FA-90996 / Quantum circuit simulation / Open access

Tableau CNOT sign rule drops the constant term · case 01

The CNOT sign update fires for generators such as X_c Z_t that should keep their sign, and misses X_c Y_t style cases.

Verified by executionVariant 1 · 7 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The CNOT phase formula uses x_a z_b (x_b xor z_a) without the xor 1 from the Aaronson-Gottesman rule.

VERIFIED REPAIR

Use r ^= x_a z_b (x_b xor z_a xor 1).

Unsuccessful approach: The attempted repair restores the xor 1 but reads the target z bit instead of the control z bit in the parity term.

Case 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.

Why this case matters

Stabilizer simulators verify Clifford circuits and error-correction encoders; a phase-bit rule error yields wrong syndromes.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    n, gates = x
    xs = [[0] * n for _ in range(n)]
    zs = [[1 if i == j else 0 for j in range(n)] for i in range(n)]
    rs = [0] * n
    for g in gates:
        op = g[0]
        for row in range(n):
            X, Z = xs[row], zs[row]
            if op == 'h':
                a = g[1]
                rs[row] ^= X[a] & Z[a]
                X[a], Z[a] = Z[a], X[a]
            elif op == 's':
                a = g[1]
                rs[row] ^= X[a] & Z[a]
                Z[a] ^= X[a]
            elif op == 'x':
                rs[row] ^= Z[g[1]]
            elif op == 'z':
                rs[row] ^= X[g[1]]
            elif op == 'cx':
                a, b = g[1], g[2]
                rs[row] ^= X[a] & Z[b] & (X[b] ^ Z[a])
                X[b] ^= X[a]
                Z[a] ^= Z[b]
    letters = {(0, 0): 'I', (1, 0): 'X', (0, 1): 'Z', (1, 1): 'Y'}
    return [('-' if rs[r] else '+') + ''.join(letters[(xs[r][q], zs[r][q])] for q in range(n)) for r in range(n)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: random clifford 18', [3, [['cx', 1, 0], ['z', 0], ['z', 1], ['x', 2], ['h', 0], ['s', 2], ['z', 1], ['z', 2], ['cx', 0, 1], ['z', 1]]], ['+YYI', '+ZZI', '-IIZ']], ['regression: 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']], ['repair check: random clifford 4', [3, [['cx', 1, 2], ['h', 1], ['cx', 1, 0], ['s', 1], ['x', 2], ['cx', 1, 2], ['cx', 1, 2], ['h', 0], ['cx', 0, 2], ['z', 0], ['s', 2], ['h', 2], ['z', 0]]], ['-XZY', '+ZYI', '-IYX']], ['control: bell preparation', [2, [['h', 0], ['cx', 0, 1]]], ['+XX', '+ZZ']], ['control: h then s', [1, [['h', 0], ['s', 0]]], ['+Y']], ['control: s twice after h', [1, [['h', 0], ['s', 0], ['s', 0]]], ['-X']], ['control: x flips z sign', [1, [['x', 0]]], ['-Z']]], [['regression: random clifford 41', [3, [['s', 2], ['s', 0], ['s', 1], ['cx', 1, 2], ['h', 1], ['cx', 2, 1], ['cx', 1, 2], ['h', 1], ['s', 2], ['cx', 1, 0]]], ['+ZZI', '+IZY', '-XYX']], ['regression: random clifford 42', [3, [['h', 2], ['cx', 1, 0], ['h', 2], ['s', 1], ['h', 0], ['cx', 2, 1], ['x', 2], ['x', 2], ['cx', 0, 2], ['h', 0], ['cx', 0, 2]]], ['-XZZ', '-YZY', '-YIY']], ['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']], ['control: z on plus', [1, [['h', 0], ['z', 0]]], ['-X']], ['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: h on y eigenstate', [1, [['h', 0], ['s', 0], ['h', 0]]], ['-Y']]], [['regression: random clifford 49', [2, [['cx', 0, 1], ['x', 1], ['h', 