Full-Stack Algorithm Trace

Compile the oracle and count the physical consequences#

def one_iteration(marked, apply_oracle=True):
    if marked not in range(4) or type(apply_oracle) is not bool:
        raise ValueError("marked must be a four-item oracle index")
    amplitudes = [0.5] * 4
    if apply_oracle:
        amplitudes[marked] *= -1
    assert abs(sum(a*a for a in amplitudes) - 1.0) < 1e-12
    mean = sum(amplitudes) / 4
    amplitudes = [2*mean - a for a in amplitudes]
    assert abs(sum(a*a for a in amplitudes) - 1.0) < 1e-12
    return amplitudes
baseline = one_iteration(2)
alternate = one_iteration(0)
oracle_omitted = one_iteration(2, False)
for marked in range(4):
    result = one_iteration(marked)
    assert result[marked] == 1.0 and sum(abs(a) for i, a in enumerate(result) if i != marked) == 0
assert baseline == [0.0, 0.0, 1.0, 0.0] and alternate == [1.0, 0.0, 0.0, 0.0]
assert oracle_omitted == [0.5, 0.5, 0.5, 0.5]
print(f"PASS: 83 full-stack Grover baseline={baseline} alternate={alternate} no_oracle_success={oracle_omitted[2]**2:.2f}")

For marked index 2, the phase vector is [1/2, 1/2, -1/2, 1/2]. Its mean is 1/4. Applying $a_i\mapsto 2\bar{a}-a_i$ yields [0, 0, 1, 0]. The table records that state evolution. The code repeats it for all four possible marked indices, checks normalization at every material step, and separates one oracle query from the gates needed to implement that oracle.

Artifact contract. A semantic state table, OpenQASM-adjacent gate ledger, executable amplitude fixture, and resource-account rubric. The fixture normalizes every state, returns the marked item with probability one in the ideal one-iteration case, and the report separates query count from compiled gates, shots, and error assumptions.

Exact validation command: python3 tools/validate_briefs.py --briefs data/editorial_briefs_64_87.json --from 64 --through 87 --check-rewritten-sources --execute-artifacts