n                rs[row] ^= Z[g[1]]\n            elif op == 'z':\n                rs[row] ^= X[g[1]]\n            elif op == 'cx':\n                a, b = g[1], g[2]\n                rs[row] ^= X[a] & Z[b] & (X[b] ^ Z[a] ^ 1)\n                X[b] ^= X[a]\n                Z[a] ^= Z[b]\n    letters = {(0, 0): 'I', (1, 0): 'X', (0, 1): 'Z', (1, 1): 'Y'}\n    return [('-' if rs[r] else '+') + ''.join(letters[(xs[r][q], zs[r][q])] for q in range(n)) for r in range(n)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression: h then s', [1, [['h', 0], ['s', 0]]], ['+Y']], ['regression: h on y eigenstate', [1, [['h', 0], ['s', 0], ['h', 0]]], ['-Y']], ['repair check: random clifford 1', [1, [['z', 0], ['s', 0], ['x', 0], ['x', 0], ['x', 0], ['z', 0], ['z', 0], ['z', 0]]], ['-Z']], ['control: bell preparation', [2, [['h', 0], ['cx', 0, 1]]], ['+XX', '+ZZ']], ['control: s twice after h', [1, [['h', 0], ['s', 0], ['s', 0]]], ['-X']], ['control: x flips z sign', [1, [['x', 0]]], ['-Z']], ['control: z on plus', [1, [['h', 0], ['z', 0]]], ['-X']]], [['regression: random clifford 11', [2, [['s', 1], ['h', 0], ['cx', 0, 1], ['s', 0], ['x', 0]]], ['-YX', '-ZZ']], ['regression: random clifford 17', [1, [['h', 0], ['s', 0], ['h', 0], ['h', 0], ['x', 0], ['s', 0], ['s', 0]]], ['+Y']], ['repair check: random clifford 3', [1, [['s', 0], ['h', 0], ['h', 0], ['x', 0], ['h', 0], ['h', 0], ['s', 0], ['s', 0]]], ['-Z']], ['control: cx on excited control', [2, [['x', 0], ['cx', 0, 1]]], ['-ZI', '+ZZ']], ['control: ghz', [3, [['h', 0], ['cx', 0, 1], ['cx', 0, 2]]], ['+XXX', '+ZZI', '+ZIZ']], ['control: random clifford 0', [3, [['cx', 1, 2]]], ['+ZII', '+IZI', '+IZZ']], ['control: random clifford 8', [3, [['cx', 0, 1], ['h', 2], ['h', 2], ['h', 0], ['cx', 2, 1], ['h', 2], ['z', 0], ['cx', 1, 2]]], ['-XII', '-XZX', '+IIX']]], [['regression: random clifford 28', [3, [['h', 1], ['cx', 0, 1], ['h', 0], ['cx', 2, 1], ['z', 0], ['x', 0], ['cx', 2, 1], ['h', 1], ['h', 2], ['s', 0], ['h', 0], ['cx', 1, 2]]], ['+YII', '+IZI', '+IIX']], ['regression: random clifford 29', [3, [['h', 2], ['s', 0], ['z', 1], ['h', 0], ['s', 0], ['z', 2], ['x', 1], ['z', 0], ['h', 2]]], ['-YII', '-IZI', '-IIZ']], ['repair check: random clifford 5', [1, [['h', 0], ['h', 0], ['h', 0], ['h', 0], ['z', 0], ['s', 0], ['s', 0], ['s', 0], ['x', 0], ['h', 0], ['x', 0], ['h', 0]]], ['-Z']], ['control: random clifford 10', [1, [['z', 0], ['z', 0], ['s', 0], ['z', 0], ['h', 0], ['h', 0], ['s', 0]]], ['+Z']], ['control: random clifford 12', [1, [['h', 0], ['s', 0], ['h', 0], ['x', 0], ['s', 0], ['x', 0], ['x', 0], ['z', 0], ['h', 0], ['s', 0], ['s', 0]]], ['+Z']], ['control: random clifford 15', [2, [['z', 1], ['cx', 0, 1], ['x', 1], ['h', 1]]], ['+ZI', '-ZX']], ['control: random clifford 16', [1, [['x', 0], ['h', 0], ['h', 0], ['h', 0], ['h', 0], ['z', 0], ['z', 0], ['h', 0], ['x', 0], ['h', 