{"abstract":"Damping |1> with g = 0.5 gives z = -1 instead of 0; the channel pushes population the wrong way.","category":"Quantum circuit simulation","checks":7,"contract":"Input [[x, y, z], channels] (decimal strings). Apply in order: depol p (r -> (1-p) r), dephase p (x, y scaled by 1-2p), bitflip p (y, z scaled by 1-2p), ampdamp g (x, y scaled by sqrt(1-g), z -> g + (1-g) z toward |0> at z=+1), h ((x,y,z) -> (z,-y,x)), s ((x,y) -> (-y,x)), x ((y,z) -> (-y,-z)). Return the final vector rounded to 6 decimals.","evaluation_group":"w2-quantum_circuit_simulation-bloch-noise-channels","failed_approach":"The attempted repair uses g + sqrt(1-g) z, borrowing the coherence scale for the population.","family":"w2-quantum_circuit_simulation-bloch-noise-channels-damping-fixed-point","id":"FA-91241","implementations":{"attempt":{"sha256":"6d2abb5cf6199f851046f5eac5f0866bffaa5f5bcbcb578208e4d064454911f1","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    bx, by, bz = [float(v) for v in x[0]]\n    for ch in x[1]:\n        kind = ch[0]\n        if kind == 'depol':\n            p = float(ch[1])\n            bx, by, bz = (1 - p) * bx, (1 - p) * by, (1 - p) * bz\n        elif kind == 'dephase':\n            p = float(ch[1])\n            bx, by = (1 - 2 * p) * bx, (1 - 2 * p) * by\n        elif kind == 'bitflip':\n            p = float(ch[1])\n            by, bz = (1 - 2 * p) * by, (1 - 2 * p) * bz\n        elif kind == 'ampdamp':\n            g = float(ch[1])\n            s = math.sqrt(1 - g)\n            bx, by, bz = s * bx, s * by, g + s * bz\n        elif kind == 'h':\n            bx, by, bz = bz, -by, bx\n        elif kind == 's':\n            bx, by = -by, bx\n        elif kind == 'x':\n            by, bz = -by, -bz\n    return [round(v, 6) + 0.0 for v in (bx, by, bz)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression: amplitude damping from |1>', [['0', '0', '-1'], [['ampdamp', '0.5']]], [0.0, 0.0, 0.0]], ['regression: random channel chain 1', [['0.2317', '0.4662', '-0.3393'], [['h'], ['ampdamp', '0.1'], ['h'], ['h']]], [-0.321888, -0.442276, 0.30853]], ['regression: random channel chain 7', [['0.2531', '-0.7095', '0.5685'], [['ampdamp', '0.2'], ['bitflip', '0.1'], ['dephase', '0.2'], ['x']]], [0.135828, 0.304606, -0.52384]], ['control: dephasing plus state', [['1', '0', '0'], [['dephase', '0.25']]], [0.5, 0.0, 0.0]], ['control: bit flip on |0>', [['0', '0', '1'], [['bitflip', '0.25']]], [0.0, 0.0, 0.5]], ['control: hadamard on y', [['0', '1', '0'], [['h']]], [0.0, -1.0, 0.0]], ['control: s on x', [['1', '0', '0'], [['s']]], [0.0, 1.0, 0.0]]], [['regression: random channel chain 9', [['0.2932', '0.3716', '-0.2949'], [['x'], ['bitflip', '0.2'], ['ampdamp', '0.3']]], [0.245309, -0.186542, 0.423858]], ['regression: random channel chain 10', [['0.0325', '0.65', '0.2184'], [['depol', '0.2'], ['ampdamp', '0.05'], ['bitflip', '0.05'], ['h']]], [0.194386, -0.45615, 0.025342]], ['regression: random channel chain 7', [['0.2531', '-0.7095', '0.5685'], [['ampdamp', '0.2'], ['bitflip', '0.1'], ['dephase', '0.2'], ['x']]], [0.135828, 