FA-91126 / Quantum circuit simulation / Open access

Shot sampler writes qubit 0 as the leftmost character · case 01

An outcome on basis index 1 of two qubits is counted as "10" instead of "01".

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

ROOT CAUSE

The formatted index string is reversed before use as the key.

VERIFIED REPAIR

Use the zero-padded binary index directly (qubit n-1 leftmost).

Unsuccessful approach: The attempted repair removes the reversal but also drops zero padding, producing keys like "1" for "01".

Case contract

Input [n, weights, uniforms]; weights are nonnegative integers for basis indices 0..2**n-1 and uniforms are exact decimal or fraction strings in [0, 1). Each uniform u selects the first index i with u * total < cumulative weight through i. Return counts {bitstring: count} with qubit n-1 leftmost. Errors: "bad-length", "negative-weight", "no-support", ["bad-uniform", position].

Why this case matters

Deterministic replay of sampled shots makes simulator results reproducible; CDF boundary slips bias counts toward impossible outcomes.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(x):
    n, weights, us = x
    if len(weights) != 1 << n:
        return 'bad-length'
    if any(w < 0 for w in weights):
        return 'negative-weight'
    total = sum(weights)
    if total == 0:
        return 'no-support'
    counts = {}
    for idx, s in enumerate(us):
        u = Fraction(s)
        if u < 0 or u >= 1:
            return ['bad-uniform', idx]
        target = u * total
        cum = 0
        for i, w in enumerate(weights):
            cum += w
            if target < cum:
                break
        key = format(i, '0%db' % n)[::-1]
        counts[key] = counts.get(key, 0) + 1
    return counts
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: high qubit outcome', [2, [0, 0, 1, 0], ['0.3', '0.9']], {'10': 2}], ['regression: random shots 1', [3, [5, 0, 2, 0, 5, 3, 0, 1], ['9/16', '9/16']], {'100': 2}], ['repair check: zero weight first outcome', [2, [0, 1, 1, 2], ['0', '0.25']], {'01': 1, '10': 1}], ['control: boundary uniform on cumulative edge', [1, [1, 1], ['0.5']], {'1': 1}], ['control: uniform exactly one', [1, [1, 1], ['1']], ['bad-uniform', 0]], ['control: negative uniform', [1, [1, 1], ['-0.25']], ['bad-uniform', 0]], ['control: negative weight', [1, [2, -1], ['0.5']], 'negative-weight']], [['regression: random shots 6', [3, [1, 1, 0, 0, 0, 3, 3, 0], ['0.597', '5/8', '0.601']], {'101': 2, '110': 1}], ['regression: random shots 7', [2, [0, 1, 0, 0], ['0/1', '0.123']], {'01': 2}], ['repair check: random shots 8', [2, [1, 0, 1, 3], ['0.813', '2/5', '4/5', '0.149', '0.53']], {'11': 4, '00': 1}], ['control: all zero weights', [1, [0, 0], ['0.5']], 'no-support'], ['control: bad length', [2, [1, 1], ['0.1']], 'bad-length'], ['control: random shots 0', [1, [0, 1], ['0/1', '0.952', '0/1']], {'1': 