FAILURE MAP
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FA-91096 / Quantum circuit simulation / Open access

Reduced density matrix matches on the kept qubit instead of the environment · case 01

A Bell state reduces to a matrix with coherences instead of the maximally mixed I/2.

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

ROOT CAUSE

Pairs (i, j) are accepted when their kept bits agree rather than when their environment bits agree.

THE FAILURE

Pairs (i, j) are accepted when their kept bits agree rather than when their environment bits agree.

Unsuccessful approach: The attempted repair accepts pairs whose index difference is exactly the kept mask, which also admits pairs that differ in several bits.

Case contract

Input [n, amps, keep]; trace out every qubit except keep (0 = LSB) from the pure state and return {"rho": 2x2 matrix of [re, im] entries with rho[r][c] = sum psi_r psi_c^*, trace-normalized, "purity": sum |rho_rc|^2}, all rounded to 6 decimals.

Why this case matters

Reduced states quantify entanglement and are used in debugging subsystem behavior; index or conjugation slips give non-physical matrices.

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, keep = x
    psi = [complex(a, b) for a, b in amps]
    m = 1 << keep
    rho = [[0j, 0j], [0j, 0j]]
    for i in range(len(psi)):
        for j in range(len(psi)):
            if (i & m) != (j & m):
                continue
            rho[(i >> keep) & 1][(j >> keep) & 1] += psi[i] * psi[j].conjugate()
    tr = (rho[0][0] + rho[1][1]).real
    rho = [[v / tr for v in row] for row in rho]
    purity = sum(abs(rho[r][c]) ** 2 for r in range(2) for c in range(2))
    f = lambda v: [round(v.real, 6) + 0.0, round(v.imag, 6) + 0.0]
    return {'rho': [[f(v) for v in row] for row in rho], 'purity': round(purity, 6) + 0.0}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: product keep 0 complex', [2, [[0.6, 0], [0, 0.8], [0, 0], [0, 0]], 0], {'rho': [[[0.36, 0.0], [0.0, -0.48]], [[0.0, 0.48], [0.64, 0.0]]], 'purity': 1.0}], ['regression: random reduction 0', [3, [[0.069, -0.179], [-0.176, -0.715], [0.749, 0.757], [-0.786, 0.461], [0.287, -0.288], [-0.462, 0.389], [-0.216, 0.203], [0.456, 0.037]], 0], {'rho': [[[0.422483, 0.0], [-0.136327, -0.218796]], [[-0.136327, 0.218796], [0.577517, 0.0]]], 'purity': 0.644932}], ['regression: random reduction 1', [3, [[0.986, 1.972], [-1.424, 1.98], [-1.308, 1.935], [1.338, 1.563], [-1.898, 1.945], [-1.572, 1.06], [1.832, 0.52], [0.807, -1.748]], 0], {'rho': [[[0.549537, 0.0], [0.241932, 0.063109]], [[0.241932, -0.063109], [0.450463, 0.0]]], 'purity': 0.629935}], ['control: bell keep 0', [2, [[0.707107, 0], [0, 0], [0, 0], [0.707107, 0]], 0], {'rho': [[[0.5, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.5, 0.0]]], 'purity': 0.5}], ['control: product keep 1', [2, [[0.6, 0], [0, 0.8], [0, 0], [0, 0]], 1], {'rho': [[[1.0, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.0, 0.0]]], 'purity': 