0.304606, -0.52384]], ['control: x on |+i>', [['0', '1', '0'], [['x']]], [0.0, -1.0, 0.0]], ['control: depolarize', [['0.6', '0', '0.8'], [['depol', '0.1']]], [0.54, 0.0, 0.72]], ['control: random channel chain 0', [['0.0691', '-0.4004', '0.0791'], [['dephase', '0.2'], ['bitflip', '0.3'], ['s']]], [0.096096, 0.04146, 0.03164]], ['control: random channel chain 2', [['0.0766', '-0.6718', '0.0357'], [['s']]], [0.6718, 0.0766, 0.0357]]], [['regression: random channel chain 16', [['0.0125', '-0.322', '0.0664'], [['h'], ['ampdamp', '0.05']]], [0.064719, 0.313847, 0.061875]], ['regression: random channel chain 26', [['-0.4382', '0.0441', '-0.3433'], [['depol', '0.1'], ['bitflip', '0.5'], ['ampdamp', '0.2']]], [-0.352744, 0.0, 0.2]], ['regression: random channel chain 10', [['0.0325', '0.65', '0.2184'], [['depol', '0.2'], ['ampdamp', '0.05'], ['bitflip', '0.05'], ['h']]], [0.194386, -0.45615, 0.025342]], ['control: random channel chain 3', [['0.2389', '-0.1722', '0.2639'], [['dephase', '0.1'], ['bitflip', '0.2'], ['x']]], [0.19112, 0.082656, -0.15834]], ['control: random channel chain 4', [['-0.0477', '-0.2431', '-0.2391'], [['x'], ['depol', '0.5'], ['x'], ['bitflip', '0.1']]], [-0.02385, -0.09724, -0.09564]], ['control: random channel chain 5', [['-0.4729', '-0.0797', '-0.3692'], [['h'], ['s'], ['dephase', '0.1']]], [-0.06376, -0.29536, -0.4729]], ['control: random channel chain 6', [['0.394', '0.1792', '-0.6952'], [['x']]], [0.394, -0.1792, 0.6952]]], [['regression: random channel chain 28', [['-0.4727', '0.0368', '-0.4788'], [['h'], ['ampdamp', '0.2']]], [-0.428252, -0.032915, -0.17816]], ['regression: random channel chain 32', [['0.089', '-0.4706', '-0.3715'], [['ampdamp', '0.2'], ['bitflip', '0.3'], ['ampdamp', '0.3']]], [0.066602, -0.140866, 0.272784]], ['regression: random channel chain 16', [['0.0125', '-0.322', '0.0664'], [['h'], ['ampdamp', '0.05']]], [0.064719, 0.313847, 0.061875]], ['control: random channel chain 8', [['0.255', '-0.4128', '-0.2664'], [['x'], ['dephase', '0.05'], ['h'], ['depol', '0.05']]], [0.25308, -0.352944, 0.218025]], ['control: random channel chain 11', [['0.2608', '0.1361', '-0.2576'], [['x'], ['depol', '0.05']]], [0.24776, -0.129295, 0.24472]], ['control: random channel chain 12', [['0.3838', '0.2434', '0.1995'], [['x'], ['s'], ['depol', '0.5'], ['dephase', '0.05']]], [0.10953, 0.17271, -0.09975]], ['control: random channel chain 13', [['-0.3842', '-0.4838', '0.2088'], [['h'], ['depol', '0.05']]], [0.19836, 0.45961, -0.36499]]], [['regression: random channel chain 36', [['0.2754', '-0.5471', '-0.3106'], [['dephase', '0.5'], ['s'], ['ampdamp', '0.3'], ['x']]], [0.0, 0.0, -0.08258]], ['regression: random channel chain 41', [['0.1671', '-0.4264', '-0.1284'], [['ampdamp', '0.1'], ['bitflip', '0.3']]], [0.158525, -0.161807, -0.006224]], ['regression: random channel chain 28', [['-0.4727', '0.0368', '-0.4788'], [['h'], ['ampdamp', '0.2']]], [-0.428252, -0.032915, -0.17816]], ['control: random channel chain 14', [['-0.1159', '-0.3227', '0.1975'], [['bitflip', '0.3'], ['h'], ['bitflip', '0.1'], ['dephase', '0.3']]], [0.0316, 