FA-91321 / Quantum circuit simulation / Open access

T-count charges identity rotations as Clifford gates · case 01

rz(0) and rz(2pi) each add one Clifford.

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ROOT CAUSE

The zero-angle skip is missing, so reduced angle 0 falls into the multiple-of-1/2 branch.

VERIFIED REPAIR

Skip rotations whose angle reduces to 0 mod 2.

Unsuccessful approach: The attempted repair tests the raw angle for zero before reduction, so rz(2pi) and rz(-2pi) are still charged.

Case contract

Input a gate list. t and tdg count one T each; h, s, sdg, x, y, z, cx, cz, swap count one Clifford; ccx costs 7 T and 8 Clifford; ["rz", q, a] with a in units of pi reduced mod 2 is skipped if 0, Clifford if a multiple of 1/2, one T if an odd multiple of 1/4, else ["unsupported", index]; other names give ["unknown-gate", index]. Return {"t_count", "clifford_count"}.

Why this case matters

T-count is the dominant fault-tolerant cost metric; misclassifying rotations skews resource estimates.

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):
    t = cliff = 0
    for idx, op in enumerate(x):
        name = op[0]
        if name in ('t', 'tdg'):
            t += 1
        elif name in ('h', 's', 'sdg', 'x', 'y', 'z', 'cx', 'cz', 'swap'):
            cliff += 1
        elif name == 'ccx':
            t += 7
            cliff += 8
        elif name == 'rz':
            a = Fraction(op[2]) % 2
            if (a * 2).denominator == 1:
                cliff += 1
            elif (a * 4).denominator == 1:
                t += 1
            else:
                return ['unsupported', idx]
        else:
            return ['unknown-gate', idx]
    return {'t_count': t, 'clifford_count': cliff}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: rz two pi', [['rz', 0, '2']], {'t_count': 0, 'clifford_count': 0}], ['regression: rz zero', [['rz', 0, '0']], {'t_count': 0, 'clifford_count': 0}], ['regression: rz four pi', [['rz', 0, '4']], {'t_count': 0, 'clifford_count': 0}], ['control: rz pi is Z', [['rz', 0, '1']], {'t_count': 0, 'clifford_count': 1}], ['control: rz half pi is S', [['rz', 0, '1/2']], {'t_count': 0, 'clifford_count': 1}], ['control: rz quarter pi', [['rz', 0, '1/4']], {'t_count': 1, 'clifford_count': 0}], ['control: tdg', [['tdg', 0]], {'t_count': 1, 'clifford_count': 0}]], [['regression: random t-count 0', [['rz', 0, '-1/4'], ['rz', 0, '3/4'], ['rz', 0, '4']], {'t_count': 2, 'clifford_count': 0}], ['regression: random t-count 1', [['rz', 0, '-2'], ['ccx', 0, 1, 2], ['rz', 0, '1'], ['rz', 0, '1'], ['rz', 0, '0'], ['x', 0]], {'t_count': 7, 'clifford_count': 11}], ['regression: random t-count 16', [['rz', 0, '3/4'], ['rz', 0, '-1'], ['tdg', 0], ['sdg', 0], ['rz', 0, '-2'], ['rz', 0, '3/2'], ['sdg', 0]], {'t_count': 2, 'clifford_count': 4}], ['control: toffoli', [['ccx', 0, 1, 2]], {'t_count': 7, 'clifford_count': 8}], ['control: unsupported angle', [['h', 0], ['rz', 0, '1/8']], ['unsupported', 1]], ['control: negative angles', [['rz', 0, '-1/4'], ['rz', 1, '-3/2']], {'t_count': 1, 'clifford_count': 1}], ['control: unknown gate', [['u3', 0]], ['unknown-gate', 0]]], [['regression: random t-count 6', [['ccx', 0, 1, 2], ['x', 0], ['x', 0], ['rz', 0, '0'], ['sdg', 0], ['t', 0], ['ccx', 0, 1, 2]], {'t_count': 15, 'clifford_count': 19}], ['regression: random t-count 16', [['rz', 0, '3/4'], ['rz', 0, '-1'], ['tdg', 0], ['sdg', 0], ['rz', 