0], ['z', 1], ['cx', 0, 1], ['cx', 1, 0], ['cx', 1, 0]]], ['+XX', '+YY']], ['regression: random clifford 51', [2, [['cx', 0, 1], ['h', 0], ['cx', 1, 0], ['h', 0], ['x', 1], ['x', 0], ['cx', 0, 1], ['cx', 0, 1], ['h', 0], ['cx', 0, 1], ['x', 1]]], ['-XX', '+YY']], ['regression: random clifford 42', [3, [['h', 2], ['cx', 1, 0], ['h', 2], ['s', 1], ['h', 0], ['cx', 2, 1], ['x', 2], ['x', 2], ['cx', 0, 2], ['h', 0], ['cx', 0, 2]]], ['-XZZ', '-YZY', '-YIY']], ['control: random clifford 0', [3, [['cx', 1, 2]]], ['+ZII', '+IZI', '+IZZ']], ['control: random clifford 1', [1, [['z', 0], ['s', 0], ['x', 0], ['x', 0], ['x', 0], ['z', 0], ['z', 0], ['z', 0]]], ['-Z']], ['control: random clifford 2', [3, [['cx', 0, 2], ['z', 2], ['s', 2], ['h', 0], ['cx', 2, 1], ['x', 1], ['cx', 1, 0], ['x', 1], ['x', 1], ['z', 0], ['cx', 2, 1], ['h', 1], ['h', 0]]], ['-ZII', '-IXI', '-ZIZ']], ['control: random clifford 3', [1, [['s', 0], ['h', 0], ['h', 0], ['x', 0], ['h', 0], ['h', 0], ['s', 0], ['s', 0]]], ['-Z']]], [['regression: random clifford 18', [3, [['cx', 1, 0], ['z', 0], ['z', 1], ['x', 2], ['h', 0], ['s', 2], ['z', 1], ['z', 2], ['cx', 0, 1], ['z', 1]]], ['+YYI', '+ZZI', '-IIZ']], ['regression: 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']], ['regression: random clifford 45', [2, [['z', 1], ['h', 0], ['cx', 0, 1], ['cx', 1, 0], ['cx', 0, 1], ['s', 1], ['z', 0], ['h', 0], ['s', 1], ['z', 1], ['cx', 0, 1], ['h', 1], ['cx', 0, 1], ['z', 1]]], ['+ZZ', '+YY']], ['control: 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 6', [1, [['h', 0], ['z', 0], ['h', 0], ['z', 0], ['x', 0], ['h', 0], ['h', 0], ['h', 0], ['h', 0], ['h', 0], ['h', 0], ['s', 0], ['x', 0]]], ['-Z']], ['control: 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 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 41', [3, [['s', 2], ['s', 0], ['s', 1], ['cx', 1, 2], ['h', 1], ['cx', 2, 1], ['cx', 1, 2], ['h', 1], ['s', 2], ['cx', 1, 0]]], ['+ZZI', '+IZY', '-XYX']], ['regression: random clifford 42', [3, [['h', 2], ['cx', 1, 0], ['h', 2], ['s', 1], ['h', 0], ['cx', 2, 1], ['x', 2], ['x', 2], ['cx', 0, 2], ['h', 0], ['cx', 0, 2]]], ['-XZZ', '-YZY', '-YIY']], ['regression: random clifford 51', [2, [['cx', 0, 1], ['h', 0], ['cx', 1, 0], ['h', 0], ['x', 1], ['x', 0], ['cx', 0, 1], ['cx', 0, 1], ['h', 0], ['cx', 0, 1], ['x', 1]]], ['-XX', '+YY']], ['control: random clifford 9', [2, [['cx', 1, 0], ['cx', 1, 0], ['x', 0], ['s', 0], ['cx', 1, 0], ['h', 1], ['x', 0], ['z', 1], ['cx', 0, 1]]], ['-ZX', '-IX']], ['control: random clifford 10', [1, [['z', 0], ['z', 0], ['s', 0], ['z', 0], ['h', 0], ['h', 0], ['s', 0]]], ['+Z']], ['control: random clifford 11', [2, [['s', 1], ['h', 0], ['cx', 0, 1], ['s', 0], ['x', 0]]], ['-YX', '-ZZ']], ['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']]]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
regression: random clifford 18	`['-YYI', '+ZZI', '-IIZ']`	`['+YYI', '+ZZI', '-IIZ']`	Failed
regression: random clifford 19	`['+XZ', '+YY']`	`['+XZ', '-YY']`	Failed
repair check: random clifford 4	`['-XZY', '+ZYI', '-IYX']`	`['-XZY', '+ZYI', '-IYX']`	Passed
control: bell preparation	`['+XX', '+ZZ']`	`['+XX', '+ZZ']`	Passed
control: h then s	`['+Y']`	`['+Y']`	Passed
control: s twice after h	`['-X']`	`['-X']`	Passed
control: x flips z sign	`['-Z']`	`['-Z']`	Passed

