FA-91216 / Quantum circuit simulation / Open access

Grover planner rounds the iteration count to nearest · case 01

Some sizes plan one extra iteration, overshooting the peak and lowering success.

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

ROOT CAUSE

k is computed with round(pi/(4 theta)) instead of the contract floor.

THE FAILURE

k is computed with round(pi/(4 theta)) instead of the contract floor.

Unsuccessful approach: The attempted repair uses ceil, overshooting even more often.

Case contract

Input [N, M]. "invalid" if N < 1, M < 0 or M > N; "no-solution" if M == 0; if 2M >= N return {"iterations": 0, "success": M/N}; else theta = asin(sqrt(M/N)), k = floor(pi/(4 theta)) and success = sin^2((2k+1) theta). Probabilities rounded to 6 decimals.

Why this case matters

Choosing the Grover iteration count wrongly overshoots the amplitude peak and collapses the success probability.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    N, M = x
    if N < 1 or M < 0 or M > N:
        return 'invalid'
    if M == 0:
        return 'no-solution'
    if 2 * M >= N:
        return {'iterations': 0, 'success': round(M / N, 6)}
    theta = math.asin(math.sqrt(M / N))
    k = round(math.pi / (4 * theta))
    return {'iterations': k, 'success': round(math.sin((2 * k + 1) * theta) ** 2, 6)}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: single marked N=4', [4, 1], {'iterations': 1, 'success': 1.0}], ['regression: N=8 M=2', [8, 2], {'iterations': 1, 'success': 1.0}], ['repair check: odd N just under half', [5, 2], {'iterations': 1, 'success': 0.784}], ['control: half marked N=4 M=2', [4, 2], {'iterations': 0, 'success': 0.5}], ['control: no marked items', [8, 0], 'no-solution'], ['control: M greater than N', [4, 5], 'invalid'], ['control: negative M', [4, -1], 'invalid']], [['regression: N=32 M=3', [32, 3], {'iterations': 2, 'success': 0.999779}], ['regression: N=32 M=5', [32, 5], {'iterations': 1, 'success': 0.881348}], ['repair check: N=7 M=3', [7, 3], {'iterations': 1, 'success': 0.708455}], ['control: empty space', [0, 0], 'invalid'], ['control: all marked', [8, 8], {'iterations': 0, 'success': 1.0}], ['control: one over the space', [4, 5], 'invalid'], ['control: all marked N=1', [1, 1], {'iterations': 0, 'success': 1.0}]], [['regression: N=64 M=3', [64, 3], {'iterations': 3, 'success': 0.998139}], ['regression: N=64 M=5', [64, 5], {'iterations': 2, 'success': 0.976354}], ['repair check: N=8 M=1', [8, 1], {'iterations': 2, 'success': 0.945312}], ['control: all marked N=3', [3, 3], {'iterations': 0, 'success': 1.0}], ['control: N=8 M=5', [8, 5], {'iterations': 0, 'success': 0.625}], ['control: N=8 M=7', [8, 7], {'iterations': 0, 'success': 0.875}], ['control: N=16 M=13', [16, 13], {'iterations': 0, 'success': 0.8125}]], [['regression: N=100 M=1', [100, 1], {'iterations': 7, 'success': 0.995344}], ['regression: N=100 M=2', [100, 2], {'iterations': 5, 'success': 0.999901}], ['repair check: N=8 M=3', [8, 3], {'iterations': 1, 'success': 0.84375}], ['control: half marked N=4 M=2', [4, 2], {'iterations': 0, 'success': 0.5}], ['control: no marked items', [8, 0], 'no-solution'], ['control: M greater than N', [4, 5], 'invalid'], ['control: negative M', [4, -1], 'invalid']], [['regression: N=100 M=7', [100, 7], {'iterations': 2, 'success': 0.947144}], ['regression: N=128 M=1', [128, 1], {'iterations': 8, 'success': 0.99562}], ['repair check: N=16 M=2', [16, 2], {'iterations': 2, 'success': 0.945312}], ['control: empty space', [0, 0], 'invalid'], ['control: all marked', [8, 8], {'iterations': 0, 'success': 1.0}], ['control: one over the space', [4, 5], 'invalid'], ['control: all marked N=1', [1, 1], {'iterations': 0, 'success': 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: single marked N=4	`{'iterations': 2, 'success': 0.25}`	`{'iterations': 1, 'success': 1.0}`	Failed
regression: N=8 M=2	`{'iterations': 2, 'success': 0.25}`	`{'iterations': 1, 'success': 1.0}`	Failed
repair check: odd N just under half	`{'iterations': 1, 'success': 0.784}`	`{'iterations': 1, 'success': 0.784}`	Passed
control: half marked N=4 M=2	`{'iterations': 0, 'success': 0.5}`	`{'iterations': 0, 'success': 0.5}`	Passed
control: no marked items	`no-solution`	`no-solution`	Passed
control: M greater than N	`invalid`	`invalid`	Passed
control: negative M	`invalid`	`invalid`	Passed

