FAILURE MAP
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FA-91116 / Quantum circuit simulation / Open access

Reduced density purity ignores off-diagonal entries · case 01

A pure product qubit such as |+> reports purity 0.5 instead of 1.

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

ROOT CAUSE

Purity sums only squared diagonal entries.

VERIFIED REPAIR

Sum |rho_rc|^2 over all four entries (tr rho^2).

Unsuccessful approach: The attempted repair sums all entries but forgets to square the magnitudes.

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][r]) ** 2 for r 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}], ['repair check: 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 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 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 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}], ['repair check: 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: 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 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 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}], ['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 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 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: 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 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}]], [['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 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}], ['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 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}], ['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 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 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}], ['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 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}], ['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 7', [2, [[-0.319, 0.362], [0.196, -0.039], [0.357, 0.708], [-0.468, -0.352]], 1], {'rho': [[[0.219179, 0.0], [0.051763, 0.355461]], [[0.051763, -0.355461], [0.780821, 0.0]]], 'purity': 0.915786}]]]
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, -0.48]], [[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]]]}Failed
regression: random reduction 0{'purity': 0.512018, 'rho': [[[0.422483, 0.0], [-0.136327, -0.218796]], [[-0.136327, 0.218796], [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
repair check: 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
regression: random reduction 1{'purity': 0.504908, 'rho': [[[0.549537, 0.0], [0.241932, 0.063109]], [[0.241932, -0.063109], [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
regression: random reduction 2{'purity': 0.569303, 'rho': [[[0.313851, 0.0], [-0.134578, -0.188226]], [[-0.134578, 0.188226], [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
regression: random reduction 3{'purity': 0.502645, 'rho': [[[0.536366, 0.0], [0.005901, 0.046665]], [[0.005901, -0.046665], [0.463634, 0.0]]]}{'purity': 0.50707, 'rho': [[[0.536366, 0.0], [0.005901, 0.046665]], [[0.005901, -0.046665], [0.463634, 0.0]]]}Failed

SHA-256 / 43182d74eb223562e2abbf28911b85149707d18455bb647daf02da0aef47b69e

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 (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]) 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}], ['repair check: 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 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 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 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}], ['repair check: 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: 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 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 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}], ['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 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 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: 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 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}]], [['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 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}], ['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 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}], ['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 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 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}], ['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 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}], ['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 7', [2, [[-0.319, 0.362], [0.196, -0.039], [0.357, 0.708], [-0.468, -0.352]], 1], {'rho': [[[0.219179, 0.0], [0.051763, 0.355461]], [[0.051763, -0.355461], [0.780821, 0.0]]], 'purity': 0.915786}]]]
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': 1.96, '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]]]}Failed
regression: random reduction 0{'purity': 1.515585, 'rho': [[[0.422483, 0.0], [-0.136327, -0.218796]], [[-0.136327, 0.218796], [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
repair check: bell keep 0{'purity': 1.0, '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]]]}Failed
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
regression: random reduction 1{'purity': 1.500055, 'rho': [[[0.549537, 0.0], [0.241932, 0.063109]], [[0.241932, -0.063109], [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
regression: random reduction 2{'purity': 1.462776, 'rho': [[[0.313851, 0.0], [-0.134578, -0.188226]], [[-0.134578, 0.188226], [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
regression: random reduction 3{'purity': 1.094072, 'rho': [[[0.536366, 0.0], [0.005901, 0.046665]], [[0.005901, -0.046665], [0.463634, 0.0]]]}{'purity': 0.50707, 'rho': [[[0.536366, 0.0], [0.005901, 0.046665]], [[0.005901, -0.046665], [0.463634, 0.0]]]}Failed

SHA-256 / cd26db595356ad4e780853059076ccd176f1916d1cf3411bc5bdc3cda8cb24c5

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, 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}], ['repair check: 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 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 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 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}], ['repair check: 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: 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 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 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}], ['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 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 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: 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 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}]], [['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 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}], ['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 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}], ['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 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 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}], ['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 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}], ['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 7', [2, [[-0.319, 0.362], [0.196, -0.039], [0.357, 0.708], [-0.468, -0.352]], 1], {'rho': [[[0.219179, 0.0], [0.051763, 0.355461]], [[0.051763, -0.355461], [0.780821, 0.0]]], 'purity': 0.915786}]]]
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': 0.644932, 'rho': [[[0.422483, 0.0], [-0.136327, -0.218796]], [[-0.136327, 0.218796], [0.577517, 0.0]]]}{'purity': 0.644932, 'rho': [[[0.422483, 0.0], [-0.136327, -0.218796]], [[-0.136327, 0.218796], [0.577517, 0.0]]]}Passed
repair check: 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
regression: random reduction 1{'purity': 0.629935, 'rho': [[[0.549537, 0.0], [0.241932, 0.063109]], [[0.241932, -0.063109], [0.450463, 0.0]]]}{'purity': 0.629935, 'rho': [[[0.549537, 0.0], [0.241932, 0.063109]], [[0.241932, -0.063109], [0.450463, 0.0]]]}Passed
regression: random reduction 2{'purity': 0.676383, 'rho': [[[0.313851, 0.0], [-0.134578, -0.188226]], [[-0.134578, 0.188226], [0.686149, 0.0]]]}{'purity': 0.676383, 'rho': [[[0.313851, 0.0], [-0.134578, -0.188226]], [[-0.134578, 0.188226], [0.686149, 0.0]]]}Passed
regression: random reduction 3{'purity': 0.50707, 'rho': [[[0.536366, 0.0], [0.005901, 0.046665]], [[0.005901, -0.046665], [0.463634, 0.0]]]}{'purity': 0.50707, 'rho': [[[0.536366, 0.0], [0.005901, 0.046665]], [[0.005901, -0.046665], [0.463634, 0.0]]]}Passed

SHA-256 / 5ddf5ff903e8fe63274b3fccf879e33b1d198b3ecd70979f9748df2165ff3477

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 2026-09-29T14:51:32.945761+00:00.

Case digest / 634aa4c6370676e98476ef2255b5a0e4a13b9a84e53d3c6d18a6152684d964ef