SHA-256 / 6ee43e886b0509345671db046b253d84014adc1553cc13bb9ca5454b2d6dbe91

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    n, gates = x
    xs = [[0] * n for _ in range(n)]
    zs = [[1 if i == j else 0 for j in range(n)] for i in range(n)]
    rs = [0] * n
    for g in gates:
        op = g[0]
        for row in range(n):
            X, Z = xs[row], zs[row]
            if op == 'h':
                a = g[1]
                rs[row] ^= X[a] & Z[a]
                X[a], Z[a] = Z[a], X[a]
            elif op == 's':
                a = g[1]
                rs[row] ^= X[a] & Z[a]
                Z[a] ^= X[a]
            elif op == 'x':
                rs[row] ^= Z[g[1]]
            elif op == 'z':
                rs[row] ^= X[g[1]]
            elif op == 'cx':
                a, b = g[1], g[2]
                rs[row] ^= X[a] & Z[b] & (X[b] ^ Z[b] ^ 1)
                X[b] ^= X[a]
                Z[a] ^= Z[b]
    letters = {(0, 0): 'I', (1, 0): 'X', (0, 1): 'Z', (1, 1): 'Y'}
    return [('-' if rs[r] else '+') + ''.join(letters[(xs[r][q], zs[r][q])] for q in range(n)) for r in range(n)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: random clifford 18', [3, [['cx', 1, 0], ['z', 0], ['z', 1], ['x', 2], ['h', 0], ['s', 2], ['z', 1], ['z', 2], ['cx', 0, 1], ['z', 1]]], ['+YYI', '+ZZI', '-IIZ']], ['regression: 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']], ['repair check: random clifford 4', [3, [['cx', 1, 2], ['h', 1], ['cx', 1, 0], ['s', 1], ['x', 2], ['cx', 1, 2], ['cx', 1, 2], ['h', 0], ['cx', 0, 2], ['z', 0], ['s', 2], ['h', 2], ['z', 0]]], ['-XZY', '+ZYI', '-IYX']], ['control: bell preparation', [2, [['h', 0], ['cx', 0, 1]]], ['+XX', '+ZZ']], ['control: h then s', [1, [['h', 0], ['s', 0]]], ['+Y']], ['control: s twice after h', [1, [['h', 0], ['s', 0], ['s', 0]]], ['-X']], ['control: x flips z sign', [1, [['x', 0]]], ['-Z']]], [['regression: random clifford 41', [3, [['s', 2], ['s', 0], ['s', 1], ['cx', 1, 2], ['h', 1], ['cx', 2, 1], ['cx', 1, 2], ['h', 1], ['s', 2], ['cx', 1, 0]]], ['+ZZI', '+IZY', '-XYX']], ['regression: random clifford 42', [3, [['h', 2], ['cx', 1, 0], ['h', 2], ['s', 1], ['h', 0], ['cx', 2, 1], ['x', 2], ['x', 2], ['cx', 0, 2], ['h', 0], ['cx', 0, 2]]], ['-XZZ', '-YZY', '-YIY']], ['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']], ['control: z on plus', [1, [['h', 0], ['z', 0]]], ['-X']], ['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: h on y eigenstate', [1, [['h', 0], ['s', 0], ['h', 0]]], ['-Y']]], [['regression: random clifford 49', [2, [['cx', 0, 1], ['x', 1], ['h', 0], ['z', 1], ['cx', 0, 1], ['cx', 1, 0], ['cx', 1, 0]]], ['+XX', '+YY']], ['regression: random clifford 51', [2, [['cx', 0, 1], ['h', 0], ['cx', 1, 0], ['h', 0], ['x', 1], ['x', 0], ['cx', 0, 1], ['cx', 0, 1], ['h', 0], ['cx', 0, 1], ['x', 1]]], ['-XX', '+YY']], ['regression: random clifford 42', [3, [['h', 2], ['cx', 1, 0], ['h', 2], ['s', 1], ['h', 0], ['cx', 2, 