{"abstract":"X*Z is reported as +iY instead of -iY, so commutation-derived signs are wrong.","category":"Quantum circuit simulation","checks":7,"contract":"Input [[k1, s1], [k2, s2]] representing i**k1 * s1 and i**k2 * s2 (Pauli strings over IXYZ, equal length). Return [k mod 4, s] with i**k * s = (i**k1 s1)(i**k2 s2), using XY=iZ, YZ=iX, ZX=iY and the reversed products with -i. Error \"length-mismatch\".","contract_signature":"x","evaluation_group":"w2-quantum_circuit_simulation-pauli-product-phase","failed_approach":"The attempted repair sets both ZX and XZ to power 3, breaking the cyclic ZX = iY entry.","family":"w2-quantum_circuit_simulation-pauli-product-phase-xz-product-sign","id":"FA-90961","implementations":{"attempt":{"sha256":"34e23a33535ab63c20a6ea71eabf5d86c31f30180d87e401e4f108103cdbc30c","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(x):\n    (k1, s1), (k2, s2) = x\n    if len(s1) != len(s2):\n        return 'length-mismatch'\n    table = {('X', 'Y'): (1, 'Z'), ('Y', 'Z'): (1, 'X'), ('Z', 'X'): (3, 'Y'),\n             ('Y', 'X'): (3, 'Z'), ('Z', 'Y'): (3, 'X'), ('X', 'Z'): (3, 'Y')}\n    k = k1 + k2\n    out = []\n    for a, b in zip(s1, s2):\n        if a == 'I':\n            out.append(b)\n        elif b == 'I':\n            out.append(a)\n        elif a == b:\n            out.append('I')\n        else:\n            dk, c = table[(a, b)]\n            k += dk\n            out.append(c)\n    return [k % 4, ''.join(out)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression: X times Z', [[0, 'X'], [0, 'Z']], [3, 'Y']], ['regression: random product 4', [[0, 'YXY'], [1, 'IZZ']], [1, 'YYX']], ['repair check: Z times X', [[0, 'Z'], [0, 'X']], [1, 'Y']], ['control: X times Y', [[0, 'X'], [0, 'Y']], [1, 'Z']], ['control: Y times X', [[0, 'Y'], [0, 'X']], [3, 'Z']], ['control: square of Y', [[0, 'Y'], [0, 'Y']], [0, 'I']], ['control: identity factors', [[1, 'II'], [2, 'IZ']], [3, 'IZ']]], [['regression: random product 11', [[-2, 'ZXI'], [3, 'IZX']], [0, 'ZYX']], ['regression: random product 22', [[0, 'XYYI'], [1, 'ZZZX']], [2, 'YXXX']], ['repair check: random product 1', [[-2, 'ZZI'], [2, 'ZXI']], [1, 'IYI']], ['control: anticommuting pair twice', [[0, 'XY'], [0, 'YX']], [0, 'ZZ']], ['control: length mismatch', [[0, 'X'], [0, 'XY']], 'length-mismatch'], ['control: phases wrap', [[3, 'XX'], [3, 'ZZ']], [0, 'YY']], ['control: random product 0', [[0, 'YY'], [2, 'ZY']], [3, 'XI']]], [['regression: random product 48', [[-2, 'ZIXI'], [1, 'ZIZX']], [2, 'IIYX']], ['regression: X times Z', [[0, 'X'], [0, 'Z']], [3, 'Y']], ['repair check: random product 13', [[-1, 'Z'], [3, 'X']], [3, 'Y']], ['control: random product 2', [[0, 'Y'], [1, 'X']], [0, 'Z']], ['control: random product 3', [[1, 'Y'], [0, 'Z']], [2, 'X']], ['control: random product 5', [[0, 'YIXX'], [2, 'ZIYY']], [1, 'XIZZ']], ['control: random product 6', [[0, 'Z'], [0, 'Z']], [0, 'I']]], [['regression: random product 10', [[1, 'XIZX'], [0, 'IYIZ']], [0, 'XYZY']], ['regression: random product 11', [[-2, 'ZXI'], [3, 'IZX']], [0, 'ZYX']], ['repair check: random product 15', [[0, 'YYZI'], [0, 'XYXZ']], [0, 'ZIYZ']], ['control: random product 7', [[3, 'Z'], [2, 'Y']], [0, 'X']], ['control: random product 9', [[0, 'I'], [3, 'I']], [3, 'I']], ['control: random product 12', [[-2, 'ZXIX'], [1, 'ZYXX']], [0, 'IZXI']], ['control: random product 16', [[-1, 'YZI'], [2, 'ZIX']], [2, 'XZX']]], [['regression: random product 38', [[0, 'IIIX'], [1, 'YXYZ']], [0, 'YXYY']], ['regression: random product 48', [[-2, 'ZIXI'], [1, 