FA-90896 / Quantum circuit simulation / Open access

Marginal rounds the numerator before normalizing · case 01

Unnormalized states produce probabilities such as 0.3076923076 with many digits instead of values rounded to 6 decimals.

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

ROOT CAUSE

Rounding is applied to the unnormalized weight and total separately, and the division result is never rounded.

VERIFIED REPAIR

Normalize first, then round the probability once to 6 decimals.

Unsuccessful approach: The attempted repair rounds the weight, divides by the exact total and rounds again, a double rounding that drifts from single rounding.

Case contract

Input [n, amps, qubits]; amps are 2**n [re, im] pairs (qubit 0 = LSB), possibly unnormalized. Return the marginal outcome distribution over the listed qubits as {bitstring: probability} where the first listed qubit is the rightmost character, probabilities are normalized by the total squared norm, rounded to 6 decimals after summation, and zero entries are omitted. Errors: "bad-length", "duplicate-qubit", "bad-qubit", "zero-state" (total squared norm <= 1e-12).

Why this case matters

Marginal readout distributions are what users compare against hardware counts; ordering or normalization slips mislabel every histogram.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    n, amps, qubits = x
    if len(amps) != 1 << n:
        return 'bad-length'
    if len(set(qubits)) != len(qubits):
        return 'duplicate-qubit'
    if any(q < 0 or q >= n for q in qubits):
        return 'bad-qubit'
    total = sum(re * re + im * im for re, im in amps)
    if total <= 1e-12:
        return 'zero-state'
    acc = {}
    for idx, (a, b) in enumerate(amps):
        p = a * a + b * b
        if p == 0:
            continue
        key = ''.join('1' if idx >> q & 1 else '0' for q in reversed(qubits))
        acc[key] = acc.get(key, 0.0) + p
    out = {}
    for key in sorted(acc):
        v = round(acc[key], 6) / round(total, 6)
        if v > 0:
            out[key] = v
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: bell state on both qubits', [2, [[0.707107, 0], [0, 0], [0, 0], [0.707107, 0]], [0, 1]], {'00': 0.5, '11': 0.5}], ['regression: random state 0', [2, [[0.0, 0.0], [0.282, -0.043], [-0.278, 0.017], [0.0, 0.0]], [0, 1]], {'01': 0.511954, '10': 0.488046}], ['repair check: random state 1', [2, [[0.129, 0.125], [0.0, 0.0], [0.0, 0.0], [0.0, 0.0]], [1, 0]], {'00': 1.0}], ['control: reversed qubit list', [2, [[0, 0], [1, 0], [0, 0], [0, 0]], [1, 0]], {'10': 1.0}], ['control: single qubit marginal of |01>', [2, [[0, 0], [1, 0], [0, 0], [0, 0]], [1]], {'0': 1.0}], ['control: out of range qubit equals n', [2, [[1, 0], [0, 0], [0, 0], [0, 0]], [2]], 'bad-qubit'], ['control: negative qubit index', [2, [[1, 0], [0, 0], [0, 0], [0, 0]], [-1]], 'bad-qubit']], [['regression: random state 3', [2, [[0.379, 0.308], [-0.129, -0.524], [0.79, -0.299], [-0.403, -0.327]], [0, 1]], {'00': 0.157683, '01': 0.192532, '10': 0.471717, '11': 0.178068}], ['regression: random state 4', [1, [[-0.217, 0.525], [-0.308, -0.181]], [0]], {'0': 0.716602, '1': 0.283398}], ['regression: random state 2', [1, [[0.541, -0.923], [-0.479, -0.646]], [0]], {'0': 0.638959, '1': 0.361041}], ['control: duplicate qubits', [2, [[0.6, 0], [0, 0.8], [0, 0], [0, 0]], [0, 0]], 'duplicate-qubit'], ['control: wrong amplitude count', [2, [[1, 0], [0, 0]], [0]], 'bad-length'], ['control: all-zero state', [1, [[0, 0], [0, 0]], [0]], 'zero-state'], ['control: unnormalized pair', [1, [[3, 0], [0, 4]], [0]], {'0': 