0]]], ['-Z']]], [['regression: random clifford 37', [3, [['z', 0], ['cx', 0, 2], ['s', 1], ['z', 1], ['h', 2], ['cx', 0, 1], ['s', 2], ['cx', 1, 0], ['h', 2], ['cx', 1, 0]]], ['+ZII', '+ZZI', '-ZIY']], ['regression: random clifford 38', [3, [['z', 1], ['h', 0], ['h', 2], ['h', 2], ['cx', 1, 2], ['cx', 2, 1], ['h', 1], ['h', 1], ['cx', 0, 1], ['h', 2], ['cx', 2, 1], ['s', 1], ['x', 0], ['s', 2]]], ['+XYI', '+ZXX', '-ZZZ']], ['repair check: random clifford 7', [3, [['cx', 0, 2], ['cx', 2, 1], ['s', 0], ['cx', 0, 2], ['cx', 2, 1], ['z', 1], ['z', 0], ['h', 1], ['x', 1]]], ['+ZII', '+ZXI', '+IIZ']], ['control: random clifford 19', [2, [['h', 0], ['cx', 1, 0], ['cx', 1, 0], ['cx', 0, 1], ['h', 0], ['cx', 1, 0], ['cx', 1, 0], ['cx', 0, 1], ['cx', 0, 1], ['cx', 1, 0], ['cx', 0, 1]]], ['+XZ', '-YY']], ['control: random clifford 20', [3, [['cx', 2, 0], ['h', 2], ['z', 0], ['cx', 2, 1], ['cx', 0, 2], ['cx', 2, 1]]], ['+ZIX', '+ZZI', '+IIX']], ['control: random clifford 22', [3, [['h', 2], ['h', 0], ['cx', 1, 0], ['s', 1], ['cx', 0, 1], ['cx', 1, 0], ['s', 0], ['cx', 2, 1]]], ['+IXI', '+ZII', '+IXX']], ['control: random clifford 24', [1, [['x', 0]]], ['-Z']]], [['regression: random clifford 52', [1, [['h', 0], ['h', 0], ['s', 0], ['x', 0], ['x', 0], ['x', 0], ['z', 0], ['s', 0], ['h', 0], ['s', 0]]], ['-Y']], ['regression: random clifford 54', [1, [['h', 0], ['h', 0], ['x', 0], ['s', 0], ['h', 0], ['s', 0], ['h', 0], ['h', 0], ['h', 0], ['h', 0]]], ['-Y']], ['repair check: random clifford 13', [1, [['z', 0], ['x', 0], ['z', 0], ['z', 0], ['s', 0], ['x', 0], ['h', 0], ['h', 0], ['z', 0], ['h', 0]]], ['+X']], ['control: random clifford 25', [2, [['cx', 1, 0], ['cx', 1, 0]]], ['+ZI', '+IZ']], ['control: random clifford 27', [2, [['cx', 1, 0], ['x', 0], ['h', 0], ['cx', 1, 0], ['cx', 1, 0], ['cx', 1, 0], ['h', 0], ['cx', 0, 1], ['cx', 0, 1], ['h', 0], ['z', 1], ['h', 1]]], ['-XX', '+IX']], ['control: random clifford 32', [3, [['z', 1], ['x', 1], ['cx', 1, 0], ['cx', 1, 2], ['cx', 2, 1], ['x', 0], ['cx', 1, 2], ['z', 1], ['z', 1], ['cx', 2, 1], ['z', 2], ['x', 0], ['cx', 0, 2]]], ['+IIZ', '-ZIZ', '+ZZZ']], ['control: random clifford 34', [1, [['z', 0], ['h', 0], ['z', 0], ['h', 0]]], ['-Z']]]]\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":"eece4bc0677c59fe2258030414a1e368b0ae9bc7a1462a2c07e1808d1d543dd5","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(x):\n    n, gates = x\n    xs = [[0] * n for _ in range(n)]\n    zs = [[1 if i == j else 0 for j in range(n)] for i in range(n)]\n    rs = [0] * n\n    for g in gates:\n        op = g[0]\n        for row in range(n):\n            X, Z = xs[row], zs[row]\n            if op == 'h':\n                a = g[1]\n                rs[row] ^= X[a] & Z[a]\n                X[a], Z[a] = Z[a], X[a]\n            elif op == 's':\n                a = g[1]\n                Z[a] ^= X[a]\n                rs[row] ^= X[a] & Z[a]\n            