3}], ['control: random shots 2', [1, [0, 5], ['0.967', '0.119', '0.012', '1/5', '0.243', '0/5']], {'1': 6}]], [['regression: random shots 11', [2, [1, 2, 0, 2], ['0.643', '0.519', '0.64', '0.875']], {'11': 3, '01': 1}], ['regression: random shots 14', [3, [0, 1, 2, 0, 0, 3, 1, 0], ['0.559', '6/7', '2/7', '0.29', '0.711', '5/7']], {'101': 3, '110': 1, '010': 2}], ['repair check: random shots 12', [3, [5, 5, 5, 5, 1, 3, 0, 0], ['14/24', '0/24', '0.202']], {'010': 1, '000': 2}], ['control: random shots 3', [1, [3, 5], ['0.916', '3/8', '0.642']], {'1': 3}], ['control: random shots 10', [3, [3, 0, 1, 2, 0, 3, 0, 5], ['10/14', '0.687', '0.608']], {'111': 2, '101': 1}], ['control: random shots 13', [1, [3, 0], ['0.586', '1/3']], {'0': 2}], ['control: random shots 15', [1, [0, 1], ['0/1', '0.769', '0.573', '0.347', '0.401', '0/1']], {'1': 6}]], [['regression: random shots 25', [3, [0, 0, 3, 3, 0, 0, 0, 3], ['5/9', '0.444', '0.463']], {'011': 3}], ['regression: random shots 26', [3, [2, 1, 1, 2, 0, 0, 5, 5], ['14/16', '0.295']], {'111': 1, '011': 1}], ['regression: random shots 14', [3, [0, 1, 2, 0, 0, 3, 1, 0], ['0.559', '6/7', '2/7', '0.29', '0.711', '5/7']], {'101': 3, '110': 1, '010': 2}], ['control: random shots 16', [1, [0, 1], ['0.929', '0.975', '0.277', '0/1', '0.216']], {'1': 5}], ['control: random shots 17', [1, [2, 1], ['0.153', '0.906', '0/3', '0.007', '1/3']], {'0': 4, '1': 1}], ['control: random shots 18', [1, [5, 3], ['4/8', '4/8', '0.129', '0.153', '1/8', '0.326']], {'0': 6}], ['control: random shots 19', [1, [3, 2], ['0.826', '0.88']], {'1': 2}]], [['regression: random shots 30', [3, [0, 1, 3, 3, 0, 2, 0, 0], ['0/9', '0.411', '7/9', '0.796', '0.678', '0/9']], {'001': 2, '010': 1, '101': 2, '011': 1}], ['regression: random shots 31', [2, [3, 2, 0, 1], ['2/6', '0.726', '2/6', '0/6', '0.328', '0.558']], {'00': 4, '01': 2}], ['regression: random shots 25', [3, [0, 0, 3, 3, 0, 0, 0, 3], ['5/9', '0.444', '0.463']], {'011': 3}], ['control: random shots 20', [1, [5, 1], ['0.272', '0/6', '0.203', '0/6']], {'0': 4}], ['control: random shots 21', [1, [1, 3], ['1/4', '0.282', '0.17']], {'1': 2, '0': 1}], ['control: random shots 22', [1, [0, 5], ['0.608', '1/5', '2/5']], {'1': 3}], ['control: random shots 23', [1, [2, 0], ['1/2', '0.071', '0/2', '0/2', '0.086', '0.733']], {'0': 6}]]]
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: high qubit outcome	`{'01': 2}`	`{'10': 2}`	Failed
regression: random shots 1	`{'001': 2}`	`{'100': 2}`	Failed
repair check: zero weight first outcome	`{'01': 1, '10': 1}`	`{'01': 1, '10': 1}`	Passed
control: boundary uniform on cumulative edge	`{'1': 1}`	`{'1': 1}`	Passed
control: uniform exactly one	`['bad-uniform', 0]`	`['bad-uniform', 0]`	Passed
control: negative uniform	`['bad-uniform', 0]`	`['bad-uniform', 0]`	Passed
control: negative weight	`negative-weight`	`negative-weight`	Passed