SHA-256 / cdc6b607461775af9973e4aba555538436c5601c8f78ec01231663154397bd77

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, M = x
    if N < 1 or M < 0 or M > N:
        return 'invalid'
    if M == 0:
        return 'no-solution'
    if 2 * M >= N:
        return {'iterations': 0, 'success': round(M / N, 6)}
    theta = math.asin(math.sqrt(M / N))
    k = math.ceil(math.pi / (4 * theta))
    return {'iterations': k, 'success': round(math.sin((2 * k + 1) * theta) ** 2, 6)}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: single marked N=4', [4, 1], {'iterations': 1, 'success': 1.0}], ['regression: N=8 M=2', [8, 2], {'iterations': 1, 'success': 1.0}], ['repair check: odd N just under half', [5, 2], {'iterations': 1, 'success': 0.784}], ['control: half marked N=4 M=2', [4, 2], {'iterations': 0, 'success': 0.5}], ['control: no marked items', [8, 0], 'no-solution'], ['control: M greater than N', [4, 5], 'invalid'], ['control: negative M', [4, -1], 'invalid']], [['regression: N=32 M=3', [32, 3], {'iterations': 2, 'success': 0.999779}], ['regression: N=32 M=5', [32, 5], {'iterations': 1, 'success': 0.881348}], ['repair check: N=7 M=3', [7, 3], {'iterations': 1, 'success': 0.708455}], ['control: empty space', [0, 0], 'invalid'], ['control: all marked', [8, 8], {'iterations': 0, 'success': 1.0}], ['control: one over the space', [4, 5], 'invalid'], ['control: all marked N=1', [1, 1], {'iterations': 0, 'success': 1.0}]], [['regression: N=64 M=3', [64, 3], {'iterations': 3, 'success': 0.998139}], ['regression: N=64 M=5', [64, 5], {'iterations': 2, 'success': 0.976354}], ['repair check: N=8 M=1', [8, 1], {'iterations': 2, 'success': 0.945312}], ['control: all marked N=3', [3, 3], {'iterations': 0, 'success': 1.0}], ['control: N=8 M=5', [8, 5], {'iterations': 0, 'success': 0.625}], ['control: N=8 M=7', [8, 7], {'iterations': 0, 'success': 0.875}], ['control: N=16 M=13', [16, 13], {'iterations': 0, 'success': 0.8125}]], [['regression: N=100 M=1', [100, 1], {'iterations': 7, 'success': 0.995344}], ['regression: N=100 M=2', [100, 2], {'iterations': 5, 'success': 0.999901}], ['repair check: N=8 M=3', [8, 3], {'iterations': 1, 'success': 0.84375}], ['control: half marked N=4 M=2', [4, 2], {'iterations': 0, 'success': 0.5}], ['control: no marked items', [8, 0], 'no-solution'], ['control: M greater than N', [4, 5], 'invalid'], ['control: negative M', [4, -1], 'invalid']], [['regression: N=100 M=7', [100, 7], {'iterations': 2, 'success': 0.947144}], ['regression: N=128 M=1', [128, 1], {'iterations': 8, 'success': 0.99562}], ['repair check: N=16 M=2', [16, 2], {'iterations': 2, 'success': 0.945312}], ['control: empty space', [0, 0], 'invalid'], ['control: all marked', [8, 8], {'iterations': 0, 'success': 1.0}], ['control: one over the space', [4, 5], 'invalid'], ['control: all marked N=1', [1, 1], {'iterations': 0, 'success': 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: single marked N=4	`{'iterations': 2, 'success': 0.25}`	`{'iterations': 1, 'success': 1.0}`	Failed
regression: N=8 M=2	`{'iterations': 2, 'success': 0.25}`	`{'iterations': 1, 'success': 1.0}`	Failed
repair check: odd N just under half	`{'iterations': 2, 'success': 0.07744}`	`{'iterations': 1, 'success': 0.784}`	Failed
control: half marked N=4 M=2	`{'iterations': 0, 'success': 0.5}`	`{'iterations': 0, 'success': 0.5}`	Passed
control: no marked items	`no-solution`	`no-solution`	Passed
control: M greater than N	`invalid`	`invalid`	Passed
control: negative M	`invalid`	`invalid`	Passed

SHA-256 / cf7b07905300ad2da4af5406ccd75c11760ec09c75c77a507c669418d40f1188

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 2026-09-29T14:51:33.848509+00:00.

Case digest / 31b9fe14d253a4df6afb609f515ca6e3d23cb77f3c256242d2791b54f9977ebb