elif op == 'x':\n                rs[row] ^= Z[g[1]]\n            elif op == 'z':\n                rs[row] ^= X[g[1]]\n            elif op == 'cx':\n                a, b = g[1], g[2]\n                rs[row] ^= X[a] & Z[b] & (X[b] ^ Z[a] ^ 1)\n                X[b] ^= X[a]\n                Z[a] ^= Z[b]\n    letters = {(0, 0): 'I', (1, 0): 'X', (0, 1): 'Z', (1, 1): 'Y'}\n    return [('-' if rs[r] else '+') + ''.join(letters[(xs[r][q], zs[r][q])] for q in range(n)) for r in range(n)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression: h then s', [1, [['h', 0], ['s', 0]]], ['+Y']], ['regression: h on y eigenstate', [1, [['h', 0], ['s', 0], ['h', 0]]], ['-Y']], ['repair check: random clifford 1', [1, [['z', 0], ['s', 0], ['x', 0], ['x', 0], ['x', 0], ['z', 0], ['z', 0], ['z', 0]]], ['-Z']], ['control: bell preparation', [2, [['h', 0], ['cx', 0, 1]]], ['+XX', '+ZZ']], ['control: s twice after h', [1, [['h', 0], ['s', 0], ['s', 0]]], ['-X']], ['control: x flips z sign', [1, [['x', 0]]], ['-Z']], ['control: z on plus', [1, [['h', 0], ['z', 0]]], ['-X']]], [['regression: random clifford 11', [2, [['s', 1], ['h', 0], ['cx', 0, 1], ['s', 0], ['x', 0]]], ['-YX', '-ZZ']], ['regression: random clifford 17', [1, [['h', 0], ['s', 0], ['h', 0], ['h', 0], ['x', 0], ['s', 0], ['s', 0]]], ['+Y']], ['repair check: random clifford 3', [1, [['s', 0], ['h', 0], ['h', 0], ['x', 0], ['h', 0], ['h', 0], ['s', 0], ['s', 0]]], ['-Z']], ['control: cx on excited control', [2, [['x', 0], ['cx', 0, 1]]], ['-ZI', '+ZZ']], ['control: ghz', [3, [['h', 0], ['cx', 0, 1], ['cx', 0, 2]]], ['+XXX', '+ZZI', '+ZIZ']], ['control: random clifford 0', [3, [['cx', 1, 2]]], ['+ZII', '+IZI', '+IZZ']], ['control: random clifford 8', [3, [['cx', 0, 1], ['h', 2], ['h', 2], ['h', 0], ['cx', 2, 1], ['h', 2], ['z', 0], ['cx', 1, 2]]], ['-XII', '-XZX', '+IIX']]], [['regression: random clifford 28', [3, [['h', 1], ['cx', 0, 1], ['h', 0], ['cx', 2, 1], ['z', 0], ['x', 0], ['cx', 2, 1], ['h', 1], ['h', 2], ['s', 0], ['h', 0], ['cx', 1, 2]]], ['+YII', '+IZI', '+IIX']], ['regression: random clifford 29', [3, [['h', 2], ['s', 0], ['z', 1], ['h', 0], ['s', 0], ['z', 2], ['x', 1], ['z', 0], ['h', 2]]], ['-YII', '-IZI', '-IIZ']], ['repair check: random clifford 5', [1, [['h', 0], ['h', 0], ['h', 0], ['h', 0], ['z', 0], ['s', 0], ['s', 0], ['s', 0], ['x', 0], ['h', 0], ['x', 0], ['h', 0]]], ['-Z']], ['control: random clifford 10', [1, [['z', 0], ['z', 0], ['s', 0], ['z', 0], ['h', 0], ['h', 0], ['s', 0]]], ['+Z']], ['control: random clifford 12', [1, [['h', 0], ['s', 0], ['h', 0], ['x', 0], ['s', 0], ['x', 0], ['x', 0], ['z', 0], ['h', 0], ['s', 0], ['s', 0]]], ['+Z']], ['control: random clifford 15', [2, [['z', 1], ['cx', 0, 1], ['x', 1], ['h', 1]]], ['+ZI', '-ZX']], ['control: random clifford 16', [1, [['x', 0], ['h', 0], ['h', 0], ['h', 0], ['h', 0], ['z', 0], ['z', 0], ['h', 0], ['x', 