0, '-2'], ['rz', 0, '3/2'], ['sdg', 0]], {'t_count': 2, 'clifford_count': 4}], ['regression: random t-count 18', [['t', 0], ['rz', 0, '4'], ['rz', 0, '3/2'], ['ccx', 0, 1, 2], ['rz', 0, '3/4'], ['rz', 0, '-2']], {'t_count': 9, 'clifford_count': 9}], ['control: random t-count 2', [['sdg', 0], ['rz', 0, '1/4'], ['cx', 0]], {'t_count': 1, 'clifford_count': 2}], ['control: random t-count 4', [['ccx', 0, 1, 2]], {'t_count': 7, 'clifford_count': 8}], ['control: random t-count 5', [['ccx', 0, 1, 2], ['rz', 0, '1'], ['rz', 0, '5/4'], ['tdg', 0]], {'t_count': 9, 'clifford_count': 9}], ['control: random t-count 7', [['rz', 0, '1/2'], ['tdg', 0], ['rz', 0, '1'], ['h', 0]], {'t_count': 1, 'clifford_count': 3}]], [['regression: random t-count 23', [['rz', 0, '-2'], ['tdg', 0], ['ccx', 0, 1, 2], ['t', 0], ['rz', 0, '4'], ['rz', 0, '-1']], {'t_count': 9, 'clifford_count': 9}], ['regression: random t-count 31', [['rz', 0, '2'], ['h', 0], ['x', 0], ['x', 0], ['t', 0], ['rz', 0, '-2']], {'t_count': 1, 'clifford_count': 3}], ['regression: random t-count 36', [['rz', 0, '-2'], ['ccx', 0, 1, 2], ['cx', 0], ['x', 0], ['rz', 0, '4'], ['t', 0]], {'t_count': 8, 'clifford_count': 10}], ['control: random t-count 8', [['rz', 0, '-1/4'], ['ccx', 0, 1, 2], ['ccx', 0, 1, 2], ['ccx', 0, 1, 2], ['cx', 0]], {'t_count': 22, 'clifford_count': 25}], ['control: random t-count 9', [['rz', 0, '1/4']], {'t_count': 1, 'clifford_count': 0}], ['control: random t-count 10', [['ccx', 0, 1, 2], ['s', 0], ['ccx', 0, 1, 2], ['tdg', 0]], {'t_count': 15, 'clifford_count': 17}], ['control: random t-count 11', [['s', 0], ['rz', 0, '5/4'], ['rz', 0, '-1'], ['x', 0], ['t', 0]], {'t_count': 2, 'clifford_count': 3}]], [['regression: random t-count 36', [['rz', 0, '-2'], ['ccx', 0, 1, 2], ['cx', 0], ['x', 0], ['rz', 0, '4'], ['t', 0]], {'t_count': 8, 'clifford_count': 10}], ['regression: random t-count 37', [['t', 0], ['rz', 0, '-1'], ['cx', 0], ['t', 0], ['rz', 0, '1/4'], ['rz', 0, '2'], ['tdg', 0]], {'t_count': 4, 'clifford_count': 2}], ['regression: random t-count 42', [['cx', 0], ['rz', 0, '2'], ['rz', 0, '-1'], ['rz', 0, '1/4'], ['rz', 0, '3/4'], ['tdg', 0]], {'t_count': 3, 'clifford_count': 2}], ['control: random t-count 12', [['t', 0], ['tdg', 0], ['rz', 0, '-1']], {'t_count': 2, 'clifford_count': 1}], ['control: random t-count 13', [['rz', 0, '-1/4'], ['rz', 0, '7/2'], ['rz', 0, '3/4'], ['s', 0]], {'t_count': 2, 'clifford_count': 2}], ['control: random t-count 14', [['sdg', 0]], {'t_count': 0, 'clifford_count': 1}], ['control: random t-count 15', [['ccx', 0, 1, 2], ['sdg', 0], ['t', 0], ['rz', 0, '3/2']], {'t_count': 8, 'clifford_count': 10}]]]
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: rz two pi	`{'clifford_count': 1, 't_count': 0}`	`{'clifford_count': 0, 't_count': 0}`	Failed
regression: rz zero	`{'clifford_count': 1, 't_count': 0}`	`{'clifford_count': 0, 't_count': 0}`	Failed
regression: rz four pi	`{'clifford_count': 1, 't_count': 0}`	`{'clifford_count': 0, 't_count': 0}`	Failed
control: rz pi is Z	`{'clifford_count': 1, 't_count': 0}`	`{'clifford_count': 1, 't_count': 0}`	Passed
control: rz half pi is S	`{'clifford_count': 1, 't_count': 0}`	`{'clifford_count': 1, 't_count': 0}`	Passed
control: rz quarter pi	`{'clifford_count': 0, 't_count': 1}`	`{'clifford_count': 0, 't_count': 1}`	Passed
control: tdg	`{'clifford_count': 0, 't_count': 1}`	`{'clifford_count': 0, 't_count': 1}`	Passed