1], ['x', 2], ['x', 2], ['cx', 0, 2], ['h', 0], ['cx', 0, 2]]], ['-XZZ', '-YZY', '-YIY']], ['control: random clifford 0', [3, [['cx', 1, 2]]], ['+ZII', '+IZI', '+IZZ']], ['control: random clifford 1', [1, [['z', 0], ['s', 0], ['x', 0], ['x', 0], ['x', 0], ['z', 0], ['z', 0], ['z', 0]]], ['-Z']], ['control: random clifford 2', [3, [['cx', 0, 2], ['z', 2], ['s', 2], ['h', 0], ['cx', 2, 1], ['x', 1], ['cx', 1, 0], ['x', 1], ['x', 1], ['z', 0], ['cx', 2, 1], ['h', 1], ['h', 0]]], ['-ZII', '-IXI', '-ZIZ']], ['control: random clifford 3', [1, [['s', 0], ['h', 0], ['h', 0], ['x', 0], ['h', 0], ['h', 0], ['s', 0], ['s', 0]]], ['-Z']]], [['regression: random clifford 18', [3, [['cx', 1, 0], ['z', 0], ['z', 1], ['x', 2], ['h', 0], ['s', 2], ['z', 1], ['z', 2], ['cx', 0, 1], ['z', 1]]], ['+YYI', '+ZZI', '-IIZ']], ['regression: 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']], ['regression: random clifford 45', [2, [['z', 1], ['h', 0], ['cx', 0, 1], ['cx', 1, 0], ['cx', 0, 1], ['s', 1], ['z', 0], ['h', 0], ['s', 1], ['z', 1], ['cx', 0, 1], ['h', 1], ['cx', 0, 1], ['z', 1]]], ['+ZZ', '+YY']], ['control: 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 6', [1, [['h', 0], ['z', 0], ['h', 0], ['z', 0], ['x', 0], ['h', 0], ['h', 0], ['h', 0], ['h', 0], ['h', 0], ['h', 0], ['s', 0], ['x', 0]]], ['-Z']], ['control: 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 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 41', [3, [['s', 2], ['s', 0], ['s', 1], ['cx', 1, 2], ['h', 1], ['cx', 2, 1], ['cx', 1, 2], ['h', 1], ['s', 2], ['cx', 1, 0]]], ['+ZZI', '+IZY', '-XYX']], ['regression: random clifford 42', [3, [['h', 2], ['cx', 1, 0], ['h', 2], ['s', 1], ['h', 0], ['cx', 2, 1], ['x', 2], ['x', 2], ['cx', 0, 2], ['h', 0], ['cx', 0, 2]]], ['-XZZ', '-YZY', '-YIY']], ['regression: random clifford 51', [2, [['cx', 0, 1], ['h', 0], ['cx', 1, 0], ['h', 0], ['x', 1], ['x', 0], ['cx', 0, 1], ['cx', 0, 1], ['h', 0], ['cx', 0, 1], ['x', 1]]], ['-XX', '+YY']], ['control: random clifford 9', [2, [['cx', 1, 0], ['cx', 1, 0], ['x', 0], ['s', 0], ['cx', 1, 0], ['h', 1], ['x', 0], ['z', 1], ['cx', 0, 1]]], ['-ZX', '-IX']], ['control: random clifford 10', [1, [['z', 0], ['z', 0], ['s', 0], ['z', 0], ['h', 0], ['h', 0], ['s', 0]]], ['+Z']], ['control: random clifford 11', [2, [['s', 1], ['h', 0], ['cx', 0, 1], ['s', 0], ['x', 0]]], ['-YX', '-ZZ']], ['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']]]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
regression: random clifford 18	`['-YYI', '+ZZI', '-IIZ']`	`['+YYI', '+ZZI', '-IIZ']`	Failed
regression: random clifford 19	`['+XZ', '-YY']`	`['+XZ', '-YY']`	Passed
repair check: random clifford 4	`['-XZY', '+ZYI', '+IYX']`	`['-XZY', '+ZYI', '-IYX']`	Failed
control: bell preparation	`['+XX', '+ZZ']`	`['+XX', '+ZZ']`	Passed
control: h then s	`['+Y']`	`['+Y']`	Passed
control: s twice after h	`['-X']`	`['-X']`	Passed
control: x flips z sign	`['-Z']`	`['-Z']`	Passed