0.36, '1': 0.64}]], [['regression: random state 6', [3, [[-0.119, 0.092], [0.264, -0.223], [-0.189, 0.034], [-0.22, -0.267], [-0.291, -0.092], [0.09, -0.02], [0.062, -0.284], [-0.239, 0.039]], [2]], {'0': 0.54953, '1': 0.45047}], ['regression: random state 7', [1, [[0.725, -0.825], [-0.233, -0.266]], [0]], {'0': 0.906073, '1': 0.093927}], ['regression: random state 4', [1, [[-0.217, 0.525], [-0.308, -0.181]], [0]], {'0': 0.716602, '1': 0.283398}], ['control: near zero state', [1, [[1e-08, 0], [0, 1e-08]], [0]], 'zero-state'], ['control: reversed qubit list', [2, [[0, 0], [1, 0], [0, 0], [0, 0]], [1, 0]], {'10': 1.0}], ['control: single qubit marginal of |01>', [2, [[0, 0], [1, 0], [0, 0], [0, 0]], [1]], {'0': 1.0}], ['control: out of range qubit equals n', [2, [[1, 0], [0, 0], [0, 0], [0, 0]], [2]], 'bad-qubit']], [['regression: random state 10', [3, [[-0.064, 0.212], [0.264, -0.114], [-0.15, -0.24], [0.031, 0.141], [0.037, -0.002], [0.023, -0.229], [0.193, -0.153], [0.251, 0.097]], [0, 1, 2]], {'000': 0.116738, '001': 0.196846, '010': 0.190676, '011': 0.049614, '100': 0.003268, '101': 0.126094, '110': 0.144395, '111': 0.17237}], ['regression: random state 11', [2, [[-0.211, 0.28], [0.154, -0.18], [-0.016, -0.095], [-0.157, 0.075]], [0]], {'0': 0.604789, '1': 0.395211}], ['regression: random state 6', [3, [[-0.119, 0.092], [0.264, -0.223], [-0.189, 0.034], [-0.22, -0.267], [-0.291, -0.092], [0.09, -0.02], [0.062, -0.284], [-0.239, 0.039]], [2]], {'0': 0.54953, '1': 0.45047}], ['control: negative qubit index', [2, [[1, 0], [0, 0], [0, 0], [0, 0]], [-1]], 'bad-qubit'], ['control: duplicate qubits', [2, [[0.6, 0], [0, 0.8], [0, 0], [0, 0]], [0, 0]], 'duplicate-qubit'], ['control: wrong amplitude count', [2, [[1, 0], [0, 0]], [0]], 'bad-length'], ['control: all-zero state', [1, [[0, 0], [0, 0]], [0]], 'zero-state']], [['regression: random state 13', [3, [[0.624, -0.422], [-0.596, 0.926], [-0.719, 1.0], [-0.208, -0.957], [-0.398, 0.533], [-0.189, -0.721], [-0.845, -0.901], [0.144, -0.267]], [0, 1, 2]], {'000': 0.082574, '001': 0.176465, '010': 0.220741, '011': 0.139566, '100': 0.064389, '101': 0.080843, '110': 0.222031, '111': 0.013391}], ['regression: random state 14', [3, [[-0.144, 0.15], [-0.052, 0.123], [0.0, 0.0], [0.145, -0.129], [0.077, 0.218], [0.248, 0.026], [0.0, 0.0], [0.256, 0.015]], [2, 0, 1]], {'000': 0.154343, '001': 0.190816, '010': 0.06366, '011': 0.221969, '110': 0.134459, '111': 0.234753}], ['regression: random state 8', [2, [[0.258, -0.148], [-0.044, -0.154], [0.09, 0.21], [0.28, 0.265]], [0]], {'0': 0.446643, '1': 0.553357}], ['control: unnormalized pair', [1, [[3, 0], [0, 4]], [0]], {'0': 0.36, '1': 0.64}], ['control: near zero state', [1, [[1e-08, 0], [0, 1e-08]], [0]], 'zero-state'], ['control: reversed qubit list', [2, [[0, 0], [1, 0], [0, 0], [0, 0]], [1, 0]], {'10': 1.0}], ['control: single qubit marginal of |01>', [2, [[0, 0], [1, 0], [0, 0], [0, 0]], [1]], {'0': 1.0}]]]
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: bell state on both qubits	`{'00': 0.49999950000050003, '11': 0.49999950000050003}`	`{'00': 0.5, '11': 0.5}`	Failed
regression: random state 0	`{'01': 0.5119537452971449, '10': 0.48804625470285506}`	`{'01': 0.511954, '10': 0.488046}`	Failed
repair check: random state 1	`{'00': 1.0}`	`{'00': 1.0}`	Passed
control: reversed qubit list	`{'10': 1.0}`	`{'10': 1.0}`	Passed
control: single qubit marginal of \|01>	`{'0': 1.0}`	`{'0': 1.0}`	Passed
control: out of range qubit equals n	`bad-qubit`	`bad-qubit`	Passed
control: negative qubit index	`bad-qubit`	`bad-qubit`	Passed