SHA-256 / 5bc1b505f7fdcbe7ec9533dfba198f62aab12e7667b72bd824f3e41587617d6b

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(x):
    n, weights, us = x
    if len(weights) != 1 << n:
        return 'bad-length'
    if any(w < 0 for w in weights):
        return 'negative-weight'
    total = sum(weights)
    if total == 0:
        return 'no-support'
    counts = {}
    for idx, s in enumerate(us):
        u = Fraction(s)
        if u < 0 or u >= 1:
            return ['bad-uniform', idx]
        target = u * total
        cum = 0
        for i, w in enumerate(weights):
            cum += w
            if target < cum:
                break
        key = format(i, 'b')
        counts[key] = counts.get(key, 0) + 1
    return counts
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: high qubit outcome', [2, [0, 0, 1, 0], ['0.3', '0.9']], {'10': 2}], ['regression: random shots 1', [3, [5, 0, 2, 0, 5, 3, 0, 1], ['9/16', '9/16']], {'100': 2}], ['repair check: zero weight first outcome', [2, [0, 1, 1, 2], ['0', '0.25']], {'01': 1, '10': 1}], ['control: boundary uniform on cumulative edge', [1, [1, 1], ['0.5']], {'1': 1}], ['control: uniform exactly one', [1, [1, 1], ['1']], ['bad-uniform', 0]], ['control: negative uniform', [1, [1, 1], ['-0.25']], ['bad-uniform', 0]], ['control: negative weight', [1, [2, -1], ['0.5']], 'negative-weight']], [['regression: random shots 6', [3, [1, 1, 0, 0, 0, 3, 3, 0], ['0.597', '5/8', '0.601']], {'101': 2, '110': 1}], ['regression: random shots 7', [2, [0, 1, 0, 0], ['0/1', '0.123']], {'01': 2}], ['repair check: random shots 8', [2, [1, 0, 1, 3], ['0.813', '2/5', '4/5', '0.149', '0.53']], {'11': 4, '00': 1}], ['control: all zero weights', [1, [0, 0], ['0.5']], 'no-support'], ['control: bad length', [2, [1, 1], ['0.1']], 'bad-length'], ['control: random shots 0', [1, [0, 1], ['0/1', '0.952', '0/1']], {'1': 3}], ['control: random shots 2', [1, [0, 5], ['0.967', '0.119', '0.012', '1/5', '0.243', '0/5']], {'1': 6}]], [['regression: random shots 11', [2, [1, 2, 0, 2], ['0.643', '0.519', '0.64', '0.875']], {'11': 3, '01': 1}], ['regression: random shots 14', [3, [0, 1, 2, 0, 0, 3, 1, 0], ['0.559', '6/7', '2/7', '0.29', '0.711', '5/7']], {'101': 3, '110': 1, '010': 2}], ['repair check: random shots 12', [3, [5, 5, 5, 5, 1, 3, 0, 0], ['14/24', '0/24', '0.202']], {'010': 1, '000': 2}], ['control: random shots 3', [1, [3, 5], ['0.916', '3/8', '0.642']], {'1': 3}], ['control: random shots 10', [3, [3, 0, 1, 2, 0, 3, 0, 5], ['10/14', '0.687', '0.608']], {'111': 2, '101': 1}], ['control: random shots 13', [1, [3, 0], ['0.586', '1/3']], {'0': 2}], ['control: random shots 15', [1, [0, 1], ['0/1', '0.769', '0.573', '0.347', '0.401', '0/1']], {'1': 6}]], [['regression: random shots 25', [3, [0, 0, 3, 3, 0, 0, 0, 3], ['5/9', '0.444', '0.463']], {'011': 3}], ['regression: random shots 26', [3, [2, 1, 1, 2, 0, 0, 5, 5], ['14/16', '0.295']], {'111': 1, '011': 1}], ['regression: random shots 14', [3, [0, 1, 2, 0, 0, 3, 1, 0], ['0.559', '6/7', '2/7', '0.29', '0.711', '5/7']], {'101': 3, '110': 1, '010': 2}], ['control: random shots 16', [1, [0, 1], ['0.929', '0.975', '0.277', '0/1', '0.216']], {'1': 5}], ['control: random shots 17', [1, [2, 1], ['0.153', '0.906', '0/3', '0.007', '1/3']], {'0': 4, '1': 1}], ['control: random shots 18', [1, [5, 3], ['4/8', '4/8', '0.129', '0.153', '1/8', '0.326']], {'0': 6}], ['control: random shots 19', [1, [3, 2], ['0.826', '0.88']], {'1': 2}]], [['regression: random shots 30', [3, [0, 1, 3, 3, 0, 2, 0, 0], ['0/9', '0.411', '7/9', '0.796', '0.678', '0/9']], {'001': 2, '010': 1, '101': 2, '011': 1}], ['regression: random shots 31', [2, [3, 2, 0, 1], ['2/6', '0.726', '2/6', '0/6', '0.328', '0.558']], {'00': 4, '01': 2}], ['regression: random shots 25', [3, [0, 0, 3, 3, 0, 0, 0, 3], ['5/9', '0.444', '0.463']], {'011': 3}], ['control: random shots 20', [1, [5, 1], ['0.272', '0/6', '0.203', '0/6']], {'0': 4}], ['control: random shots 21', [1, [1, 3], ['1/4', '0.282', '0.17']], {'1': 2, '0': 1}], ['control: random shots 22', [1, [0, 5], ['0.608', '1/5', '2/5']], {'1': 3}], ['control: random shots 23', [1, [2, 0], ['1/2', '0.071', '0/2', '0/2', '0.086', '0.733']], {'0': 6}]]]
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: high qubit outcome	`{'10': 2}`	`{'10': 2}`	Passed
regression: random shots 1	`{'100': 2}`	`{'100': 2}`	Passed
repair check: zero weight first outcome	`{'1': 1, '10': 1}`	`{'01': 1, '10': 1}`	Failed
control: boundary uniform on cumulative edge	`{'1': 1}`	`{'1': 1}`	Passed
control: uniform exactly one	`['bad-uniform', 0]`	`['bad-uniform', 0]`	Passed
control: negative uniform	`['bad-uniform', 0]`	`['bad-uniform', 0]`	Passed
control: negative weight	`negative-weight`	`negative-weight`	Passed