SHA-256 / e236f61781945d6b442f3fce96950ce2194e5bc962aee2b7fd1092c4f37438c4

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    n, gates = x
    xs = [[0] * n for _ in range(n)]
    zs = [[1 if i == j else 0 for j in range(n)] for i in range(n)]
    rs = [0] * n
    for g in gates:
        op = g[0]
        for row in range(n):
            X, Z = xs[row], zs[row]
            if op == 'h':
                a = g[1]
                rs[row] ^= X[a] & Z[a]
                X[a], Z[a] = Z[a], X[a]
            elif op == 's':
                a = g[1]
                rs[row] ^= X[a] & Z[a]
                Z[a] ^= X[a]
            elif op == 'x':
                rs[row] ^= Z[g[1]]
            elif op == 'z':
                rs[row] ^= X[g[1]]
            elif op == 'cx':
                a, b = g[1], g[2]
                rs[row] ^= X[a] & Z[b] & (X[b] ^ Z[a] ^ 1)
                X[b] ^= X[a]
                Z[a] ^= Z[b]
    letters = {(0, 0): 'I', (1, 0): 'X', (0, 1): 'Z', (1, 1): 'Y'}
    return [('-' if rs[r] else '+') + ''.join(letters[(xs[r][q], zs[r][q])] for q in range(n)) for r in range(n)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: random clifford 18', [3, [['cx', 1, 0], ['z', 0], ['z', 1], ['x', 2], ['h', 0], ['s', 2], ['z', 1], ['z', 2], ['cx', 0, 1], ['z', 1]]], ['+YYI', '+ZZI', '-IIZ']], ['regression: 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']], ['repair check: random clifford 4', [3, [['cx', 1, 2], ['h', 1], ['cx', 1, 0], ['s', 1], ['x', 2], ['cx', 1, 2], ['cx', 1, 2], ['h', 0], ['cx', 0, 2], ['z', 0], ['s', 2], ['h', 2], ['z', 0]]], ['-XZY', '+ZYI', '-IYX']], ['control: bell preparation', [2, [['h', 0], ['cx', 0, 1]]], ['+XX', '+ZZ']], ['control: h then s', [1, [['h', 0], ['s', 0]]], ['+Y']], ['control: s twice after h', [1, [['h', 0], ['s', 0], ['s', 0]]], ['-X']], ['control: x flips z sign', [1, [['x', 0]]], ['-Z']]], [['regression: random clifford 41', [3, [['s', 2], ['s', 0], ['s', 1], ['cx', 1, 2], ['h', 1], ['cx', 2, 1], ['cx', 1, 2], ['h', 1], ['s', 2], ['cx', 1, 0]]], ['+ZZI', '+IZY', '-XYX']], ['regression: random clifford 42', [3, [['h', 2], ['cx', 1, 0], ['h', 2], ['s', 1], ['h', 0], ['cx', 2, 1], ['x', 2], ['x', 2], ['cx', 0, 2], ['h', 0], ['cx', 0, 2]]], ['-XZZ', '-YZY', '-YIY']], ['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']], ['control: z on plus', [1, [['h', 0], ['z', 0]]], ['-X']], ['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: h on y eigenstate', [1, [['h', 0], ['s', 0], ['h', 0]]], ['-Y']]], [['regression: random clifford 49', [2, [['cx', 0, 1], ['x', 1], ['h', 0], ['z', 1], ['cx', 0, 1], ['cx', 1, 0], ['cx', 1, 0]]], ['+XX', '+YY']], ['regression: random clifford 51', [2, [['cx', 0, 1], ['h', 0], ['cx', 1, 0], ['h', 0], ['x', 1], ['x', 0], ['cx', 0, 1], ['cx', 0, 1], ['h', 0], ['cx', 0, 1], ['x', 1]]], ['-XX', '+YY']], ['regression: random clifford 42', [3, [['h', 2], ['cx', 1, 0], ['h', 2], ['s', 1], ['h', 0], ['cx', 2, 1], ['x', 2], ['x', 2], ['cx', 0, 2], ['h', 0], ['cx', 0, 2]]], ['-XZZ', '-YZY', '-YIY']], ['control: random clifford 0', [3, [['cx', 1, 