0.041306, -0.09272]], ['control: random channel chain 17', [['0.1445', '-0.5422', '-0.0485'], [['s'], ['s'], ['dephase', '0.2'], ['dephase', '0.05']]], [-0.07803, 0.292788, -0.0485]], ['control: random channel chain 18', [['-0.3894', '0.6131', '-0.5953'], [['bitflip', '0.05']]], [-0.3894, 0.55179, -0.53577]], ['control: random channel chain 19', [['0.6907', '-0.2493', '0.6355'], [['depol', '0.5'], ['dephase', '0.05'], ['depol', '0.05']]], [0.295274, -0.106576, 0.301862]]]]\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":"a805e4b31b6226f21b0f59c33aee3cec9bfbc19fc78f26e5dd0f55a093d3703e","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    bx, by, bz = [float(v) for v in x[0]]\n    for ch in x[1]:\n        kind = ch[0]\n        if kind == 'depol':\n            p = float(ch[1])\n            bx, by, bz = (1 - p) * bx, (1 - p) * by, (1 - p) * bz\n        elif kind == 'dephase':\n            p = float(ch[1])\n            bx, by = (1 - 2 * p) * bx, (1 - 2 * p) * by\n        elif kind == 'bitflip':\n            p = float(ch[1])\n            by, bz = (1 - 2 * p) * by, (1 - 2 * p) * bz\n        elif kind == 'ampdamp':\n            g = float(ch[1])\n            s = math.sqrt(1 - g)\n            bx, by, bz = s * bx, s * by, (1 - g) * bz - g\n        elif kind == 'h':\n            bx, by, bz = bz, -by, bx\n        elif kind == 's':\n            bx, by = -by, bx\n        elif kind == 'x':\n            by, bz = -by, -bz\n    return [round(v, 6) + 0.0 for v in (bx, by, bz)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression: amplitude damping from |1>', [['0', '0', '-1'], [['ampdamp', '0.5']]], [0.0, 0.0, 0.0]], ['regression: random channel chain 1', [['0.2317', '0.4662', '-0.3393'], [['h'], ['ampdamp', '0.1'], ['h'], ['h']]], [-0.321888, -0.442276, 0.30853]], ['regression: random channel chain 7', [['0.2531', '-0.7095', '0.5685'], [['ampdamp', '0.2'], ['bitflip', '0.1'], ['dephase', '0.2'], ['x']]], [0.135828, 0.304606, -0.52384]], ['control: dephasing plus state', [['1', '0', '0'], [['dephase', '0.25']]], [0.5, 0.0, 0.0]], ['control: bit flip on |0>', [['0', '0', '1'], [['bitflip', '0.25']]], [0.0, 0.0, 0.5]], ['control: hadamard on y', [['0', '1', '0'], [['h']]], [0.0, -1.0, 0.0]], ['control: s on x', [['1', '0', '0'], [['s']]], [0.0, 1.0, 0.0]]], [['regression: random channel chain 9', [['0.2932', '0.3716', '-0.2949'], [['x'], ['bitflip', '0.2'], ['ampdamp', '0.3']]], [0.245309, -0.186542, 0.423858]], ['regression: random channel chain 10', [['0.0325', '0.65', '0.2184'], [['depol', '0.2'], ['ampdamp', '0.05'], ['bitflip', '0.05'], ['h']]], [0.194386, -0.45615, 0.025342]], ['regression: random channel chain 7', [['0.2531', '-0.7095', '0.5685'], [['ampdamp', '0.2'], ['bitflip', '0.1'], ['dephase', '0.2'], ['x']]], [0.135828, 0.304606, -0.52384]], ['control: x on |+i>', [['0', '1', '0'], [['x']]], [0.0, -1.0, 0.0]], ['control: depolarize', [['0.6', '0', '0.8'], [['depol', '0.1']]], [0.54, 0.0, 0.72]], ['control: random channel chain 