'ZIZX']], [2, 'IIYX']], ['repair check: random product 37', [[-2, 'IIZ'], [2, 'XZX']], [1, 'XZY']], ['control: random product 17', [[3, 'X'], [0, 'X']], [3, 'I']], ['control: random product 18', [[1, 'XX'], [1, 'YY']], [0, 'ZZ']], ['control: random product 19', [[2, 'I'], [2, 'Y']], [0, 'Y']], ['control: random product 20', [[2, 'III'], [1, 'ZZZ']], [3, 'ZZZ']]]]\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":"e13a5d1e9f86a289da9a72ce42a77a7e592e30c9e57f9e6ab66ea4a6b9957757","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(x):\n    (k1, s1), (k2, s2) = x\n    if len(s1) != len(s2):\n        return 'length-mismatch'\n    table = {('X', 'Y'): (1, 'Z'), ('Y', 'Z'): (1, 'X'), ('Z', 'X'): (1, 'Y'),\n             ('Y', 'X'): (3, 'Z'), ('Z', 'Y'): (3, 'X'), ('X', 'Z'): (1, 'Y')}\n    k = k1 + k2\n    out = []\n    for a, b in zip(s1, s2):\n        if a == 'I':\n            out.append(b)\n        elif b == 'I':\n            out.append(a)\n        elif a == b:\n            out.append('I')\n        else:\n            dk, c = table[(a, b)]\n            k += dk\n            out.append(c)\n    return [k % 4, ''.join(out)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression: X times Z', [[0, 'X'], [0, 'Z']], [3, 'Y']], ['regression: random product 4', [[0, 'YXY'], [1, 'IZZ']], [1, 'YYX']], ['repair check: Z times X', [[0, 'Z'], [0, 'X']], [1, 'Y']], ['control: X times Y', [[0, 'X'], [0, 'Y']], [1, 'Z']], ['control: Y times X', [[0, 'Y'], [0, 'X']], [3, 'Z']], ['control: square of Y', [[0, 'Y'], [0, 'Y']], [0, 'I']], ['control: identity factors', [[1, 'II'], [2, 'IZ']], [3, 'IZ']]], [['regression: random product 11', [[-2, 'ZXI'], [3, 'IZX']], [0, 'ZYX']], ['regression: random product 22', [[0, 'XYYI'], [1, 'ZZZX']], [2, 'YXXX']], ['repair check: random product 1', [[-2, 'ZZI'], [2, 'ZXI']], [1, 'IYI']], ['control: anticommuting pair twice', [[0, 'XY'], [0, 'YX']], [0, 'ZZ']], ['control: length mismatch', [[0, 'X'], [0, 'XY']], 'length-mismatch'], ['control: phases wrap', [[3, 'XX'], [3, 'ZZ']], [0, 'YY']], ['control: random product 0', [[0, 'YY'], [2, 'ZY']], [3, 'XI']]], [['regression: random product 48', [[-2, 'ZIXI'], [1, 'ZIZX']], [2, 'IIYX']], ['regression: X times Z', [[0, 'X'], [0, 'Z']], [3, 'Y']], ['repair check: random product 13', [[-1, 'Z'], [3, 'X']], [3, 'Y']], ['control: random product 2', [[0, 'Y'], [1, 'X']], [0, 'Z']], ['control: random product 3', [[1, 'Y'], [0, 'Z']], [2, 'X']], ['control: random product 5', [[0, 'YIXX'], [2, 'ZIYY']], [1, 'XIZZ']], ['control: random product 6', [[0, 'Z'], [0, 'Z']], [0, 'I']]], [['regression: random product 10', [[1, 'XIZX'], [0, 'IYIZ']], [0, 'XYZY']], ['regression: random product 11', [[-2, 'ZXI'], [3, 'IZX']], [0, 'ZYX']], ['repair check: random product 15', [[0, 'YYZI'], [0, 'XYXZ']], [0, 'ZIYZ']], ['control: random product 7', [[3, 'Z'], [2, 'Y']], [0, 'X']], ['control: random product 9', [[0, 'I'], [3, 'I']], [3, 'I']], ['control: random product 12', [[-2, 'ZXIX'], [1, 'ZYXX']], [0, 'IZXI']], ['control: random product 16', [[-1, 'YZI'], [2, 'ZIX']], [2, 'XZX']]], [['regression: random product 38', [[0, 'IIIX'], [1, 'YXYZ']], [0, 'YXYY']], ['regression: random product 48', [[-2, 'ZIXI'], [1, 'ZIZX']], [2, 'IIYX']], ['repair check: random product 37', [[-2, 'IIZ'], [2, 'XZX']], [1, 'XZY']], ['control: random product 17', [[3, 'X'], [0, 'X']], [3, 'I']], ['control: random product 18', [[1, 'XX'], [1, 'YY']], [0, 'ZZ']], ['control: random product 19', [[2, 'I'], [2, 'Y']], [0, 'Y']], ['control: random