FA-91046 / Quantum circuit simulation / Open access

Direction fixer treats couplers as undirected · case 01

A CNOT against the native direction is emitted unchanged and would be rejected by the device.

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

ROOT CAUSE

The native check accepts (c, t) when either orientation appears in the edge set.

THE FAILURE

The native check accepts (c, t) when either orientation appears in the edge set.

Unsuccessful approach: The attempted repair tests the reverse orientation first, so bidirectional couplers get needless Hadamard flips.

Case contract

Input [edges, ops]; edges are directed native CNOT pairs [c, t]. Each ["cx", c, t] is kept if [c, t] is native, else rewritten as h c, h t, cx t c, h c, h t if [t, c] is native, else the result is ["unroutable", op index]; c == t gives ["invalid", op index]. Other ops pass through. A final stack pass cancels an ["h", q] against an identical immediately preceding ["h", q].

Why this case matters

Direction fixing is a mandatory transpiler pass for devices with directed couplers; errors either break hardware constraints or bloat circuits.

1 / The failure

Exit 1

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

N = 1
observations = []
def solve(x):
    edges, ops = x
    allowed = {(a, b) for a, b in edges}
    out = []
    for idx, op in enumerate(ops):
        if op[0] != 'cx':
            out.append(list(op))
            continue
        c, t = op[1], op[2]
        if c == t:
            return ['invalid', idx]
        if (c, t) in allowed or (t, c) in allowed:
            out.append(['cx', c, t])
        elif (t, c) in allowed:
            out += [['h', c], ['h', t], ['cx', t, c], ['h', c], ['h', t]]
        else:
            return ['unroutable', idx]
    res = []
    for op in out:
        if op[0] == 'h' and res and res[-1] == op:
            res.pop()
        else:
            res.append(op)
    return res
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: reversed direction', [[[0, 1], [1, 2], [2, 3]], [['cx', 1, 0]]], [['h', 1], ['h', 0], ['cx', 0, 1], ['h', 1], ['h', 0]]], ['regression: flip then h cancels', [[[0, 1], [1, 2], [2, 3]], [['cx', 1, 0], ['h', 0]]], [['h', 1], ['h', 0], ['cx', 0, 1], ['h', 1]]], ['repair check: bidirectional edge', [[[0, 1], [1, 0]], [['cx', 1, 0]]], [['cx', 1, 0]]], ['control: native direction', [[[0, 1], [1, 2], [2, 3]], [['cx', 0, 1]]], [['cx', 0, 1]]], ['control: self loop', [[[0, 1], [1, 2], [2, 3]], [['h', 0], ['cx', 2, 2]]], ['invalid', 1]], ['control: unroutable pair', [[[0, 1], [1, 2], [2, 3]], [['h', 1], ['cx', 0, 2]]], ['unroutable', 1]], ['control: hadamards cancel', [[[0, 1], [1, 2], [2, 3]], [['h', 0], ['h', 0], ['x', 1]]], [['x', 1]]]], [['regression: random coupling 25', [[[0, 2], [2, 1], [0, 1], [2, 3], [1, 2]], [['cx', 1, 0], ['cx', 0, 2], ['x', 1], ['x', 3], ['h', 3]]], [['h', 1], ['h', 0], ['cx', 0, 1], ['h', 1], ['h', 0], ['cx', 0, 2], ['x', 1], ['x', 3], ['h', 3]]], ['regression: random coupling 33', [[[3, 2], [2, 1]], [['h', 0], ['cx', 2, 3]]], [['h', 0], ['h', 2], ['h', 3], ['cx', 3, 2], ['h', 2], ['h', 3]]], ['repair check: random coupling 27', [[[0, 1], [1, 0], [2, 3], [3, 2]], [['cx', 2, 3], ['h', 2], ['cx', 2, 3]]], [['cx', 2, 3], ['h', 2], ['cx', 2, 3]]], ['control: hadamards on different qubits', [[[0, 1], [1, 2], [2, 3]], [['h', 0], ['h', 1]]], [['h', 0], ['h', 1]]], ['control: random coupling 0', [[[2, 1], [3, 2], [1, 2], [1, 0]], [['h', 2], ['cx', 1, 0], ['cx', 2, 0], ['x', 1]]], ['unroutable', 2]], ['control: random coupling 1', [[[2, 3], [3, 2], [0, 1], [0, 2]], [['h', 1]]], [['h', 1]]], ['control: random coupling 2', [[[0, 2], [2, 3], [2, 1]], [['h', 3]]], [['h', 3]]]], [['regression: random coupling 47', [[[2, 1], [1, 2], [0, 2], [1, 0]], [['cx', 2, 0], ['cx', 0, 1], ['cx', 2, 1]]], [['h', 2], ['h', 0], ['cx', 0, 2], ['h', 2], ['h', 1], ['cx', 1, 0], ['h', 0], ['h', 1], ['cx', 2, 1]]], ['regression: random coupling 56', [[[0, 2], [1, 2], [2, 3], [1, 0], [2, 1]], [['cx', 1, 0], ['h', 3], ['cx', 2, 0], ['h', 0]]], [['cx', 1, 0], ['h', 3], ['h', 2], ['h', 0], ['cx', 0, 2], ['h', 2]]], ['repair check: random coupling 53', [[[1, 2], [2, 3], [2, 1], [3, 2]], [['cx', 1, 2]]], [['cx', 1, 2]]], ['control: random coupling 3', [[[1, 0], [2, 3]], [['cx', 1, 2], ['h', 1], ['x', 2]]], ['unroutable', 0]], ['control: random coupling 4', [[[0, 2], [2, 3]], [['h', 0], ['cx', 0, 3], ['cx', 2, 0], ['x', 3]]], ['unroutable', 1]], ['control: random coupling 5', [[[3, 2], [0, 2], [2, 3], [1, 2]], [['cx', 1, 0], ['h', 3], ['h', 0], ['cx', 0, 3]]], ['unroutable', 0]], ['control: random coupling 6', [[[0, 1], [2, 1]], [['cx', 2, 0], ['x', 2], ['cx', 0, 2], ['cx', 3, 0], ['h', 3], ['h', 3]]], ['unroutable', 0]]], [['regression: flip then h cancels', [[[0, 1], [1, 2], [2, 3]], [['cx', 1, 0], ['h', 0]]], [['h', 1], ['h', 0], ['cx', 0, 1], ['h', 1]]], ['regression: flip then h on target cancels', [[[0, 1], [1, 2], [2, 3]], [['cx', 1, 0], ['h', 1], ['cx', 0, 1]]], [['h', 1], ['h', 0], ['cx', 0, 1], ['h', 1], ['h', 0], ['h', 1], ['cx', 0, 1]]], ['repair check: random coupling 17', [[[0, 1], [2, 1], [1, 2], [2, 3], [3, 2]], [['cx', 2, 3], ['h', 3], ['x', 0], ['h', 2]]], [['cx', 2, 3], ['h', 3], ['x', 0], ['h', 2]]], ['control: random coupling 7', [[[0, 1], [2, 3], [2, 1], [1, 2]], [['cx', 1, 3]]], ['unroutable', 0]], ['control: random coupling 8', [[[2, 1], [1, 2], [3, 2]], [['x', 0], ['h', 3]]], [['x', 0], ['h', 3]]], ['control: random coupling 9', [[[0, 2], [0, 1], [1, 2], [3, 2]], [['h', 1], ['cx', 0, 2]]], [['h', 1], ['cx', 0, 2]]], ['control: random coupling 10', [[[0, 2], [2, 1], [3, 2]], [['h', 2], ['cx', 1, 0]]], ['unroutable', 1]]], [['regression: random coupling 33', [[[3, 2], [2, 1]], [['h', 0], ['cx', 2, 3]]], [['h', 0], ['h', 2], ['h', 3], ['cx', 3, 2], ['h', 2], ['h', 3]]], ['regression: random coupling 37', [[[0, 2], [0, 1], [1, 0]], [['h', 2], ['cx', 2, 0], ['cx', 0, 2]]], [['h', 0], ['cx', 0, 2], ['h', 2], ['h', 0], ['cx', 0, 2]]], ['regression: random coupling 47', [[[2, 1], [1, 2], [0, 2], [1, 0]], [['cx', 2, 0], ['cx', 0, 1], ['cx', 2, 1]]], [['h', 2], ['h', 0], ['cx', 0, 2], ['h', 2], ['h', 1], ['cx', 1, 0], ['h', 0], ['h', 1], ['cx', 2, 1]]], ['control: random coupling 11', [[[2, 3], [1, 2], [3, 2], [0, 2]], [['cx', 2, 3], ['cx', 0, 2], ['h', 2], ['cx', 1, 1], ['h', 0]]], ['invalid', 3]], ['control: random coupling 12', [[[0, 2], [3, 2]], [['x', 2], ['cx', 3, 1], ['h', 2], ['h', 3]]], ['unroutable', 1]], ['control: random coupling 13', [[[1, 0], [0, 2], [3, 2], [2, 3], [0, 1]], [['cx', 2, 1], ['cx', 3, 1], ['x', 1]]], ['unroutable', 0]], ['control: random coupling 14', [[[0, 2], [3, 2], [2, 3]], [['h', 0], ['cx', 1, 2], ['cx', 0, 1]]], ['unroutable', 1]]]]
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: reversed direction	`[['cx', 1, 0]]`	`[['h', 1], ['h', 0], ['cx', 0, 1], ['h', 1], ['h', 0]]`	Failed
regression: flip then h cancels	`[['cx', 1, 0], ['h', 0]]`	`[['h', 1], ['h', 0], ['cx', 0, 1], ['h', 1]]`	Failed
repair check: bidirectional edge	`[['cx', 1, 0]]`	`[['cx', 1, 0]]`	Passed
control: native direction	`[['cx', 0, 1]]`	`[['cx', 0, 1]]`	Passed
control: self loop	`['invalid', 1]`	`['invalid', 1]`	Passed
control: unroutable pair	`['unroutable', 1]`	`['unroutable', 1]`	Passed
control: hadamards cancel	`[['x', 1]]`	`[['x', 1]]`	Passed