SHA-256 / e45bfe16f82cd081453aae772230cb7f9de1b7f0ca4bf5924b00c8e13bfea311

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(x):
    n, weights, us = x
    if len(weights) != 1 << n:
        return 'bad-length'
    if any(w < 0 for w in weights):
        return 'negative-weight'
    total = sum(weights)
    if total == 0:
        return 'no-support'
    counts = {}
    for idx, s in enumerate(us):
        u = Fraction(s)
        if u < 0 or u >= 1:
            return ['bad-uniform', idx]
        target = u * total
        cum = 0
        for i, w in enumerate(weights):
            cum += w
            if target < cum:
                break
        key = format(i, '0%db' % n)
        counts[key] = counts.get(key, 0) + 1
    return counts
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: high qubit outcome', [2, [0, 0, 1, 0], ['0.3', '0.9']], {'10': 2}], ['regression: random shots 1', [3, [5, 0, 2, 0, 5, 3, 0, 1], ['9/16', '9/16']], {'100': 2}], ['repair check: zero weight first outcome', [2, [0, 1, 1, 2], ['0', '0.25']], {'01': 1, '10': 1}], ['control: boundary uniform on cumulative edge', [1, [1, 1], ['0.5']], {'1': 1}], ['control: uniform exactly one', [1, [1, 1], ['1']], ['bad-uniform', 0]], ['control: negative uniform', [1, [1, 1], ['-0.25']], ['bad-uniform', 0]], ['control: negative weight', [1, [2, -1], ['0.5']], 'negative-weight']], [['regression: random shots 6', [3, [1, 1, 0, 0, 0, 3, 3, 0], ['0.597', '5/8', '0.601']], {'101': 2, '110': 1}], ['regression: random shots 7', [2, [0, 1, 0, 0], ['0/1', '0.123']], {'01': 2}], ['repair check: random shots 8', [2, [1, 0, 1, 3], ['0.813', '2/5', '4/5', '0.149', '0.53']], {'11': 4, '00': 1}], ['control: all zero weights', [1, [0, 0], ['0.5']], 'no-support'], ['control: bad length', [2, [1, 1], ['0.1']], 'bad-length'], ['control: random shots 0', [1, [0, 1], ['0/1', '0.952', '0/1']], {'1': 3}], ['control: random shots 2', [1, [0, 5], ['0.967', '0.119', '0.012', '1/5', '0.243', '0/5']], {'1': 6}]], [['regression: random shots 11', [2, [1, 2, 0, 2], ['0.643', '0.519', '0.64', '0.875']], {'11': 3, '01': 1}], ['regression: random shots 14', [3, [0, 1, 2, 0, 0, 3, 1, 0], ['0.559', '6/7', '2/7', '0.29', '0.711', '5/7']], {'101': 3, '110': 1, '010': 2}], ['repair check: random shots 12', [3, [5, 5, 5, 5, 1, 3, 0, 0], ['14/24', '0/24', '0.202']], {'010': 1, '000': 2}], ['control: random shots 3', [1, [3, 5], ['0.916', '3/8', '0.642']], {'1': 3}], ['control: random shots 10', [3, [3, 0, 1, 2, 0, 3, 0, 