SHA-256 / 393edbcd645d7f671a65ad31bff122bd439c024f51779c38e464b1cb7cc20c97

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    n, amps, qubits = x
    if len(amps) != 1 << n:
        return 'bad-length'
    if len(set(qubits)) != len(qubits):
        return 'duplicate-qubit'
    if any(q < 0 or q >= n for q in qubits):
        return 'bad-qubit'
    total = sum(re * re + im * im for re, im in amps)
    if total <= 1e-12:
        return 'zero-state'
    acc = {}
    for idx, (a, b) in enumerate(amps):
        p = a * a + b * b
        if p == 0:
            continue
        key = ''.join('1' if idx >> q & 1 else '0' for q in reversed(qubits))
        acc[key] = acc.get(key, 0.0) + p
    out = {}
    for key in sorted(acc):
        v = round(round(acc[key], 3) / total, 6)
        if v > 0:
            out[key] = v
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: bell state on both qubits', [2, [[0.707107, 0], [0, 0], [0, 0], [0.707107, 0]], [0, 1]], {'00': 0.5, '11': 0.5}], ['regression: random state 0', [2, [[0.0, 0.0], [0.282, -0.043], [-0.278, 0.017], [0.0, 0.0]], [0, 1]], {'01': 0.511954, '10': 0.488046}], ['repair check: random state 1', [2, [[0.129, 0.125], [0.0, 0.0], [0.0, 0.0], [0.0, 0.0]], [1, 0]], {'00': 1.0}], ['control: reversed qubit list', [2, [[0, 0], [1, 0], [0, 0], [0, 0]], [1, 0]], {'10': 1.0}], ['control: single qubit marginal of |01>', [2, [[0, 0], [1, 0], [0, 0], [0, 0]], [1]], {'0': 1.0}], ['control: out of range qubit equals n', [2, [[1, 0], [0, 0], [0, 0], [0, 0]], [2]], 'bad-qubit'], ['control: negative qubit index', [2, [[1, 0], [0, 0], [0, 0], [0, 0]], [-1]], 'bad-qubit']], [['regression: random state 3', [2, [[0.379, 0.308], [-0.129, -0.524], [0.79, -0.299], [-0.403, -0.327]], [0, 1]], {'00': 0.157683, '01': 0.192532, '10': 0.471717, '11': 0.178068}], ['regression: random state 4', [1, [[-0.217, 0.525], [-0.308, -0.181]], [0]], {'0': 0.716602, '1': 0.283398}], ['regression: random state 2', [1, [[0.541, -0.923], [-0.479, -0.646]], [0]], {'0': 0.638959, '1': 0.361041}], ['control: duplicate qubits', [2, [[0.6, 0], [0, 0.8], [0, 0], [0, 0]], [0, 0]], 'duplicate-qubit'], ['control: wrong amplitude count', [2, [[1, 0], [0, 0]], [0]], 'bad-length'], ['control: all-zero state', [1, [[0, 0], [0, 0]], [0]], 'zero-state'], ['control: unnormalized pair', [1, [[3, 0], [0, 4]], [0]], {'0': 0.36, '1': 0.64}]], [['regression: random state 6', [3, [[-0.119, 0.092], [0.264, -0.223], [-0.189, 0.034], [-0.22, -0.267], [-0.291, -0.092], [0.09, -0.02], [0.062, -0.284], [-0.239, 0.039]], [2]], {'0': 0.54953, '1': 0.45047}], ['regression: random state 7', [1, [[0.725, -0.825], [-0.233, -0.266]], [0]], {'0': 0.906073, '1': 0.093927}], ['regression: random state 4', [1, [[-0.217, 0.525], [-0.308, -0.181]], [0]], {'0': 0.716602, '1': 0.283398}], ['control: near zero state', [1, [[1e-08, 0], [0, 1e-08]], [0]], 'zero-state'], ['control: reversed qubit list', [2, [[0, 0], [1, 