1.0}], ['control: unnormalized ghz keep 2', [3, [[2, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [2, 0]], 2], {'rho': [[[0.5, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.5, 0.0]]], 'purity': 0.5}], ['regression: random reduction 2', [3, [[-0.436, -0.609], [0.766, -0.544], [-0.426, -0.406], [0.661, 0.537], [-0.32, -0.358], [0.306, 0.359], [-0.048, -0.239], [-0.254, -0.85]], 0], {'rho': [[[0.313851, 0.0], [-0.134578, -0.188226]], [[-0.134578, 0.188226], [0.686149, 0.0]]], 'purity': 0.676383}]], [['regression: random reduction 2', [3, [[-0.436, -0.609], [0.766, -0.544], [-0.426, -0.406], [0.661, 0.537], [-0.32, -0.358], [0.306, 0.359], [-0.048, -0.239], [-0.254, -0.85]], 0], {'rho': [[[0.313851, 0.0], [-0.134578, -0.188226]], [[-0.134578, 0.188226], [0.686149, 0.0]]], 'purity': 0.676383}], ['regression: random reduction 3', [3, [[1.49, -1.9], [-1.815, 0.487], [-1.545, 1.465], [1.903, 1.324], [1.584, -1.799], [1.763, -0.058], [-0.233, 1.643], [-1.856, 0.918]], 0], {'rho': [[[0.536366, 0.0], [0.005901, 0.046665]], [[0.005901, -0.046665], [0.463634, 0.0]]], 'purity': 0.50707}], ['regression: random reduction 4', [3, [[-0.633, 0.511], [0.239, 0.051], [0.129, 0.555], [0.414, -0.526], [-0.93, 0.617], [-0.487, -0.199], [0.609, 0.703], [0.243, -0.571]], 1], {'rho': [[[0.525894, 0.0], [0.032047, 0.296983]], [[0.032047, -0.296983], [0.474106, 0.0]]], 'purity': 0.679793}], ['control: product keep 1', [2, [[0.6, 0], [0, 0.8], [0, 0], [0, 0]], 1], {'rho': [[[1.0, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.0, 0.0]]], 'purity': 1.0}], ['control: unnormalized ghz keep 2', [3, [[2, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [2, 0]], 2], {'rho': [[[0.5, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.5, 0.0]]], 'purity': 0.5}], ['control: bell keep 0', [2, [[0.707107, 0], [0, 0], [0, 0], [0.707107, 0]], 0], {'rho': [[[0.5, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.5, 0.0]]], 'purity': 0.5}], ['regression: random reduction 1', [3, [[0.986, 1.972], [-1.424, 1.98], [-1.308, 1.935], [1.338, 1.563], [-1.898, 1.945], [-1.572, 1.06], [1.832, 0.52], [0.807, -1.748]], 0], {'rho': [[[0.549537, 0.0], [0.241932, 0.063109]], [[0.241932, -0.063109], [0.450463, 0.0]]], 'purity': 0.629935}]], [['regression: random reduction 5', [2, [[-0.972, -0.109], [0.26, 0.259], [-0.134, -0.66], [-0.522, -0.043]], 0], {'rho': [[[0.775173, 0.0], [-0.100385, 0.309012]], [[-0.100385, -0.309012], [0.224827, 0.0]]], 'purity': 0.862571}], ['regression: random reduction 6', [3, [[-0.509, 0.635], [-0.554, 0.902], [-0.528, 0.406], [0.035, -0.166], [0.785, 0.17], [0.113, 0.282], [-0.237, -0.733], [0.778, 0.455]], 1], {'rho': [[[0.57299, 0.0], [0.059796, 0.116878]], [[0.059796, -0.116878], [0.42701, 0.0]]], 'purity': 0.545127}], ['regression: random reduction 4', [3, [[-0.633, 0.511], [0.239, 0.051], [0.129, 0.555], [0.414, -0.526], [-0.93, 0.617], [-0.487, -0.199], [0.609, 0.703], [0.243, -0.571]], 1], {'rho': [[[0.525894, 