SHA-256 / d325510ee2f843f3fe3df941d156aec89560f4cf020bac1959961060b274f814

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(x):
    edges, ops = x
    allowed = {(a, b) for a, b in edges}
    out = []
    for idx, op in enumerate(ops):
        if op[0] != 'cx':
            out.append(list(op))
            continue
        c, t = op[1], op[2]
        if c == t:
            return ['invalid', idx]
        if (t, c) in allowed:
            out += [['h', c], ['h', t], ['cx', t, c], ['h', c], ['h', t]]
        elif (c, t) in allowed:
            out.append(['cx', c, t])
        else:
            return ['unroutable', idx]
    res = []
    for op in out:
        if op[0] == 'h' and res and res[-1] == op:
            res.pop()
        else:
            res.append(op)
    return res
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: reversed direction', [[[0, 1], [1, 2], [2, 3]], [['cx', 1, 0]]], [['h', 1], ['h', 0], ['cx', 0, 1], ['h', 1], ['h', 0]]], ['regression: flip then h cancels', [[[0, 1], [1, 2], [2, 3]], [['cx', 1, 0], ['h', 0]]], [['h', 1], ['h', 0], ['cx', 0, 1], ['h', 1]]], ['repair check: bidirectional edge', [[[0, 1], [1, 0]], [['cx', 1, 0]]], [['cx', 1, 0]]], ['control: native direction', [[[0, 1], [1, 2], [2, 3]], [['cx', 0, 1]]], [['cx', 0, 1]]], ['control: self loop', [[[0, 1], [1, 2], [2, 3]], [['h', 0], ['cx', 2, 2]]], ['invalid', 1]], ['control: unroutable pair', [[[0, 1], [1, 2], [2, 3]], [['h', 1], ['cx', 0, 2]]], ['unroutable', 1]], ['control: hadamards cancel', [[[0, 1], [1, 2], [2, 3]], [['h', 0], ['h', 0], ['x', 1]]], [['x', 1]]]], [['regression: random coupling 25', [[[0, 2], [2, 1], [0, 1], [2, 3], [1, 2]], [['cx', 1, 0], ['cx', 0, 2], ['x', 1], ['x', 3], ['h', 3]]], [['h', 1], ['h', 0], ['cx', 0, 1], ['h', 1], ['h', 0], ['cx', 0, 2], ['x', 1], ['x', 3], ['h', 3]]], ['regression: random coupling 33', [[[3, 2], [2, 1]], [['h', 0], ['cx', 2, 3]]], [['h', 0], ['h', 2], ['h', 3], ['cx', 3, 2], ['h', 2], ['h', 3]]], ['repair check: random coupling 27', [[[0, 1], [1, 0], [2, 3], [3, 2]], [['cx', 2, 3], ['h', 2], ['cx', 2, 3]]], [['cx', 2, 3], ['h', 2], ['cx', 2, 3]]], ['control: hadamards on different qubits', [[[0, 1], [1, 2], [2, 3]], [['h', 0], ['h', 1]]], [['h', 0], ['h', 1]]], ['control: random coupling 0', [[[2, 1], [3, 2], [1, 2], [1, 0]], [['h', 2], ['cx', 1, 0], ['cx', 2, 0], ['x', 1]]], ['unroutable', 2]], ['control: random coupling 1', [[[2, 3], [3, 2], [0, 1], [0, 2]], [['h', 1]]], [['h', 1]]], ['control: random coupling 2', [[[0, 2], [2, 3], [2, 1]], [['h', 3]]], [['h', 3]]]], [['regression: random coupling 47', [[[2, 1], [1, 2], [0, 2], [1, 0]], [['cx', 2, 0], ['cx', 0, 1], ['cx', 2, 1]]], [['h', 2], ['h', 0], ['cx', 0, 2], ['h', 2], ['h', 1], ['cx', 1, 0], ['h', 0], ['h', 1], ['cx', 2, 1]]], ['regression: random coupling 56', [[[0, 2], [1, 2], [2, 3], [1, 0], [2, 1]], [['cx', 1, 0], ['h', 3], ['cx', 2, 0], ['h', 0]]], [['cx', 1, 0], ['h', 3], ['h', 2], ['h', 0], ['cx', 0, 2], ['h', 2]]], ['repair check: random coupling 53', [[[1, 2], [2, 3], [2, 1], [3, 2]], [['cx', 1, 2]]], [['cx', 1, 2]]], ['control: random coupling 3', [[[1, 0], [2, 3]], [['cx', 1, 2], ['h', 1], ['x', 2]]], ['unroutable', 0]], ['control: random coupling 4', [[[0, 2], [2, 3]], [['h', 0], ['cx', 0, 3], ['cx', 2, 0], ['x', 3]]], ['unroutable', 1]], ['control: random coupling 5', [[[3, 2], [0, 2], [2, 3], [1, 2]], [['cx', 1, 0], ['h', 3], ['h', 0], ['cx', 0, 3]]], ['unroutable', 0]], ['control: random coupling 6', [[[0, 1], [2, 1]], [['cx', 2, 0], ['x', 2], ['cx', 0, 2], ['cx', 3, 0], ['h', 3], ['h', 3]]], ['unroutable', 0]]], [['regression: flip then h cancels', [[[0, 1], [1, 2], [2, 3]], [['cx', 1, 0], ['h', 0]]], [['h', 1], ['h', 0], ['cx', 0, 1], ['h', 1]]], ['regression: flip then h on target cancels', [[[0, 1], [1, 2], [2, 3]], [['cx', 1, 0], ['h', 1], ['cx', 0, 1]]], [['h', 1], ['h', 0], ['cx', 0, 1], ['h', 1], ['h', 0], ['h', 1], ['cx', 0, 1]]], ['repair check: random coupling 17', [[[0, 1], [2, 1], [1, 2], [2, 3], [3, 2]], [['cx', 2, 3], ['h', 3], ['x', 0], ['h', 2]]], [['cx', 2, 3], ['h', 3], ['x', 0], ['h', 2]]], ['control: random coupling 7', [[[0, 1], [2, 3], [2, 1], [1, 2]], [['cx', 1, 3]]], ['unroutable', 0]], ['control: random coupling 8', [[[2, 1], [1, 2], [3, 2]], [['x', 0], ['h', 3]]], [['x', 0], ['h', 3]]], ['control: random coupling 9', [[[0, 2], [0, 1], [1, 2], [3, 2]], [['h', 1], ['cx', 0, 2]]], [['h', 1], ['cx', 0, 2]]], ['control: random coupling 10', [[[0, 2], [2, 1], [3, 2]], [['h', 2], ['cx', 1, 0]]], ['unroutable', 1]]], [['regression: random coupling 33', [[[3, 2], [2, 1]], [['h', 0], ['cx', 2, 3]]], [['h', 0], ['h', 2], ['h', 3], ['cx', 3, 2], ['h', 2], ['h', 3]]], ['regression: random coupling 37', [[[0, 2], [0, 1], [1, 0]], [['h', 2], ['cx', 2, 0], ['cx', 0, 2]]], [['h', 0], ['cx', 0, 2], ['h', 2], ['h', 0], ['cx', 0, 2]]], ['regression: random coupling 47', [[[2, 1], [1, 2], [0, 2], [1, 0]], [['cx', 2, 0], ['cx', 0, 1], ['cx', 2, 1]]], [['h', 2], ['h', 0], ['cx', 0, 2], ['h', 2], ['h', 1], ['cx', 1, 0], ['h', 0], ['h', 1], ['cx', 2, 1]]], ['control: random coupling 11', [[[2, 3], [1, 2], [3, 2], [0, 2]], [['cx', 2, 3], ['cx', 0, 2], ['h', 2], ['cx', 1, 1], ['h', 0]]], ['invalid', 3]], ['control: random coupling 12', [[[0, 2], [3, 2]], [['x', 2], ['cx', 3, 1], ['h', 2], ['h', 3]]], ['unroutable', 1]], ['control: random coupling 13', [[[1, 0], [0, 2], [3, 2], [2, 3], [0, 1]], [['cx', 2, 1], ['cx', 3, 1], ['x', 1]]], ['unroutable', 0]], ['control: random coupling 14', [[[0, 2], [3, 2], [2, 3]], [['h', 0], ['cx', 1, 2], ['cx', 0, 1]]], ['unroutable', 1]]]]
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: reversed direction	`[['h', 1], ['h', 0], ['cx', 0, 1], ['h', 1], ['h', 0]]`	`[['h', 1], ['h', 0], ['cx', 0, 1], ['h', 1], ['h', 0]]`	Passed
regression: flip then h cancels	`[['h', 1], ['h', 0], ['cx', 0, 1], ['h', 1]]`	`[['h', 1], ['h', 0], ['cx', 0, 1], ['h', 1]]`	Passed
repair check: bidirectional edge	`[['h', 1], ['h', 0], ['cx', 0, 1], ['h', 1], ['h', 0]]`	`[['cx', 1, 0]]`	Failed
control: native direction	`[['cx', 0, 1]]`	`[['cx', 0, 1]]`	Passed
control: self loop	`['invalid', 1]`	`['invalid', 1]`	Passed
control: unroutable pair	`['unroutable', 1]`	`['unroutable', 1]`	Passed
control: hadamards cancel	`[['x', 1]]`	`[['x', 1]]`	Passed

SHA-256 / 880d35aa8033b6fbbcf653748db66bd9c6b86e25ed821c06b8c5edea8ea21ea6

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 7 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

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 2026-09-29T14:51:32.286966+00:00.

Case digest / 5a8e6b47db2501f74582f3dd03d4f605c7c10e9d57379bba0331e3f23ebcdc3b