SHA-256 / 418b41cf6833c570d47ac04eba44fe20a81bcc863894e8d903ad02fc50c148fe

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):
    t = cliff = 0
    for idx, op in enumerate(x):
        name = op[0]
        if name in ('t', 'tdg'):
            t += 1
        elif name in ('h', 's', 'sdg', 'x', 'y', 'z', 'cx', 'cz', 'swap'):
            cliff += 1
        elif name == 'ccx':
            t += 7
            cliff += 8
        elif name == 'rz':
            a = Fraction(op[2]) % 2
            if Fraction(op[2]) == 0:
                continue
            if (a * 2).denominator == 1:
                cliff += 1
            elif (a * 4).denominator == 1:
                t += 1
            else:
                return ['unsupported', idx]
        else:
            return ['unknown-gate', idx]
    return {'t_count': t, 'clifford_count': cliff}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: rz two pi', [['rz', 0, '2']], {'t_count': 0, 'clifford_count': 0}], ['regression: rz zero', [['rz', 0, '0']], {'t_count': 0, 'clifford_count': 0}], ['regression: rz four pi', [['rz', 0, '4']], {'t_count': 0, 'clifford_count': 0}], ['control: rz pi is Z', [['rz', 0, '1']], {'t_count': 0, 'clifford_count': 1}], ['control: rz half pi is S', [['rz', 0, '1/2']], {'t_count': 0, 'clifford_count': 1}], ['control: rz quarter pi', [['rz', 0, '1/4']], {'t_count': 1, 'clifford_count': 0}], ['control: tdg', [['tdg', 0]], {'t_count': 1, 'clifford_count': 0}]], [['regression: random t-count 0', [['rz', 0, '-1/4'], ['rz', 0, '3/4'], ['rz', 0, '4']], {'t_count': 2, 'clifford_count': 0}], ['regression: random t-count 1', [['rz', 0, '-2'], ['ccx', 0, 1, 2], ['rz', 0, '1'], ['rz', 0, '1'], ['rz', 0, '0'], ['x', 0]], {'t_count': 7, 'clifford_count': 11}], ['regression: random t-count 16', [['rz', 0, '3/4'], ['rz', 0, '-1'], ['tdg', 0], ['sdg', 0], ['rz', 0, '-2'], ['rz', 0, '3/2'], ['sdg', 0]], {'t_count': 2, 'clifford_count': 4}], ['control: toffoli', [['ccx', 0, 1, 2]], {'t_count': 7, 'clifford_count': 8}], ['control: unsupported angle', [['h', 0], ['rz', 0, '1/8']], ['unsupported', 1]], ['control: negative angles', [['rz', 0, '-1/4'], ['rz', 1, '-3/2']], {'t_count': 1, 'clifford_count': 1}], ['control: unknown gate', [['u3', 0]], ['unknown-gate', 0]]], [['regression: random t-count 6', [['ccx', 0, 1, 2], ['x', 0], ['x', 0], ['rz', 0, '0'], ['sdg', 0], ['t', 0], ['ccx', 0, 1, 2]], {'t_count': 15, 'clifford_count': 19}], ['regression: random t-count 16', [['rz', 0, '3/4'], ['rz', 0, '-1'], ['tdg', 0], ['sdg', 0], ['rz', 0, '-2'], ['rz', 0, '3/2'], ['sdg', 0]], {'t_count': 2, 'clifford_count': 4}], ['regression: random t-count 18', [['t', 0], ['rz', 0, '4'], ['rz', 0, '3/2'], ['ccx', 0, 1, 2], ['rz', 0, '3/4'], ['rz', 0, '-2']], {'t_count': 9, 'clifford_count': 9}], ['control: random t-count 2', [['sdg', 0], ['rz', 0, '1/4'], ['cx', 0]], {'t_count': 1, 'clifford_count': 2}], ['control: random t-count 4', [['ccx', 0, 1, 2]], {'t_count': 7, 'clifford_count': 