0], [0, 0], [0, 0]], [1, 0]], {'10': 1.0}], ['control: single qubit marginal of |01>', [2, [[0, 0], [1, 0], [0, 0], [0, 0]], [1]], {'0': 1.0}], ['control: out of range qubit equals n', [2, [[1, 0], [0, 0], [0, 0], [0, 0]], [2]], 'bad-qubit']], [['regression: random state 10', [3, [[-0.064, 0.212], [0.264, -0.114], [-0.15, -0.24], [0.031, 0.141], [0.037, -0.002], [0.023, -0.229], [0.193, -0.153], [0.251, 0.097]], [0, 1, 2]], {'000': 0.116738, '001': 0.196846, '010': 0.190676, '011': 0.049614, '100': 0.003268, '101': 0.126094, '110': 0.144395, '111': 0.17237}], ['regression: random state 11', [2, [[-0.211, 0.28], [0.154, -0.18], [-0.016, -0.095], [-0.157, 0.075]], [0]], {'0': 0.604789, '1': 0.395211}], ['regression: random state 6', [3, [[-0.119, 0.092], [0.264, -0.223], [-0.189, 0.034], [-0.22, -0.267], [-0.291, -0.092], [0.09, -0.02], [0.062, -0.284], [-0.239, 0.039]], [2]], {'0': 0.54953, '1': 0.45047}], ['control: negative qubit index', [2, [[1, 0], [0, 0], [0, 0], [0, 0]], [-1]], 'bad-qubit'], ['control: duplicate qubits', [2, [[0.6, 0], [0, 0.8], [0, 0], [0, 0]], [0, 0]], 'duplicate-qubit'], ['control: wrong amplitude count', [2, [[1, 0], [0, 0]], [0]], 'bad-length'], ['control: all-zero state', [1, [[0, 0], [0, 0]], [0]], 'zero-state']], [['regression: random state 13', [3, [[0.624, -0.422], [-0.596, 0.926], [-0.719, 1.0], [-0.208, -0.957], [-0.398, 0.533], [-0.189, -0.721], [-0.845, -0.901], [0.144, -0.267]], [0, 1, 2]], {'000': 0.082574, '001': 0.176465, '010': 0.220741, '011': 0.139566, '100': 0.064389, '101': 0.080843, '110': 0.222031, '111': 0.013391}], ['regression: random state 14', [3, [[-0.144, 0.15], [-0.052, 0.123], [0.0, 0.0], [0.145, -0.129], [0.077, 0.218], [0.248, 0.026], [0.0, 0.0], [0.256, 0.015]], [2, 0, 1]], {'000': 0.154343, '001': 0.190816, '010': 0.06366, '011': 0.221969, '110': 0.134459, '111': 0.234753}], ['regression: random state 8', [2, [[0.258, -0.148], [-0.044, -0.154], [0.09, 0.21], [0.28, 0.265]], [0]], {'0': 0.446643, '1': 0.553357}], ['control: unnormalized pair', [1, [[3, 0], [0, 4]], [0]], {'0': 0.36, '1': 0.64}], ['control: near zero state', [1, [[1e-08, 0], [0, 1e-08]], [0]], 'zero-state'], ['control: reversed qubit list', [2, [[0, 0], [1, 0], [0, 0], [0, 0]], [1, 0]], {'10': 1.0}], ['control: single qubit marginal of |01>', [2, [[0, 0], [1, 0], [0, 0], [0, 0]], [1]], {'0': 1.0}]]]
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: bell state on both qubits	`{'00': 0.5, '11': 0.5}`	`{'00': 0.5, '11': 0.5}`	Passed
regression: random state 0	`{'01': 0.509607, '10': 0.490733}`	`{'01': 0.511954, '10': 0.488046}`	Failed
repair check: random state 1	`{'00': 0.991756}`	`{'00': 1.0}`	Failed
control: reversed qubit list	`{'10': 1.0}`	`{'10': 1.0}`	Passed
control: single qubit marginal of \|01>	`{'0': 1.0}`	`{'0': 1.0}`	Passed
control: out of range qubit equals n	`bad-qubit`	`bad-qubit`	Passed
control: negative qubit index	`bad-qubit`	`bad-qubit`	Passed