0', [['0.0691', '-0.4004', '0.0791'], [['dephase', '0.2'], ['bitflip', '0.3'], ['s']]], [0.096096, 0.04146, 0.03164]], ['control: random channel chain 2', [['0.0766', '-0.6718', '0.0357'], [['s']]], [0.6718, 0.0766, 0.0357]]], [['regression: random channel chain 16', [['0.0125', '-0.322', '0.0664'], [['h'], ['ampdamp', '0.05']]], [0.064719, 0.313847, 0.061875]], ['regression: random channel chain 26', [['-0.4382', '0.0441', '-0.3433'], [['depol', '0.1'], ['bitflip', '0.5'], ['ampdamp', '0.2']]], [-0.352744, 0.0, 0.2]], ['regression: random channel chain 10', [['0.0325', '0.65', '0.2184'], [['depol', '0.2'], ['ampdamp', '0.05'], ['bitflip', '0.05'], ['h']]], [0.194386, -0.45615, 0.025342]], ['control: random channel chain 3', [['0.2389', '-0.1722', '0.2639'], [['dephase', '0.1'], ['bitflip', '0.2'], ['x']]], [0.19112, 0.082656, -0.15834]], ['control: random channel chain 4', [['-0.0477', '-0.2431', '-0.2391'], [['x'], ['depol', '0.5'], ['x'], ['bitflip', '0.1']]], [-0.02385, -0.09724, -0.09564]], ['control: random channel chain 5', [['-0.4729', '-0.0797', '-0.3692'], [['h'], ['s'], ['dephase', '0.1']]], [-0.06376, -0.29536, -0.4729]], ['control: random channel chain 6', [['0.394', '0.1792', '-0.6952'], [['x']]], [0.394, -0.1792, 0.6952]]], [['regression: random channel chain 28', [['-0.4727', '0.0368', '-0.4788'], [['h'], ['ampdamp', '0.2']]], [-0.428252, -0.032915, -0.17816]], ['regression: random channel chain 32', [['0.089', '-0.4706', '-0.3715'], [['ampdamp', '0.2'], ['bitflip', '0.3'], ['ampdamp', '0.3']]], [0.066602, -0.140866, 0.272784]], ['regression: random channel chain 16', [['0.0125', '-0.322', '0.0664'], [['h'], ['ampdamp', '0.05']]], [0.064719, 0.313847, 0.061875]], ['control: random channel chain 8', [['0.255', '-0.4128', '-0.2664'], [['x'], ['dephase', '0.05'], ['h'], ['depol', '0.05']]], [0.25308, -0.352944, 0.218025]], ['control: random channel chain 11', [['0.2608', '0.1361', '-0.2576'], [['x'], ['depol', '0.05']]], [0.24776, -0.129295, 0.24472]], ['control: random channel chain 12', [['0.3838', '0.2434', '0.1995'], [['x'], ['s'], ['depol', '0.5'], ['dephase', '0.05']]], [0.10953, 0.17271, -0.09975]], ['control: random channel chain 13', [['-0.3842', '-0.4838', '0.2088'], [['h'], ['depol', '0.05']]], [0.19836, 0.45961, -0.36499]]], [['regression: random channel chain 36', [['0.2754', '-0.5471', '-0.3106'], [['dephase', '0.5'], ['s'], ['ampdamp', '0.3'], ['x']]], [0.0, 0.0, -0.08258]], ['regression: random channel chain 41', [['0.1671', '-0.4264', '-0.1284'], [['ampdamp', '0.1'], ['bitflip', '0.3']]], [0.158525, -0.161807, -0.006224]], ['regression: random channel chain 28', [['-0.4727', '0.0368', '-0.4788'], [['h'], ['ampdamp', '0.2']]], [-0.428252, -0.032915, -0.17816]], ['control: random channel chain 14', [['-0.1159', '-0.3227', '0.1975'], [['bitflip', '0.3'], ['h'], ['bitflip', '0.1'], ['dephase', '0.3']]], [0.0316, 0.041306, -0.09272]], ['control: random channel chain 17', [['0.1445', '-0.5422', '-0.0485'], [['s'], ['s'], ['dephase', '0.2'], ['dephase', '0.05']]], [-0.07803, 0.292788, -0.0485]], ['control: random channel