8}], ['control: random t-count 5', [['ccx', 0, 1, 2], ['rz', 0, '1'], ['rz', 0, '5/4'], ['tdg', 0]], {'t_count': 9, 'clifford_count': 9}], ['control: random t-count 7', [['rz', 0, '1/2'], ['tdg', 0], ['rz', 0, '1'], ['h', 0]], {'t_count': 1, 'clifford_count': 3}]], [['regression: random t-count 23', [['rz', 0, '-2'], ['tdg', 0], ['ccx', 0, 1, 2], ['t', 0], ['rz', 0, '4'], ['rz', 0, '-1']], {'t_count': 9, 'clifford_count': 9}], ['regression: random t-count 31', [['rz', 0, '2'], ['h', 0], ['x', 0], ['x', 0], ['t', 0], ['rz', 0, '-2']], {'t_count': 1, 'clifford_count': 3}], ['regression: random t-count 36', [['rz', 0, '-2'], ['ccx', 0, 1, 2], ['cx', 0], ['x', 0], ['rz', 0, '4'], ['t', 0]], {'t_count': 8, 'clifford_count': 10}], ['control: random t-count 8', [['rz', 0, '-1/4'], ['ccx', 0, 1, 2], ['ccx', 0, 1, 2], ['ccx', 0, 1, 2], ['cx', 0]], {'t_count': 22, 'clifford_count': 25}], ['control: random t-count 9', [['rz', 0, '1/4']], {'t_count': 1, 'clifford_count': 0}], ['control: random t-count 10', [['ccx', 0, 1, 2], ['s', 0], ['ccx', 0, 1, 2], ['tdg', 0]], {'t_count': 15, 'clifford_count': 17}], ['control: random t-count 11', [['s', 0], ['rz', 0, '5/4'], ['rz', 0, '-1'], ['x', 0], ['t', 0]], {'t_count': 2, 'clifford_count': 3}]], [['regression: random t-count 36', [['rz', 0, '-2'], ['ccx', 0, 1, 2], ['cx', 0], ['x', 0], ['rz', 0, '4'], ['t', 0]], {'t_count': 8, 'clifford_count': 10}], ['regression: random t-count 37', [['t', 0], ['rz', 0, '-1'], ['cx', 0], ['t', 0], ['rz', 0, '1/4'], ['rz', 0, '2'], ['tdg', 0]], {'t_count': 4, 'clifford_count': 2}], ['regression: random t-count 42', [['cx', 0], ['rz', 0, '2'], ['rz', 0, '-1'], ['rz', 0, '1/4'], ['rz', 0, '3/4'], ['tdg', 0]], {'t_count': 3, 'clifford_count': 2}], ['control: random t-count 12', [['t', 0], ['tdg', 0], ['rz', 0, '-1']], {'t_count': 2, 'clifford_count': 1}], ['control: random t-count 13', [['rz', 0, '-1/4'], ['rz', 0, '7/2'], ['rz', 0, '3/4'], ['s', 0]], {'t_count': 2, 'clifford_count': 2}], ['control: random t-count 14', [['sdg', 0]], {'t_count': 0, 'clifford_count': 1}], ['control: random t-count 15', [['ccx', 0, 1, 2], ['sdg', 0], ['t', 0], ['rz', 0, '3/2']], {'t_count': 8, 'clifford_count': 10}]]]
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: rz two pi	`{'clifford_count': 1, 't_count': 0}`	`{'clifford_count': 0, 't_count': 0}`	Failed
regression: rz zero	`{'clifford_count': 0, 't_count': 0}`	`{'clifford_count': 0, 't_count': 0}`	Passed
regression: rz four pi	`{'clifford_count': 1, 't_count': 0}`	`{'clifford_count': 0, 't_count': 0}`	Failed
control: rz pi is Z	`{'clifford_count': 1, 't_count': 0}`	`{'clifford_count': 1, 't_count': 0}`	Passed
control: rz half pi is S	`{'clifford_count': 1, 't_count': 0}`	`{'clifford_count': 1, 't_count': 0}`	Passed
control: rz quarter pi	`{'clifford_count': 0, 't_count': 1}`	`{'clifford_count': 0, 't_count': 1}`	Passed
control: tdg	`{'clifford_count': 0, 't_count': 1}`	`{'clifford_count': 0, 't_count': 1}`	Passed