SHA-256 / 4b66dfb4e6b12e68c2a2e3bd714e923098f8ec55b3057dbff3ecc81a33aefa54

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    n, amps, qubits = x
    if len(amps) != 1 << n:
        return 'bad-length'
    if len(set(qubits)) != len(qubits):
        return 'duplicate-qubit'
    if any(q < 0 or q >= n for q in qubits):
        return 'bad-qubit'
    total = sum(re * re + im * im for re, im in amps)
    if total <= 1e-12:
        return 'zero-state'
    acc = {}
    for idx, (a, b) in enumerate(amps):
        p = a * a + b * b
        if p == 0:
            continue
        key = ''.join('1' if idx >> q & 1 else '0' for q in reversed(qubits))
        acc[key] = acc.get(key, 0.0) + p
    out = {}
    for key in sorted(acc):
        v = round(acc[key] / total, 6)
        if v > 0:
            out[key] = v
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: bell state on both qubits', [2, [[0.707107, 0], [0, 0], [0, 0], [0.707107, 0]], [0, 1]], {'00': 0.5, '11': 0.5}], ['regression: random state 0', [2, [[0.0, 0.0], [0.282, -0.043], [-0.278, 0.017], [0.0, 0.0]], [0, 1]], {'01': 0.511954, '10': 0.488046}], ['repair check: random state 1', [2, [[0.129, 0.125], [0.0, 0.0], [0.0, 0.0], [0.0, 0.0]], [1, 0]], {'00': 1.0}], ['control: reversed qubit list', [2, [[0, 0], [1, 0], [0, 0], [0, 0]], [1, 0]], {'10': 1.0}], ['control: single qubit marginal of |01>', [2, [[0, 0], [1, 0], [0, 0], [0, 0]], [1]], {'0': 1.0}], ['control: out of range qubit equals n', [2, [[1, 0], [0, 0], [0, 0], [0, 0]], [2]], 'bad-qubit'], ['control: negative qubit index', [2, [[1, 0], [0, 0], [0, 0], [0, 0]], [-1]], 'bad-qubit']], [['regression: random state 3', [2, [[0.379, 0.308], [-0.129, -0.524], [0.79, -0.299], [-0.403, -0.327]], [0, 1]], {'00': 0.157683, '01': 0.192532, '10': 0.471717, '11': 0.178068}], ['regression: random state 4', [1, [[-0.217, 0.525], [-0.308, -0.181]], [0]], {'0': 0.716602, '1': 0.283398}], ['regression: random state 2', [1, [[0.541, -0.923], [-0.479, -0.646]], [0]], {'0': 0.638959, '1': 0.361041}], ['control: duplicate qubits', [2, [[0.6, 0], [0, 0.8], [0, 0], [0, 0]], [0, 0]], 'duplicate-qubit'], ['control: wrong amplitude count', [2, [[1, 0], [0, 0]], [0]], 'bad-length'], ['control: all-zero state', [1, [[0, 0], [0, 0]], [0]], 'zero-state'], ['control: unnormalized pair', [1, [[3, 0], [0, 4]], [0]], {'0': 0.36, '1': 0.64}]], [['regression: random state 6', [3, [[-0.119, 0.092], [0.264, -0.223], [-0.189, 0.034], [-0.22, -0.267], [-0.291, -0.092], [0.09, -0.02], [0.062, -0.284], [-0.239, 0.039]], [2]], {'0': 0.54953, '1': 0.45047}], ['regression: random state 7', [1, [[0.725, -0.825], [-0.233, -0.266]], [0]], {'0': 0.906073, '1': 0.093927}], ['regression: random state 4', [1, [[-0.217, 0.525], [-0.308, -0.181]], [0]], {'0': 0.716602, '1': 0.283398}], ['control: near zero state', [1, [[1e-08, 0], [0, 1e-08]], [0]], 'zero-state'], ['control: reversed qubit list', [2, [[0, 0], [1, 0], [0, 0], [0, 0]], [1, 0]], {'10': 1.0}], ['control: single qubit marginal of |01>', [2, [[0, 0], [1, 0], [0, 0], [0, 