chain 18', [['-0.3894', '0.6131', '-0.5953'], [['bitflip', '0.05']]], [-0.3894, 0.55179, -0.53577]], ['control: random channel chain 19', [['0.6907', '-0.2493', '0.6355'], [['depol', '0.5'], ['dephase', '0.05'], ['depol', '0.05']]], [0.295274, -0.106576, 0.301862]]]]\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"},"fixed":{"sha256":"01e498ba82f3237b120e7febff89c4496002b7f22cb0f211a8e4f9450dc8c92c","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    bx, by, bz = [float(v) for v in x[0]]\n    for ch in x[1]:\n        kind = ch[0]\n        if kind == 'depol':\n            p = float(ch[1])\n            bx, by, bz = (1 - p) * bx, (1 - p) * by, (1 - p) * bz\n        elif kind == 'dephase':\n            p = float(ch[1])\n            bx, by = (1 - 2 * p) * bx, (1 - 2 * p) * by\n        elif kind == 'bitflip':\n            p = float(ch[1])\n            by, bz = (1 - 2 * p) * by, (1 - 2 * p) * bz\n        elif kind == 'ampdamp':\n            g = float(ch[1])\n            s = math.sqrt(1 - g)\n            bx, by, bz = s * bx, s * by, g + (1 - g) * bz\n        elif kind == 'h':\n            bx, by, bz = bz, -by, bx\n        elif kind == 's':\n            bx, by = -by, bx\n        elif kind == 'x':\n            by, bz = -by, -bz\n    return [round(v, 6) + 0.0 for v in (bx, by, bz)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression: amplitude damping from |1>', [['0', '0', '-1'], [['ampdamp', '0.5']]], [0.0, 0.0, 0.0]], ['regression: random channel chain 1', [['0.2317', '0.4662', '-0.3393'], [['h'], ['ampdamp', '0.1'], ['h'], ['h']]], [-0.321888, -0.442276, 0.30853]], ['regression: random channel chain 7', [['0.2531', '-0.7095', '0.5685'], [['ampdamp', '0.2'], ['bitflip', '0.1'], ['dephase', '0.2'], ['x']]], [0.135828, 0.304606, -0.52384]], ['control: dephasing plus state', [['1', '0', '0'], [['dephase', '0.25']]], [0.5, 0.0, 0.0]], ['control: bit flip on |0>', [['0', '0', '1'], [['bitflip', '0.25']]], [0.0, 0.0, 0.5]], ['control: hadamard on y', [['0', '1', '0'], [['h']]], [0.0, -1.0, 0.0]], ['control: s on x', [['1', '0', '0'], [['s']]], [0.0, 1.0, 0.0]]], [['regression: random channel chain 9', [['0.2932', '0.3716', '-0.2949'], [['x'], ['bitflip', '0.2'], ['ampdamp', '0.3']]], [0.245309, -0.186542, 0.423858]], ['regression: random channel chain 10', [['0.0325', '0.65', '0.2184'], [['depol', '0.2'], ['ampdamp', '0.05'], ['bitflip', '0.05'], ['h']]], [0.194386, -0.45615, 0.025342]], ['regression: random channel chain 7', [['0.2531', '-0.7095', '0.5685'], [['ampdamp', '0.2'], ['bitflip', '0.1'], ['dephase', '0.2'], ['x']]], [0.135828, 0.304606, -0.52384]], ['control: x on |+i>', [['0', '1', '0'], [['x']]], [0.0, -1.0, 0.0]], ['control: depolarize', [['0.6', '0', '0.8'], [['depol', '0.1']]], [0.54, 0.0, 0.72]], ['control: random channel chain 0', [['0.0691', '-0.4004', '0.0791'], [['dephase', '0.2'], ['bitflip', '0.3'], ['s']]], [0.096096, 0.04146, 0.03164]], ['control: random channel chain 2', [['0.0766', '-0.6718', '0.0357'], [['s']]], [0.6718, 0.0766, 0.0357]]], [['regression: random channel chain 