5], ['10/14', '0.687', '0.608']], {'111': 2, '101': 1}], ['control: random shots 13', [1, [3, 0], ['0.586', '1/3']], {'0': 2}], ['control: random shots 15', [1, [0, 1], ['0/1', '0.769', '0.573', '0.347', '0.401', '0/1']], {'1': 6}]], [['regression: random shots 25', [3, [0, 0, 3, 3, 0, 0, 0, 3], ['5/9', '0.444', '0.463']], {'011': 3}], ['regression: random shots 26', [3, [2, 1, 1, 2, 0, 0, 5, 5], ['14/16', '0.295']], {'111': 1, '011': 1}], ['regression: random shots 14', [3, [0, 1, 2, 0, 0, 3, 1, 0], ['0.559', '6/7', '2/7', '0.29', '0.711', '5/7']], {'101': 3, '110': 1, '010': 2}], ['control: random shots 16', [1, [0, 1], ['0.929', '0.975', '0.277', '0/1', '0.216']], {'1': 5}], ['control: random shots 17', [1, [2, 1], ['0.153', '0.906', '0/3', '0.007', '1/3']], {'0': 4, '1': 1}], ['control: random shots 18', [1, [5, 3], ['4/8', '4/8', '0.129', '0.153', '1/8', '0.326']], {'0': 6}], ['control: random shots 19', [1, [3, 2], ['0.826', '0.88']], {'1': 2}]], [['regression: random shots 30', [3, [0, 1, 3, 3, 0, 2, 0, 0], ['0/9', '0.411', '7/9', '0.796', '0.678', '0/9']], {'001': 2, '010': 1, '101': 2, '011': 1}], ['regression: random shots 31', [2, [3, 2, 0, 1], ['2/6', '0.726', '2/6', '0/6', '0.328', '0.558']], {'00': 4, '01': 2}], ['regression: random shots 25', [3, [0, 0, 3, 3, 0, 0, 0, 3], ['5/9', '0.444', '0.463']], {'011': 3}], ['control: random shots 20', [1, [5, 1], ['0.272', '0/6', '0.203', '0/6']], {'0': 4}], ['control: random shots 21', [1, [1, 3], ['1/4', '0.282', '0.17']], {'1': 2, '0': 1}], ['control: random shots 22', [1, [0, 5], ['0.608', '1/5', '2/5']], {'1': 3}], ['control: random shots 23', [1, [2, 0], ['1/2', '0.071', '0/2', '0/2', '0.086', '0.733']], {'0': 6}]]]
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: high qubit outcome	`{'10': 2}`	`{'10': 2}`	Passed
regression: random shots 1	`{'100': 2}`	`{'100': 2}`	Passed
repair check: zero weight first outcome	`{'01': 1, '10': 1}`	`{'01': 1, '10': 1}`	Passed
control: boundary uniform on cumulative edge	`{'1': 1}`	`{'1': 1}`	Passed
control: uniform exactly one	`['bad-uniform', 0]`	`['bad-uniform', 0]`	Passed
control: negative uniform	`['bad-uniform', 0]`	`['bad-uniform', 0]`	Passed
control: negative weight	`negative-weight`	`negative-weight`	Passed

SHA-256 / 6d3d7919f59116ea102a8bdb15fd992841fb8bc7f74e28de502ca2d1521d51d6

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 2026-09-29T14:51:33.000681+00:00.

Case digest / 9224697326c18e3515bc819ce05293d63fa2b71c70a95cb5720372315f7a7720