0]], [1]], {'0': 1.0}], ['control: out of range qubit equals n', [2, [[1, 0], [0, 0], [0, 0], [0, 0]], [2]], 'bad-qubit']], [['regression: random state 10', [3, [[-0.064, 0.212], [0.264, -0.114], [-0.15, -0.24], [0.031, 0.141], [0.037, -0.002], [0.023, -0.229], [0.193, -0.153], [0.251, 0.097]], [0, 1, 2]], {'000': 0.116738, '001': 0.196846, '010': 0.190676, '011': 0.049614, '100': 0.003268, '101': 0.126094, '110': 0.144395, '111': 0.17237}], ['regression: random state 11', [2, [[-0.211, 0.28], [0.154, -0.18], [-0.016, -0.095], [-0.157, 0.075]], [0]], {'0': 0.604789, '1': 0.395211}], ['regression: random state 6', [3, [[-0.119, 0.092], [0.264, -0.223], [-0.189, 0.034], [-0.22, -0.267], [-0.291, -0.092], [0.09, -0.02], [0.062, -0.284], [-0.239, 0.039]], [2]], {'0': 0.54953, '1': 0.45047}], ['control: negative qubit index', [2, [[1, 0], [0, 0], [0, 0], [0, 0]], [-1]], 'bad-qubit'], ['control: duplicate qubits', [2, [[0.6, 0], [0, 0.8], [0, 0], [0, 0]], [0, 0]], 'duplicate-qubit'], ['control: wrong amplitude count', [2, [[1, 0], [0, 0]], [0]], 'bad-length'], ['control: all-zero state', [1, [[0, 0], [0, 0]], [0]], 'zero-state']], [['regression: random state 13', [3, [[0.624, -0.422], [-0.596, 0.926], [-0.719, 1.0], [-0.208, -0.957], [-0.398, 0.533], [-0.189, -0.721], [-0.845, -0.901], [0.144, -0.267]], [0, 1, 2]], {'000': 0.082574, '001': 0.176465, '010': 0.220741, '011': 0.139566, '100': 0.064389, '101': 0.080843, '110': 0.222031, '111': 0.013391}], ['regression: random state 14', [3, [[-0.144, 0.15], [-0.052, 0.123], [0.0, 0.0], [0.145, -0.129], [0.077, 0.218], [0.248, 0.026], [0.0, 0.0], [0.256, 0.015]], [2, 0, 1]], {'000': 0.154343, '001': 0.190816, '010': 0.06366, '011': 0.221969, '110': 0.134459, '111': 0.234753}], ['regression: random state 8', [2, [[0.258, -0.148], [-0.044, -0.154], [0.09, 0.21], [0.28, 0.265]], [0]], {'0': 0.446643, '1': 0.553357}], ['control: unnormalized pair', [1, [[3, 0], [0, 4]], [0]], {'0': 0.36, '1': 0.64}], ['control: near zero state', [1, [[1e-08, 0], [0, 1e-08]], [0]], 'zero-state'], ['control: reversed qubit list', [2, [[0, 0], [1, 0], [0, 0], [0, 0]], [1, 0]], {'10': 1.0}], ['control: single qubit marginal of |01>', [2, [[0, 0], [1, 0], [0, 0], [0, 0]], [1]], {'0': 1.0}]]]
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: bell state on both qubits	`{'00': 0.5, '11': 0.5}`	`{'00': 0.5, '11': 0.5}`	Passed
regression: random state 0	`{'01': 0.511954, '10': 0.488046}`	`{'01': 0.511954, '10': 0.488046}`	Passed
repair check: random state 1	`{'00': 1.0}`	`{'00': 1.0}`	Passed
control: reversed qubit list	`{'10': 1.0}`	`{'10': 1.0}`	Passed
control: single qubit marginal of \|01>	`{'0': 1.0}`	`{'0': 1.0}`	Passed
control: out of range qubit equals n	`bad-qubit`	`bad-qubit`	Passed
control: negative qubit index	`bad-qubit`	`bad-qubit`	Passed

SHA-256 / 82ff888aa8cce2d3499dcc4d08ed44f12300c92f3fccb0003d5925ea5856f95d

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 2026-09-29T14:51:30.948968+00:00.

Case digest / 8425cf2db17f4cafada2565a8e6994531a0d24d6c00ebc83f0d4ebec3ff452d3