0.0], [0.032047, 0.296983]], [[0.032047, -0.296983], [0.474106, 0.0]]], 'purity': 0.679793}], ['control: unnormalized ghz keep 2', [3, [[2, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [2, 0]], 2], {'rho': [[[0.5, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.5, 0.0]]], 'purity': 0.5}], ['control: bell keep 0', [2, [[0.707107, 0], [0, 0], [0, 0], [0.707107, 0]], 0], {'rho': [[[0.5, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.5, 0.0]]], 'purity': 0.5}], ['control: product keep 1', [2, [[0.6, 0], [0, 0.8], [0, 0], [0, 0]], 1], {'rho': [[[1.0, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.0, 0.0]]], 'purity': 1.0}], ['regression: random reduction 2', [3, [[-0.436, -0.609], [0.766, -0.544], [-0.426, -0.406], [0.661, 0.537], [-0.32, -0.358], [0.306, 0.359], [-0.048, -0.239], [-0.254, -0.85]], 0], {'rho': [[[0.313851, 0.0], [-0.134578, -0.188226]], [[-0.134578, 0.188226], [0.686149, 0.0]]], 'purity': 0.676383}]], [['regression: random reduction 8', [3, [[-1.677, 1.763], [0.965, -0.593], [-1.405, -0.16], [0.617, -0.175], [-0.069, 0.647], [0.956, 1.91], [1.615, 1.856], [-0.044, 0.633]], 1], {'rho': [[[0.578893, 0.0], [0.238878, -0.116767]], [[0.238878, 0.116767], [0.421107, 0.0]]], 'purity': 0.653843}], ['regression: random reduction 9', [3, [[0.61, 0.432], [0.921, -0.251], [-0.196, 0.927], [-0.808, 0.05], [0.743, -0.342], [0.487, 0.369], [-0.844, 0.867], [-0.169, 0.678]], 2], {'rho': [[[0.502365, 0.0], [0.299281, -0.000926]], [[0.299281, 0.000926], [0.497635, 0.0]]], 'purity': 0.679151}], ['regression: random reduction 6', [3, [[-0.509, 0.635], [-0.554, 0.902], [-0.528, 0.406], [0.035, -0.166], [0.785, 0.17], [0.113, 0.282], [-0.237, -0.733], [0.778, 0.455]], 1], {'rho': [[[0.57299, 0.0], [0.059796, 0.116878]], [[0.059796, -0.116878], [0.42701, 0.0]]], 'purity': 0.545127}], ['control: bell keep 0', [2, [[0.707107, 0], [0, 0], [0, 0], [0.707107, 0]], 0], {'rho': [[[0.5, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.5, 0.0]]], 'purity': 0.5}], ['control: product keep 1', [2, [[0.6, 0], [0, 0.8], [0, 0], [0, 0]], 1], {'rho': [[[1.0, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.0, 0.0]]], 'purity': 1.0}], ['control: unnormalized ghz keep 2', [3, [[2, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [2, 0]], 2], {'rho': [[[0.5, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.5, 0.0]]], 'purity': 0.5}], ['regression: random reduction 3', [3, [[1.49, -1.9], [-1.815, 0.487], [-1.545, 1.465], [1.903, 1.324], [1.584, -1.799], [1.763, -0.058], [-0.233, 1.643], [-1.856, 0.918]], 0], {'rho': [[[0.536366, 0.0], [0.005901, 0.046665]], [[0.005901, -0.046665], [0.463634, 0.0]]], 'purity': 0.50707}]], [['regression: random reduction 11', [2, [[0.608, -1.677], [-1.453, -1.131], [-0.939, -0.925], [-1.391, 1.723]], 1], {'rho': [[[0.497404, 0.0], [0.079671, 0.470271]], [[0.079671, -0.470271], [0.502596, 0.0]]], 'purity': 0.955018}], ['regression: random reduction 12', [2, [[0.346, 0.105], [0.065, -0.046], [0.207, 