product 20', [[2, 'III'], [1, 'ZZZ']], [3, 'ZZZ']]]]\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-pauli-product-phase-xz-product-sign","generated_at":"2026-09-29T14:51:31.559158+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Pauli-frame and stabilizer bookkeeping multiply Pauli strings constantly; one phase slip flips measurement signs.","root_cause":"The lookup entry for (X, Z) stores phase power 1 instead of 3.","sha256":"df7e7fb0ea225bd80ff438ed13fd8a360fd399ecfbb7c438dc9d44ef83e8ccd9","title":"Pauli product table gives XZ a +i phase · 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":38.375,"exit_code":1,"observations":[{"actual":[3,"Y"],"check":"regression: X times Z","expected":[3,"Y"],"passed":true},{"actual":[1,"YYX"],"check":"regression: random product 4","expected":[1,"YYX"],"passed":true},{"actual":[3,"Y"],"check":"repair check: Z times X","expected":[1,"Y"],"passed":false},{"actual":[1,"Z"],"check":"control: X times Y","expected":[1,"Z"],"passed":true},{"actual":[3,"Z"],"check":"control: Y times X","expected":[3,"Z"],"passed":true},{"actual":[0,"I"],"check":"control: square of Y","expected":[0,"I"],"passed":true},{"actual":[3,"IZ"],"check":"control: identity factors","expected":[3,"IZ"],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: X times Z\", \"actual\": [3, \"Y\"], \"expected\": [3, \"Y\"], \"passed\": true}, {\"check\": \"regression: random product 4\", \"actual\": [1, \"YYX\"], \"expected\": [1, \"YYX\"], \"passed\": true}, {\"check\": \"repair check: Z times X\", \"actual\": [3, \"Y\"], \"expected\": [1, \"Y\"], \"passed\": false}, {\"check\": \"control: X times Y\", \"actual\": [1, \"Z\"], \"expected\": [1, \"Z\"], \"passed\": true}, {\"check\": \"control: Y times X\", \"actual\": [3, \"Z\"], \"expected\": [3, \"Z\"], \"passed\": true}, {\"check\": \"control: square of Y\", \"actual\": [0, \"I\"], \"expected\": [0, \"I\"], \"passed\": true}, {\"check\": \"control: identity factors\", \"actual\": [3, \"IZ\"], \"expected\": [3, \"IZ\"], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":37.192,"exit_code":1,"observations":[{"actual":[1,"Y"],"check":"regression: X times Z","expected":[3,"Y"],"passed":false},{"actual":[3,"YYX"],"check":"regression: random product 4","expected":[1,"YYX"],"passed":false},{"actual":[1,"Y"],"check":"repair check: Z times X","expected":[1,"Y"],"passed":true},{"actual":[1,"Z"],"check":"control: X times Y","expected":[1,"Z"],"passed":true},{"actual":[3,"Z"],"check":"control: Y times X","expected":[3,"Z"],"passed":true},{"actual":[0,"I"],"check":"control: square of Y","expected":[0,"I"],"passed":true},{"actual":[3,"IZ"],"check":"control: identity factors","expected":[3,"IZ"],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: X times Z\", \"actual\": [1, \"Y\"], \"expected\": [3, \"Y\"], \"passed\": false}, {\"check\": \"regression: random product 4\", \"actual\": [3, \"YYX\"], \"expected\": [1, \"YYX\"], \"passed\": false}, {\"check\": \"repair check: Z times X\", \"actual\": [1, \"Y\"], \"expected\": [1, \"Y\"], \"passed\": true}, {\"check\": \"control: X times Y\", \"actual\": [1, \"Z\"], \"expected\": [1, \"Z\"], \"passed\": true}, {\"check\": \"control: Y times X\", \"actual\": [3, \"Z\"], \"expected\": [3, \"Z\"], \"passed\": true}, {\"check\": \"control: square of Y\", \"actual\": [0, \"I\"], \"expected\": [0, \"I\"], \"passed\": true}, {\"check\": \"control: identity factors\", \"actual\": [3, \"IZ\"], \"expected\": [3, \"IZ\"], \"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."}}