0], ['h', 0]]], ['-Z']]], [['regression: random clifford 37', [3, [['z', 0], ['cx', 0, 2], ['s', 1], ['z', 1], ['h', 2], ['cx', 0, 1], ['s', 2], ['cx', 1, 0], ['h', 2], ['cx', 1, 0]]], ['+ZII', '+ZZI', '-ZIY']], ['regression: random clifford 38', [3, [['z', 1], ['h', 0], ['h', 2], ['h', 2], ['cx', 1, 2], ['cx', 2, 1], ['h', 1], ['h', 1], ['cx', 0, 1], ['h', 2], ['cx', 2, 1], ['s', 1], ['x', 0], ['s', 2]]], ['+XYI', '+ZXX', '-ZZZ']], ['repair check: random clifford 7', [3, [['cx', 0, 2], ['cx', 2, 1], ['s', 0], ['cx', 0, 2], ['cx', 2, 1], ['z', 1], ['z', 0], ['h', 1], ['x', 1]]], ['+ZII', '+ZXI', '+IIZ']], ['control: random clifford 19', [2, [['h', 0], ['cx', 1, 0], ['cx', 1, 0], ['cx', 0, 1], ['h', 0], ['cx', 1, 0], ['cx', 1, 0], ['cx', 0, 1], ['cx', 0, 1], ['cx', 1, 0], ['cx', 0, 1]]], ['+XZ', '-YY']], ['control: random clifford 20', [3, [['cx', 2, 0], ['h', 2], ['z', 0], ['cx', 2, 1], ['cx', 0, 2], ['cx', 2, 1]]], ['+ZIX', '+ZZI', '+IIX']], ['control: random clifford 22', [3, [['h', 2], ['h', 0], ['cx', 1, 0], ['s', 1], ['cx', 0, 1], ['cx', 1, 0], ['s', 0], ['cx', 2, 1]]], ['+IXI', '+ZII', '+IXX']], ['control: random clifford 24', [1, [['x', 0]]], ['-Z']]], [['regression: random clifford 52', [1, [['h', 0], ['h', 0], ['s', 0], ['x', 0], ['x', 0], ['x', 0], ['z', 0], ['s', 0], ['h', 0], ['s', 0]]], ['-Y']], ['regression: random clifford 54', [1, [['h', 0], ['h', 0], ['x', 0], ['s', 0], ['h', 0], ['s', 0], ['h', 0], ['h', 0], ['h', 0], ['h', 0]]], ['-Y']], ['repair check: random clifford 13', [1, [['z', 0], ['x', 0], ['z', 0], ['z', 0], ['s', 0], ['x', 0], ['h', 0], ['h', 0], ['z', 0], ['h', 0]]], ['+X']], ['control: random clifford 25', [2, [['cx', 1, 0], ['cx', 1, 0]]], ['+ZI', '+IZ']], ['control: random clifford 27', [2, [['cx', 1, 0], ['x', 0], ['h', 0], ['cx', 1, 0], ['cx', 1, 0], ['cx', 1, 0], ['h', 0], ['cx', 0, 1], ['cx', 0, 1], ['h', 0], ['z', 1], ['h', 1]]], ['-XX', '+IX']], ['control: random clifford 32', [3, [['z', 1], ['x', 1], ['cx', 1, 0], ['cx', 1, 2], ['cx', 2, 1], ['x', 0], ['cx', 1, 2], ['z', 1], ['z', 1], ['cx', 2, 1], ['z', 2], ['x', 0], ['cx', 0, 2]]], ['+IIZ', '-ZIZ', '+ZZZ']], ['control: random clifford 34', [1, [['z', 0], ['h', 0], ['z', 0], ['h', 0]]], ['-Z']]]]\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-stabilizer-tableau-phase-gate-update-order","generated_at":"2026-09-29T14:51:31.725812+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Stabilizer simulators verify Clifford circuits and error-correction encoders; a phase-bit rule error yields wrong syndromes.","root_cause":"The S rule adds x into z first and then computes the sign from the updated bits.","sha256":"a1dbe0341a54ca8dd06d70b4e15ff6fdb607c223639438608cdd710b1fefbbd8","title":"Tableau S gate updates z before computing the sign · 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":38.88,"exit_code":1,"observations":[{"actual":["+Y"],"check":"regression: h then s","expected":["+Y"],"passed":true},{"actual":["-Y"],"check":"regression: h on y eigenstate","expected":["-Y"],"passed":true},{"actual":["+Z"],"check":"repair check: random clifford 1","expected":["-Z"],"passed":false},{"actual":["+XX","+ZZ"],"check":"control: bell preparation","expected":["+XX","+ZZ"],"passed":true},{"actual":["-X"],"check":"control: s twice after h","expected":["-X"],"passed":true},{"actual":["-Z"],"check":"control: x flips z sign","expected":["-Z"],"passed":true},{"actual":["-X"],"check":"control: z on plus","expected":["-X"],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: h then s\", \"actual\": [\"+Y\"], \"expected\": [\"+Y\"], \"passed\": true}, {\"check\": \"regression: h on y eigenstate\", \"actual\": [\"-Y\"], \"expected\": [\"-Y\"], \"passed\": true}, {\"check\": \"repair check: random clifford 1\", \"actual\": [\"+Z\"], \"expected\": [\"-Z\"], \"passed\": false}, {\"check\": \"control: bell preparation\", \"actual\": [\"+XX\", \"+ZZ\"], \"expected\": [\"+XX\", \"+ZZ\"], \"passed\": true}, {\"check\": \"control: s twice after h\", \"actual\": [\"-X\"], \"expected\": [\"-X\"], \"passed\": true}, {\"check\": \"control: x flips z sign\", \"actual\": [\"-Z\"], \"expected\": [\"-Z\"], \"passed\": true}, {\"check\": \"control: z on plus\", \"actual\": [\"-X\"], \"expected\": [\"-X\"], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":45.242,"exit_code":1,"observations":[{"actual":["-Y"],"check":"regression: h then s","expected":["+Y"],"passed":false},{"actual":["+Y"],"check":"regression: h on y eigenstate","expected":["-Y"],"passed":false},{"actual":["-Z"],"check":"repair check: random clifford 1","expected":["-Z"],"passed":true},{"actual":["+XX","+ZZ"],"check":"control: bell preparation","expected":["+XX","+ZZ"],"passed":true},{"actual":["-X"],"check":"control: s twice after h","expected":["-X"],"passed":true},{"actual":["-Z"],"check":"control: x flips z sign","expected":["-Z"],"passed":true},{"actual":["-X"],"check":"control: z on plus","expected":["-X"],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: h then s\", \"actual\": [\"-Y\"], \"expected\": [\"+Y\"], \"passed\": false}, {\"check\": \"regression: h on y eigenstate\", \"actual\": [\"+Y\"], \"expected\": [\"-Y\"], \"passed\": false}, {\"check\": \"repair check: random clifford 1\", \"actual\": [\"-Z\"], \"expected\": [\"-Z\"], \"passed\": true}, {\"check\": \"control: bell preparation\", \"actual\": [\"+XX\", \"+ZZ\"], \"expected\": [\"+XX\", \"+ZZ\"], \"passed\": true}, {\"check\": \"control: s twice after h\", \"actual\": [\"-X\"], \"expected\": [\"-X\"], \"passed\": true}, {\"check\": \"control: x flips z sign\", \"actual\": [\"-Z\"], \"expected\": [\"-Z\"], \"passed\": true}, {\"check\": \"control: z on plus\", \"actual\": [\"-X\"], \"expected\": [\"-X\"], \"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."}}