0.409], [0.186, -0.621]], 0], {'rho': [[[0.444161, 0.0], [-0.257772, 0.296257]], [[-0.257772, -0.296257], [0.555839, 0.0]]], 'purity': 0.814665}], ['regression: random reduction 15', [2, [[0.394, 0.988], [0.617, 0.009], [0.95, 0.172], [-0.178, 0.108]], 0], {'rho': [[[0.829506, 0.0], [0.040789, 0.190078]], [[0.040789, -0.190078], [0.170494, 0.0]]], 'purity': 0.792735}], ['control: product keep 1', [2, [[0.6, 0], [0, 0.8], [0, 0], [0, 0]], 1], {'rho': [[[1.0, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.0, 0.0]]], 'purity': 1.0}], ['control: unnormalized ghz keep 2', [3, [[2, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [2, 0]], 2], {'rho': [[[0.5, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.5, 0.0]]], 'purity': 0.5}], ['control: bell keep 0', [2, [[0.707107, 0], [0, 0], [0, 0], [0.707107, 0]], 0], {'rho': [[[0.5, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.5, 0.0]]], 'purity': 0.5}], ['regression: random reduction 4', [3, [[-0.633, 0.511], [0.239, 0.051], [0.129, 0.555], [0.414, -0.526], [-0.93, 0.617], [-0.487, -0.199], [0.609, 0.703], [0.243, -0.571]], 1], {'rho': [[[0.525894, 0.0], [0.032047, 0.296983]], [[0.032047, -0.296983], [0.474106, 0.0]]], 'purity': 0.679793}]]]
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 fixtureActualExpectedOutcome
regression: product keep 0 complex{'purity': 0.5392, 'rho': [[[0.36, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.64, 0.0]]]}{'purity': 1.0, 'rho': [[[0.36, 0.0], [0.0, -0.48]], [[0.0, 0.48], [0.64, 0.0]]]}Failed
regression: random reduction 0{'purity': 0.500557, 'rho': [[[0.516691, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.483309, 0.0]]]}{'purity': 0.644932, 'rho': [[[0.422483, 0.0], [-0.136327, -0.218796]], [[-0.136327, 0.218796], [0.577517, 0.0]]]}Failed
regression: random reduction 1{'purity': 0.706295, 'rho': [[[0.821166, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.178834, 0.0]]]}{'purity': 0.629935, 'rho': [[[0.549537, 0.0], [0.241932, 0.063109]], [[0.241932, -0.063109], [0.450463, 0.0]]]}Failed
control: bell keep 0{'purity': 0.5, 'rho': [[[0.5, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.5, 0.0]]]}{'purity': 0.5, 'rho': [[[0.5, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.5, 0.0]]]}Passed
control: product keep 1{'purity': 1.0, 'rho': [[[1.0, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.0, 0.0]]]}{'purity': 1.0, 'rho': [[[1.0, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.0, 0.0]]]}Passed
control: unnormalized ghz keep 2{'purity': 0.5, 'rho': [[[0.5, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.5, 0.0]]]}{'purity': 0.5, 'rho': [[[0.5, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.5, 0.0]]]}Passed
regression: random reduction 2{'purity': 0.532768, 'rho': [[[0.628, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.372, 0.0]]]}{'purity': 0.676383, 'rho': [[[0.313851, 0.0], [-0.134578, -0.188226]], [[-0.134578, 0.188226], [0.686149, 0.0]]]}Failed