16', [['0.0125', '-0.322', '0.0664'], [['h'], ['ampdamp', '0.05']]], [0.064719, 0.313847, 0.061875]], ['regression: random channel chain 26', [['-0.4382', '0.0441', '-0.3433'], [['depol', '0.1'], ['bitflip', '0.5'], ['ampdamp', '0.2']]], [-0.352744, 0.0, 0.2]], ['regression: random channel chain 10', [['0.0325', '0.65', '0.2184'], [['depol', '0.2'], ['ampdamp', '0.05'], ['bitflip', '0.05'], ['h']]], [0.194386, -0.45615, 0.025342]], ['control: random channel chain 3', [['0.2389', '-0.1722', '0.2639'], [['dephase', '0.1'], ['bitflip', '0.2'], ['x']]], [0.19112, 0.082656, -0.15834]], ['control: random channel chain 4', [['-0.0477', '-0.2431', '-0.2391'], [['x'], ['depol', '0.5'], ['x'], ['bitflip', '0.1']]], [-0.02385, -0.09724, -0.09564]], ['control: random channel chain 5', [['-0.4729', '-0.0797', '-0.3692'], [['h'], ['s'], ['dephase', '0.1']]], [-0.06376, -0.29536, -0.4729]], ['control: random channel chain 6', [['0.394', '0.1792', '-0.6952'], [['x']]], [0.394, -0.1792, 0.6952]]], [['regression: random channel chain 28', [['-0.4727', '0.0368', '-0.4788'], [['h'], ['ampdamp', '0.2']]], [-0.428252, -0.032915, -0.17816]], ['regression: random channel chain 32', [['0.089', '-0.4706', '-0.3715'], [['ampdamp', '0.2'], ['bitflip', '0.3'], ['ampdamp', '0.3']]], [0.066602, -0.140866, 0.272784]], ['regression: random channel chain 16', [['0.0125', '-0.322', '0.0664'], [['h'], ['ampdamp', '0.05']]], [0.064719, 0.313847, 0.061875]], ['control: random channel chain 8', [['0.255', '-0.4128', '-0.2664'], [['x'], ['dephase', '0.05'], ['h'], ['depol', '0.05']]], [0.25308, -0.352944, 0.218025]], ['control: random channel chain 11', [['0.2608', '0.1361', '-0.2576'], [['x'], ['depol', '0.05']]], [0.24776, -0.129295, 0.24472]], ['control: random channel chain 12', [['0.3838', '0.2434', '0.1995'], [['x'], ['s'], ['depol', '0.5'], ['dephase', '0.05']]], [0.10953, 0.17271, -0.09975]], ['control: random channel chain 13', [['-0.3842', '-0.4838', '0.2088'], [['h'], ['depol', '0.05']]], [0.19836, 0.45961, -0.36499]]], [['regression: random channel chain 36', [['0.2754', '-0.5471', '-0.3106'], [['dephase', '0.5'], ['s'], ['ampdamp', '0.3'], ['x']]], [0.0, 0.0, -0.08258]], ['regression: random channel chain 41', [['0.1671', '-0.4264', '-0.1284'], [['ampdamp', '0.1'], ['bitflip', '0.3']]], [0.158525, -0.161807, -0.006224]], ['regression: random channel chain 28', [['-0.4727', '0.0368', '-0.4788'], [['h'], ['ampdamp', '0.2']]], [-0.428252, -0.032915, -0.17816]], ['control: random channel chain 14', [['-0.1159', '-0.3227', '0.1975'], [['bitflip', '0.3'], ['h'], ['bitflip', '0.1'], ['dephase', '0.3']]], [0.0316, 0.041306, -0.09272]], ['control: random channel chain 17', [['0.1445', '-0.5422', '-0.0485'], [['s'], ['s'], ['dephase', '0.2'], ['dephase', '0.05']]], [-0.07803, 0.292788, -0.0485]], ['control: random channel chain 18', [['-0.3894', '0.6131', '-0.5953'], [['bitflip', '0.05']]], [-0.3894, 0.55179, -0.53577]], ['control: random channel chain 19', [['0.6907', '-0.2493', '0.6355'], [['depol', '0.5'], ['dephase', '0.05'], ['depol', '0.05']]], [0.295274, -0.106576, 