SHA-256 / 6987f929be4abf2f1507578ee63a3c3de33643e56741a15d633d139e75607de8

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):
    t = cliff = 0
    for idx, op in enumerate(x):
        name = op[0]
        if name in ('t', 'tdg'):
            t += 1
        elif name in ('h', 's', 'sdg', 'x', 'y', 'z', 'cx', 'cz', 'swap'):
            cliff += 1
        elif name == 'ccx':
            t += 7
            cliff += 8
        elif name == 'rz':
            a = Fraction(op[2]) % 2
            if a == 0:
                continue
            if (a * 2).denominator == 1:
                cliff += 1
            elif (a * 4).denominator == 1:
                t += 1
            else:
                return ['unsupported', idx]
        else:
            return ['unknown-gate', idx]
    return {'t_count': t, 'clifford_count': cliff}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: rz two pi', [['rz', 0, '2']], {'t_count': 0, 'clifford_count': 0}], ['regression: rz zero', [['rz', 0, '0']], {'t_count': 0, 'clifford_count': 0}], ['regression: rz four pi', [['rz', 0, '4']], {'t_count': 0, 'clifford_count': 0}], ['control: rz pi is Z', [['rz', 0, '1']], {'t_count': 0, 'clifford_count': 1}], ['control: rz half pi is S', [['rz', 0, '1/2']], {'t_count': 0, 'clifford_count': 1}], ['control: rz quarter pi', [['rz', 0, '1/4']], {'t_count': 1, 'clifford_count': 0}], ['control: tdg', [['tdg', 0]], {'t_count': 1, 'clifford_count': 0}]], [['regression: random t-count 0', [['rz', 0, '-1/4'], ['rz', 0, '3/4'], ['rz', 0, '4']], {'t_count': 2, 'clifford_count': 0}], ['regression: random t-count 1', [['rz', 0, '-2'], ['ccx', 0, 1, 2], ['rz', 0, '1'], ['rz', 0, '1'], ['rz', 0, '0'], ['x', 0]], {'t_count': 7, 'clifford_count': 11}], ['regression: random t-count 16', [['rz', 0, '3/4'], ['rz', 0, '-1'], ['tdg', 0], ['sdg', 0], ['rz', 0, '-2'], ['rz', 0, '3/2'], ['sdg', 0]], {'t_count': 2, 'clifford_count': 4}], ['control: toffoli', [['ccx', 0, 1, 2]], {'t_count': 7, 'clifford_count': 8}], ['control: unsupported angle', [['h', 0], ['rz', 0, '1/8']], ['unsupported', 1]], ['control: negative angles', [['rz', 0, '-1/4'], ['rz', 1, '-3/2']], {'t_count': 1, 'clifford_count': 1}], ['control: unknown gate', [['u3', 0]], ['unknown-gate', 0]]], [['regression: random t-count 6', [['ccx', 0, 1, 2], ['x', 0], ['x', 0], ['rz', 0, '0'], ['sdg', 0], ['t', 0], ['ccx', 0, 1, 2]], {'t_count': 15, 'clifford_count': 19}], ['regression: random t-count 16', [['rz', 0, '3/4'], ['rz', 0, '-1'], ['tdg', 0], ['sdg', 0], ['rz', 0, '-2'], ['rz', 0, '3/2'], ['sdg', 0]], {'t_count': 2, 'clifford_count': 4}], ['regression: random t-count 18', [['t', 0], ['rz', 0, '4'], ['rz', 0, '3/2'], ['ccx', 0, 1, 2], ['rz', 0, '3/4'], ['rz', 0, '-2']], {'t_count': 9, 'clifford_count': 9}], ['control: random t-count 2', [['sdg', 0], ['rz', 0, '1/4'], ['cx', 0]], {'t_count': 1, 'clifford_count': 2}], ['control: random t-count 4', [['ccx', 0, 1, 2]], {'t_count': 7, 'clifford_count': 8}], ['control: random t-count 5', [['ccx', 0, 1, 2], ['rz', 0, '1'], ['rz', 0, '5/4'], ['tdg', 0]], {'t_count': 9, 