SHA-256 / e9e9f7d82b4b729df09d61b6a3b4c1de08614c08933a3d5c9a08c94cb42426b1

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, keep = x
    psi = [complex(a, b) for a, b in amps]
    m = 1 << keep
    rho = [[0j, 0j], [0j, 0j]]
    for i in range(len(psi)):
        for j in range(len(psi)):
            if abs(i - j) not in (0, m):
                continue
            rho[(i >> keep) & 1][(j >> keep) & 1] += psi[i] * psi[j].conjugate()
    tr = (rho[0][0] + rho[1][1]).real
    rho = [[v / tr for v in row] for row in rho]
    purity = sum(abs(rho[r][c]) ** 2 for r in range(2) for c in range(2))
    f = lambda v: [round(v.real, 6) + 0.0, round(v.imag, 6) + 0.0]
    return {'rho': [[f(v) for v in row] for row in rho], 'purity': round(purity, 6) + 0.0}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: product keep 0 complex', [2, [[0.6, 0], [0, 0.8], [0, 0], [0, 0]], 0], {'rho': [[[0.36, 0.0], [0.0, -0.48]], [[0.0, 0.48], [0.64, 0.0]]], 'purity': 1.0}], ['regression: random reduction 0', [3, [[0.069, -0.179], [-0.176, -0.715], [0.749, 0.757], [-0.786, 0.461], [0.287, -0.288], [-0.462, 0.389], [-0.216, 0.203], [0.456, 0.037]], 0], {'rho': [[[0.422483, 0.0], [-0.136327, -0.218796]], [[-0.136327, 0.218796], [0.577517, 0.0]]], 'purity': 0.644932}], ['regression: random reduction 1', [3, [[0.986, 1.972], [-1.424, 1.98], [-1.308, 1.935], [1.338, 1.563], [-1.898, 1.945], [-1.572, 1.06], [1.832, 0.52], [0.807, -1.748]], 0], {'rho': [[[0.549537, 0.0], [0.241932, 0.063109]], [[0.241932, -0.063109], [0.450463, 0.0]]], 'purity': 0.629935}], ['control: bell keep 0', [2, [[0.707107, 0], [0, 0], [0, 0], [0.707107, 0]], 0], {'rho': [[[0.5, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.5, 0.0]]], 'purity': 0.5}], ['control: product keep 1', [2, [[0.6, 0], [0, 0.8], [0, 0], [0, 0]], 1], {'rho': [[[1.0, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.0, 0.0]]], 'purity': 1.0}], ['control: unnormalized ghz keep 2', [3, [[2, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [2, 0]], 2], {'rho': [[[0.5, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.5, 0.0]]], 'purity': 0.5}], ['regression: random reduction 2', [3, [[-0.436, -0.609], [0.766, -0.544], [-0.426, -0.406], [0.661, 0.537], [-0.32, -0.358], [0.306, 0.359], [-0.048, -0.239], [-0.254, -0.85]], 0], {'rho': [[[0.313851, 0.0], [-0.134578, -0.188226]], [[-0.134578, 0.188226], [0.686149, 0.0]]], 'purity': 0.676383}]], [['regression: random reduction 2', [3, [[-0.436, -0.609], [0.766, -0.544], [-0.426, -0.406], [0.661, 0.537], [-0.32, -0.358], [0.306, 0.359], [-0.048, -0.239], [-0.254, -0.85]], 0], {'rho': [[[0.313851, 0.0], [-0.134578, -0.188226]], [[-0.134578, 0.188226], [0.686149, 0.0]]], 'purity': 0.676383}], ['regression: random reduction 3', [3, [[1.49, -1.9], [-1.815, 0.487], [-1.545, 1.465], [1.903, 1.324], [1.584, -1.799], [1.763, -0.058], [-0.233, 1.643], [-1.856, 0.918]], 0], {'rho': [[[0.536366, 0.0], [0.005901, 0.046665]], [[0.005901, -0.046665], [0.463634, 0.0]]], 'purity': 0.50707}], ['regression: random reduction 4', [3, [[-0.633, 0.511], [0.239, 0.051], [0.129, 0.555], [0.414, -0.526], [-0.93, 0.617], [-0.487, -0.199], [0.609, 0.703], [0.243, -0.571]], 1], {'rho': [[[0.525894, 0.0], [0.032047, 0.296983]], [[0.032047, -0.296983], [0.474106, 0.0]]], 'purity': 0.679793}], ['control: product keep 1', [2, [[0.6, 0], [0, 0.8], [0, 0], [0, 0]], 1], {'rho': [[[1.0, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.0, 0.0]]], 'purity': 1.0}], ['control: unnormalized ghz keep 2', [3, [[2, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [2, 0]], 2], {'rho': [[[0.5, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.5, 0.0]]], 'purity': 0.5}], ['control: bell keep 0', [2, [[0.707107, 0], [0, 