2]]], ['+ZII', '+IZI', '+IZZ']], ['control: random clifford 1', [1, [['z', 0], ['s', 0], ['x', 0], ['x', 0], ['x', 0], ['z', 0], ['z', 0], ['z', 0]]], ['-Z']], ['control: random clifford 2', [3, [['cx', 0, 2], ['z', 2], ['s', 2], ['h', 0], ['cx', 2, 1], ['x', 1], ['cx', 1, 0], ['x', 1], ['x', 1], ['z', 0], ['cx', 2, 1], ['h', 1], ['h', 0]]], ['-ZII', '-IXI', '-ZIZ']], ['control: random clifford 3', [1, [['s', 0], ['h', 0], ['h', 0], ['x', 0], ['h', 0], ['h', 0], ['s', 0], ['s', 0]]], ['-Z']]], [['regression: random clifford 18', [3, [['cx', 1, 0], ['z', 0], ['z', 1], ['x', 2], ['h', 0], ['s', 2], ['z', 1], ['z', 2], ['cx', 0, 1], ['z', 1]]], ['+YYI', '+ZZI', '-IIZ']], ['regression: 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']], ['regression: random clifford 45', [2, [['z', 1], ['h', 0], ['cx', 0, 1], ['cx', 1, 0], ['cx', 0, 1], ['s', 1], ['z', 0], ['h', 0], ['s', 1], ['z', 1], ['cx', 0, 1], ['h', 1], ['cx', 0, 1], ['z', 1]]], ['+ZZ', '+YY']], ['control: 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 6', [1, [['h', 0], ['z', 0], ['h', 0], ['z', 0], ['x', 0], ['h', 0], ['h', 0], ['h', 0], ['h', 0], ['h', 0], ['h', 0], ['s', 0], ['x', 0]]], ['-Z']], ['control: 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 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 41', [3, [['s', 2], ['s', 0], ['s', 1], ['cx', 1, 2], ['h', 1], ['cx', 2, 1], ['cx', 1, 2], ['h', 1], ['s', 2], ['cx', 1, 0]]], ['+ZZI', '+IZY', '-XYX']], ['regression: random clifford 42', [3, [['h', 2], ['cx', 1, 0], ['h', 2], ['s', 1], ['h', 0], ['cx', 2, 1], ['x', 2], ['x', 2], ['cx', 0, 2], ['h', 0], ['cx', 0, 2]]], ['-XZZ', '-YZY', '-YIY']], ['regression: random clifford 51', [2, [['cx', 0, 1], ['h', 0], ['cx', 1, 0], ['h', 0], ['x', 1], ['x', 0], ['cx', 0, 1], ['cx', 0, 1], ['h', 0], ['cx', 0, 1], ['x', 1]]], ['-XX', '+YY']], ['control: random clifford 9', [2, [['cx', 1, 0], ['cx', 1, 0], ['x', 0], ['s', 0], ['cx', 1, 0], ['h', 1], ['x', 0], ['z', 1], ['cx', 0, 1]]], ['-ZX', '-IX']], ['control: random clifford 10', [1, [['z', 0], ['z', 0], ['s', 0], ['z', 0], ['h', 0], ['h', 0], ['s', 0]]], ['+Z']], ['control: random clifford 11', [2, [['s', 1], ['h', 0], ['cx', 0, 1], ['s', 0], ['x', 0]]], ['-YX', '-ZZ']], ['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']]]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
regression: random clifford 18	`['+YYI', '+ZZI', '-IIZ']`	`['+YYI', '+ZZI', '-IIZ']`	Passed
regression: random clifford 19	`['+XZ', '-YY']`	`['+XZ', '-YY']`	Passed
repair check: random clifford 4	`['-XZY', '+ZYI', '-IYX']`	`['-XZY', '+ZYI', '-IYX']`	Passed
control: bell preparation	`['+XX', '+ZZ']`	`['+XX', '+ZZ']`	Passed
control: h then s	`['+Y']`	`['+Y']`	Passed
control: s twice after h	`['-X']`	`['-X']`	Passed
control: x flips z sign	`['-Z']`	`['-Z']`	Passed

SHA-256 / 662cfdddd16fdff598024f08935d1cc8e7b938f746df1d1e888390785b19a85f

Verification & scope

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.

Observations recorded using Python 3.12.14 at 2026-09-29T14:51:31.767225+00:00.

Case digest / 502f0633395b145e5f79859e2b062c2a912a4cf6f7b6213ad0e0da8682875d25