0.301862]]]]\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-bloch-noise-channels-damping-fixed-point","generated_at":"2026-09-29T14:51:34.182428+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Single-qubit noise channels on the Bloch ball are the standard sanity model for T1/T2 behaviour; axis or scale slips mislead calibration.","repair":"Use z -> g + (1-g) z so |0> (z = +1) is the fixed point.","root_cause":"The z update is (1-g) z - g, relaxing toward the south pole.","sha256":"ea31dedb92bd3ef7e903980778d6dc4a36aa1792fa9fd1fc1738bd3f514981ac","title":"Amplitude damping relaxes toward |1> · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":44.188,"exit_code":1,"observations":[{"actual":[0.0,0.0,-0.207107],"check":"regression: amplitude damping from |1>","expected":[0.0,0.0,0.0],"passed":false},{"actual":[-0.321888,-0.442276,0.31981],"check":"regression: random channel chain 1","expected":[-0.321888,-0.442276,0.30853],"passed":false},{"actual":[0.135828,0.304606,-0.566785],"check":"regression: random channel chain 7","expected":[0.135828,0.304606,-0.52384],"passed":false},{"actual":[0.5,0.0,0.0],"check":"control: dephasing plus state","expected":[0.5,0.0,0.0],"passed":true},{"actual":[0.0,0.0,0.5],"check":"control: bit flip on |0>","expected":[0.0,0.0,0.5],"passed":true},{"actual":[0.0,-1.0,0.0],"check":"control: hadamard on y","expected":[0.0,-1.0,0.0],"passed":true},{"actual":[0.0,1.0,0.0],"check":"control: s on x","expected":[0.0,1.0,0.0],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: amplitude damping from |1>\", \"actual\": [0.0, 0.0, -0.207107], \"expected\": [0.0, 0.0, 0.0], \"passed\": false}, {\"check\": \"regression: random channel chain 1\", \"actual\": [-0.321888, -0.442276, 0.31981], \"expected\": [-0.321888, -0.442276, 0.30853], \"passed\": false}, {\"check\": \"regression: random channel chain 7\", \"actual\": [0.135828, 0.304606, -0.566785], \"expected\": [0.135828, 0.304606, -0.52384], \"passed\": false}, {\"check\": \"control: dephasing plus state\", \"actual\": [0.5, 0.0, 0.0], \"expected\": [0.5, 0.0, 0.0], \"passed\": true}, {\"check\": \"control: bit flip on |0>\", \"actual\": [0.0, 0.0, 0.5], \"expected\": [0.0, 0.0, 0.5], \"passed\": true}, {\"check\": \"control: hadamard on y\", \"actual\": [0.0, -1.0, 0.0], \"expected\": [0.0, -1.0, 0.0], \"passed\": true}, {\"check\": \"control: s on x\", \"actual\": [0.0, 1.0, 0.0], \"expected\": [0.0, 1.0, 0.0], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":41.209,"exit_code":1,"observations":[{"actual":[0.0,0.0,-1.0],"check":"regression: amplitude damping from |1>","expected":[0.0,0.0,0.0],"passed":false},{"actual":[-0.321888,-0.442276,0.10853],"check":"regression: random channel chain 1","expected":[-0.321888,-0.442276,0.30853],"passed":false},{"actual":[0.135828,0.304606,-0.20384],"check":"regression: random channel chain 7","expected":[0.135828,0.304606,-0.52384],"passed":false},{"actual":[0.5,0.0,0.0],"check":"control: dephasing plus state","expected":[0.5,0.0,0.0],"passed":true},{"actual":[0.0,0.0,0.5],"check":"control: bit flip on |0>","expected":[0.0,0.0,0.5],"passed":true},{"actual":[0.0,-1.0,0.0],"check":"control: hadamard on y","expected":[0.0,-1.0,0.0],"passed":true},{"actual":[0.0,1.0,0.0],"check":"control: s on x","expected":[0.0,1.0,0.0],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: amplitude damping from |1>\", \"actual\": [0.0, 0.0, -1.0], \"expected\": [0.0, 0.0, 0.0], \"passed\": false}, {\"check\": \"regression: random channel chain 1\", \"actual\": [-0.321888, -0.442276, 0.10853], \"expected\": [-0.321888, -0.442276, 0.30853], \"passed\": false}, {\"check\": \"regression: random channel chain 7\", \"actual\": [0.135828, 0.304606, -0.20384], \"expected\": [0.135828, 0.304606, -0.52384], \"passed\": false}, {\"check\": \"control: dephasing plus state\", \"actual\": [0.5, 0.0, 0.0], \"expected\": [0.5, 0.0, 0.0], \"passed\": true}, {\"check\": \"control: bit flip on |0>\", \"actual\": [0.0, 0.0, 0.5], \"expected\": [0.0, 0.0, 0.5], \"passed\": true}, {\"check\": \"control: hadamard on y\", \"actual\": [0.0, -1.0, 0.0], \"expected\": [0.0, -1.0, 0.0], \"passed\": true}, {\"check\": \"control: s on x\", \"actual\": [0.0, 1.0, 0.0], \"expected\": [0.0, 1.0, 0.0], \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":40.283,"exit_code":0,"observations":[{"actual":[0.0,0.0,0.0],"check":"regression: amplitude damping from |1>","expected":[0.0,0.0,0.0],"passed":true},{"actual":[-0.321888,-0.442276,0.30853],"check":"regression: random channel chain 1","expected":[-0.321888,-0.442276,0.30853],"passed":true},{"actual":[0.135828,0.304606,-0.52384],"check":"regression: random channel chain 7","expected":[0.135828,0.304606,-0.52384],"passed":true},{"actual":[0.5,0.0,0.0],"check":"control: dephasing plus state","expected":[0.5,0.0,0.0],"passed":true},{"actual":[0.0,0.0,0.5],"check":"control: bit flip on |0>","expected":[0.0,0.0,0.5],"passed":true},{"actual":[0.0,-1.0,0.0],"check":"control: hadamard on y","expected":[0.0,-1.0,0.0],"passed":true},{"actual":[0.0,1.0,0.0],"check":"control: s on x","expected":[0.0,1.0,0.0],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: amplitude damping from |1>\", \"actual\": [0.0, 0.0, 0.0], \"expected\": [0.0, 0.0, 0.0], \"passed\": true}, {\"check\": \"regression: random channel chain 1\", \"actual\": [-0.321888, -0.442276, 0.30853], \"expected\": [-0.321888, -0.442276, 0.30853], \"passed\": true}, {\"check\": \"regression: random channel chain 7\", \"actual\": [0.135828, 0.304606, -0.52384], \"expected\": [0.135828, 0.304606, -0.52384], \"passed\": true}, {\"check\": \"control: dephasing plus state\", \"actual\": [0.5, 0.0, 0.0], \"expected\": [0.5, 0.0, 0.0], \"passed\": true}, {\"check\": \"control: bit flip on |0>\", \"actual\": [0.0, 0.0, 0.5], \"expected\": [0.0, 0.0, 0.5], \"passed\": true}, {\"check\": \"control: hadamard on y\", \"actual\": [0.0, -1.0, 0.0], \"expected\": [0.0, -1.0, 0.0], \"passed\": true}, {\"check\": \"control: s on x\", \"actual\": [0.0, 1.0, 0.0], \"expected\": [0.0, 1.0, 0.0], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}