0], [0, 0], [0.707107, 0]], 0], {'rho': [[[0.5, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.5, 0.0]]], 'purity': 0.5}], ['regression: random reduction 1', [3, [[0.986, 1.972], [-1.424, 1.98], [-1.308, 1.935], [1.338, 1.563], [-1.898, 1.945], [-1.572, 1.06], [1.832, 0.52], [0.807, -1.748]], 0], {'rho': [[[0.549537, 0.0], [0.241932, 0.063109]], [[0.241932, -0.063109], [0.450463, 0.0]]], 'purity': 0.629935}]], [['regression: random reduction 5', [2, [[-0.972, -0.109], [0.26, 0.259], [-0.134, -0.66], [-0.522, -0.043]], 0], {'rho': [[[0.775173, 0.0], [-0.100385, 0.309012]], [[-0.100385, -0.309012], [0.224827, 0.0]]], 'purity': 0.862571}], ['regression: random reduction 6', [3, [[-0.509, 0.635], [-0.554, 0.902], [-0.528, 0.406], [0.035, -0.166], [0.785, 0.17], [0.113, 0.282], [-0.237, -0.733], [0.778, 0.455]], 1], {'rho': [[[0.57299, 0.0], [0.059796, 0.116878]], [[0.059796, -0.116878], [0.42701, 0.0]]], 'purity': 0.545127}], ['regression: random reduction 4', [3, [[-0.633, 0.511], [0.239, 0.051], [0.129, 0.555], [0.414, -0.526], [-0.93, 0.617], [-0.487, -0.199], [0.609, 0.703], [0.243, -0.571]], 1], {'rho': [[[0.525894, 0.0], [0.032047, 0.296983]], [[0.032047, -0.296983], [0.474106, 0.0]]], 'purity': 0.679793}], ['control: unnormalized ghz keep 2', [3, [[2, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [2, 0]], 2], {'rho': [[[0.5, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.5, 0.0]]], 'purity': 0.5}], ['control: bell keep 0', [2, [[0.707107, 0], [0, 0], [0, 0], [0.707107, 0]], 0], {'rho': [[[0.5, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.5, 0.0]]], 'purity': 0.5}], ['control: product keep 1', [2, [[0.6, 0], [0, 0.8], [0, 0], [0, 0]], 1], {'rho': [[[1.0, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.0, 0.0]]], 'purity': 1.0}], ['regression: random reduction 2', [3, [[-0.436, -0.609], [0.766, -0.544], [-0.426, -0.406], [0.661, 0.537], [-0.32, -0.358], [0.306, 0.359], [-0.048, -0.239], [-0.254, -0.85]], 0], {'rho': [[[0.313851, 0.0], [-0.134578, -0.188226]], [[-0.134578, 0.188226], [0.686149, 0.0]]], 'purity': 0.676383}]], [['regression: random reduction 8', [3, [[-1.677, 1.763], [0.965, -0.593], [-1.405, -0.16], [0.617, -0.175], [-0.069, 0.647], [0.956, 1.91], [1.615, 1.856], [-0.044, 0.633]], 1], {'rho': [[[0.578893, 0.0], [0.238878, -0.116767]], [[0.238878, 0.116767], [0.421107, 0.0]]], 'purity': 0.653843}], ['regression: random reduction 9', [3, [[0.61, 0.432], [0.921, -0.251], [-0.196, 0.927], [-0.808, 0.05], [0.743, -0.342], [0.487, 0.369], [-0.844, 0.867], [-0.169, 0.678]], 2], {'rho': [[[0.502365, 0.0], [0.299281, -0.000926]], [[0.299281, 0.000926], [0.497635, 0.0]]], 'purity': 0.679151}], ['regression: random reduction 6', [3, [[-0.509, 0.635], [-0.554, 0.902], [-0.528, 0.406], [0.035, -0.166], [0.785, 0.17], [0.113, 0.282], [-0.237, -0.733], [0.778, 0.455]], 1], {'rho': [[[0.57299, 0.0], [0.059796, 0.116878]], [[0.059796, -0.116878], [0.42701, 0.0]]], 'purity': 0.545127}], ['control: bell keep 0', [2, [[0.707107, 0], [0, 0], [0, 0], [0.707107, 0]], 0], {'rho': [[[0.5, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.5, 0.0]]], 'purity': 0.5}], ['control: product keep 1', [2, [[0.6, 0], [0, 0.8], [0, 0], [0, 0]], 1], {'rho': [[[1.0, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.0, 0.0]]], 'purity': 1.0}], ['control: unnormalized ghz keep 2', [3, [[2, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [2, 0]], 2], {'rho': [[[0.5, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.5, 0.0]]], 'purity': 0.5}], ['regression: random reduction 3', [3, [[1.49, -1.9], [-1.815, 0.487], [-1.545, 1.465], [1.903, 1.324], [1.584, -1.799], [1.763, -0.058], [-0.233, 1.643], [-1.856, 0.918]], 0], {'rho': [[[0.536366, 