'clifford_count': 9}], ['control: random t-count 7', [['rz', 0, '1/2'], ['tdg', 0], ['rz', 0, '1'], ['h', 0]], {'t_count': 1, 'clifford_count': 3}]], [['regression: random t-count 23', [['rz', 0, '-2'], ['tdg', 0], ['ccx', 0, 1, 2], ['t', 0], ['rz', 0, '4'], ['rz', 0, '-1']], {'t_count': 9, 'clifford_count': 9}], ['regression: random t-count 31', [['rz', 0, '2'], ['h', 0], ['x', 0], ['x', 0], ['t', 0], ['rz', 0, '-2']], {'t_count': 1, 'clifford_count': 3}], ['regression: random t-count 36', [['rz', 0, '-2'], ['ccx', 0, 1, 2], ['cx', 0], ['x', 0], ['rz', 0, '4'], ['t', 0]], {'t_count': 8, 'clifford_count': 10}], ['control: random t-count 8', [['rz', 0, '-1/4'], ['ccx', 0, 1, 2], ['ccx', 0, 1, 2], ['ccx', 0, 1, 2], ['cx', 0]], {'t_count': 22, 'clifford_count': 25}], ['control: random t-count 9', [['rz', 0, '1/4']], {'t_count': 1, 'clifford_count': 0}], ['control: random t-count 10', [['ccx', 0, 1, 2], ['s', 0], ['ccx', 0, 1, 2], ['tdg', 0]], {'t_count': 15, 'clifford_count': 17}], ['control: random t-count 11', [['s', 0], ['rz', 0, '5/4'], ['rz', 0, '-1'], ['x', 0], ['t', 0]], {'t_count': 2, 'clifford_count': 3}]], [['regression: random t-count 36', [['rz', 0, '-2'], ['ccx', 0, 1, 2], ['cx', 0], ['x', 0], ['rz', 0, '4'], ['t', 0]], {'t_count': 8, 'clifford_count': 10}], ['regression: random t-count 37', [['t', 0], ['rz', 0, '-1'], ['cx', 0], ['t', 0], ['rz', 0, '1/4'], ['rz', 0, '2'], ['tdg', 0]], {'t_count': 4, 'clifford_count': 2}], ['regression: random t-count 42', [['cx', 0], ['rz', 0, '2'], ['rz', 0, '-1'], ['rz', 0, '1/4'], ['rz', 0, '3/4'], ['tdg', 0]], {'t_count': 3, 'clifford_count': 2}], ['control: random t-count 12', [['t', 0], ['tdg', 0], ['rz', 0, '-1']], {'t_count': 2, 'clifford_count': 1}], ['control: random t-count 13', [['rz', 0, '-1/4'], ['rz', 0, '7/2'], ['rz', 0, '3/4'], ['s', 0]], {'t_count': 2, 'clifford_count': 2}], ['control: random t-count 14', [['sdg', 0]], {'t_count': 0, 'clifford_count': 1}], ['control: random t-count 15', [['ccx', 0, 1, 2], ['sdg', 0], ['t', 0], ['rz', 0, '3/2']], {'t_count': 8, 'clifford_count': 10}]]]
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: rz two pi	`{'clifford_count': 0, 't_count': 0}`	`{'clifford_count': 0, 't_count': 0}`	Passed
regression: rz zero	`{'clifford_count': 0, 't_count': 0}`	`{'clifford_count': 0, 't_count': 0}`	Passed
regression: rz four pi	`{'clifford_count': 0, 't_count': 0}`	`{'clifford_count': 0, 't_count': 0}`	Passed
control: rz pi is Z	`{'clifford_count': 1, 't_count': 0}`	`{'clifford_count': 1, 't_count': 0}`	Passed
control: rz half pi is S	`{'clifford_count': 1, 't_count': 0}`	`{'clifford_count': 1, 't_count': 0}`	Passed
control: rz quarter pi	`{'clifford_count': 0, 't_count': 1}`	`{'clifford_count': 0, 't_count': 1}`	Passed
control: tdg	`{'clifford_count': 0, 't_count': 1}`	`{'clifford_count': 0, 't_count': 1}`	Passed

SHA-256 / 6e6da8bb4c4f7673138b2eed3d1d48a15603948d0f15494b3226396484f7dcff

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 2026-09-29T14:51:34.914869+00:00.

Case digest / 5a7115bc8430b68d79489676ccd003f99cdaa9245cd42226b55f1d6f3d9f6c1e