0.0], [0.005901, 0.046665]], [[0.005901, -0.046665], [0.463634, 0.0]]], 'purity': 0.50707}]], [['regression: random reduction 11', [2, [[0.608, -1.677], [-1.453, -1.131], [-0.939, -0.925], [-1.391, 1.723]], 1], {'rho': [[[0.497404, 0.0], [0.079671, 0.470271]], [[0.079671, -0.470271], [0.502596, 0.0]]], 'purity': 0.955018}], ['regression: random reduction 12', [2, [[0.346, 0.105], [0.065, -0.046], [0.207, 0.409], [0.186, -0.621]], 0], {'rho': [[[0.444161, 0.0], [-0.257772, 0.296257]], [[-0.257772, -0.296257], [0.555839, 0.0]]], 'purity': 0.814665}], ['regression: random reduction 15', [2, [[0.394, 0.988], [0.617, 0.009], [0.95, 0.172], [-0.178, 0.108]], 0], {'rho': [[[0.829506, 0.0], [0.040789, 0.190078]], [[0.040789, -0.190078], [0.170494, 0.0]]], 'purity': 0.792735}], ['control: product keep 1', [2, [[0.6, 0], [0, 0.8], [0, 0], [0, 0]], 1], {'rho': [[[1.0, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.0, 0.0]]], 'purity': 1.0}], ['control: unnormalized ghz keep 2', [3, [[2, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [2, 0]], 2], {'rho': [[[0.5, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.5, 0.0]]], 'purity': 0.5}], ['control: bell keep 0', [2, [[0.707107, 0], [0, 0], [0, 0], [0.707107, 0]], 0], {'rho': [[[0.5, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.5, 0.0]]], 'purity': 0.5}], ['regression: random reduction 4', [3, [[-0.633, 0.511], [0.239, 0.051], [0.129, 0.555], [0.414, -0.526], [-0.93, 0.617], [-0.487, -0.199], [0.609, 0.703], [0.243, -0.571]], 1], {'rho': [[[0.525894, 0.0], [0.032047, 0.296983]], [[0.032047, -0.296983], [0.474106, 0.0]]], 'purity': 0.679793}]]]
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 fixtureActualExpectedOutcome
regression: product keep 0 complex{'purity': 1.0, 'rho': [[[0.36, 0.0], [0.0, -0.48]], [[0.0, 0.48], [0.64, 0.0]]]}{'purity': 1.0, 'rho': [[[0.36, 0.0], [0.0, -0.48]], [[0.0, 0.48], [0.64, 0.0]]]}Passed
regression: random reduction 0{'purity': 0.826204, 'rho': [[[0.422483, 0.0], [-0.389299, -0.074431]], [[-0.389299, 0.074431], [0.577517, 0.0]]]}{'purity': 0.644932, 'rho': [[[0.422483, 0.0], [-0.136327, -0.218796]], [[-0.136327, 0.218796], [0.577517, 0.0]]]}Failed
regression: random reduction 1{'purity': 0.772645, 'rho': [[[0.549537, 0.0], [0.341535, 0.131235]], [[0.341535, -0.131235], [0.450463, 0.0]]]}{'purity': 0.629935, 'rho': [[[0.549537, 0.0], [0.241932, 0.063109]], [[0.241932, -0.063109], [0.450463, 0.0]]]}Failed
control: bell keep 0{'purity': 0.5, 'rho': [[[0.5, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.5, 0.0]]]}{'purity': 0.5, 'rho': [[[0.5, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.5, 0.0]]]}Passed
control: product keep 1{'purity': 1.0, 'rho': [[[1.0, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.0, 0.0]]]}{'purity': 1.0, 'rho': [[[1.0, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.0, 0.0]]]}Passed
control: unnormalized ghz keep 2{'purity': 0.5, 'rho': [[[0.5, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.5, 0.0]]]}{'purity': 0.5, 'rho': [[[0.5, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.5, 0.0]]]}Passed
regression: random reduction 2{'purity': 1.00494, 'rho': [[[0.313851, 0.0], [-0.294405, -0.362139]], [[-0.294405, 0.362139], [0.686149, 0.0]]]}{'purity': 0.676383, 'rho': [[[0.313851, 0.0], [-0.134578, -0.188226]], [[-0.134578, 0.188226], [0.686149, 0.0]]]}Failed

SHA-256 / 2df0af7b01a7271d3e9cc5f0ae17f1203164ce6f94f55b80deef568f5f92ddcb

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.

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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 2026-09-29T14:51:32.851073+00:00.

Case digest / 3ae814868b91fa06a95e4c416f0ae2cbf64a390def7310f4f44031cf6428c184