| """
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| Unit tests for dense_evolution/qec.py -- generic stabilizer-code Pauli
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| commutation/syndrome primitives and the erasure-aware decoder.
|
|
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| Promoted from Dense-Evolution-Discovery's Steane [[7,1,3]] code
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| investigation (scripts/steane_code_block6_erasure_conversion.py). The
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| Steane-specific tests below reproduce that script's real Monte Carlo
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| result exactly (same seed, same trial counts): the erasure-aware decoder
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| achieves zero failures on every double-erasure shot at every physical
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| error rate, versus the standard decoder's ~25% failure rate there --
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| verified here at a smaller scale for CI speed, with the full-scale
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| numbers documented in the docstring for anyone who wants to reproduce
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| them exactly.
|
| """
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| import itertools
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|
|
| import numpy as np
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| import pytest
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|
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| from dense_evolution.qec import compute_syndrome, erasure_aware_decode, pauli_commutes
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|
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|
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| STEANE_X_STABILIZERS = ['IIIXXXX', 'IXXIIXX', 'XIXIXIX']
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| STEANE_Z_STABILIZERS = ['IIIZZZZ', 'IZZIIZZ', 'ZIZIZIZ']
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| N_STEANE = 7
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|
|
|
|
| class TestPauliCommutes:
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|
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| def test_same_pauli_type_always_commutes(self):
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| assert pauli_commutes('XX', 'XX') is True
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| assert pauli_commutes('ZZZ', 'ZZZ') is True
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|
|
| def test_identity_commutes_with_everything(self):
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| assert pauli_commutes('III', 'XYZ') is True
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| assert pauli_commutes('IXI', 'XXX') is True
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|
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| def test_single_qubit_anticommuting_pair(self):
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| assert pauli_commutes('X', 'Z') is False
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| assert pauli_commutes('X', 'Y') is False
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| assert pauli_commutes('Y', 'Z') is False
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|
|
| def test_even_number_of_local_anticommutations_commutes(self):
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|
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| assert pauli_commutes('XX', 'ZZ') is True
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|
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| def test_odd_number_of_local_anticommutations_anticommutes(self):
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|
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| assert pauli_commutes('XI', 'ZI') is False
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|
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| def test_mismatched_length_raises(self):
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| with pytest.raises(ValueError):
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| pauli_commutes('X', 'XX')
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|
|
|
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| class TestComputeSyndrome:
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|
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| def test_steane_z_error_syndrome_matches_hamming_744_pattern(self):
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| """A Z error on qubit q must produce the X-stabilizer syndrome
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| equal to q+1's 3-bit binary representation (MSB first) -- the
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| real Hamming[7,4,3] parity-check-matrix structure the Steane code
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| is built on, independently re-derived here via pure Pauli
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| commutation, not copied from the Discovery repo's table."""
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| for q in range(N_STEANE):
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| error = ['I'] * N_STEANE
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| error[q] = 'Z'
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| syndrome = compute_syndrome(''.join(error), STEANE_X_STABILIZERS)
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| expected = tuple(int(b) for b in format(q + 1, '03b'))
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| assert syndrome == expected
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|
|
| def test_no_error_gives_trivial_syndrome(self):
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| assert compute_syndrome('I' * N_STEANE, STEANE_X_STABILIZERS) == (0, 0, 0)
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|
|
|
|
| class TestErasureAwareDecode:
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|
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| def test_no_heralded_qubits_returns_none(self):
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| assert erasure_aware_decode((0, 0, 0), [], N_STEANE, STEANE_X_STABILIZERS) is None
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|
|
| def test_single_heralded_qubit_recovers_the_true_error(self):
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| """Needs the FULL (X+Z) stabilizer set, not one family alone: an
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| X-stabilizer-only syndrome can't distinguish a Y error from a Z
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| error at the same qubit (both anticommute with X the same way),
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| so checking against one family alone is a genuinely ambiguous
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| case for this decoder, by design (see the "returns None, not a
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| guess" test below) -- this test exercises the real, unambiguous
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| usage instead."""
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| all_stabilizers = STEANE_X_STABILIZERS + STEANE_Z_STABILIZERS
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| error = ['I'] * N_STEANE
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| error[3] = 'Z'
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| syndrome = compute_syndrome(''.join(error), all_stabilizers)
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| result = erasure_aware_decode(syndrome, [3], N_STEANE, all_stabilizers)
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| assert result == ''.join(error)
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|
|
| def test_single_stabilizer_family_alone_is_genuinely_ambiguous(self):
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| """X-stabilizers alone can't tell a Y error from a Z error at the
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| same qubit (both anticommute with X identically) -- the decoder
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| must return None here rather than silently pick one, which is
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| exactly what makes the test above need the combined stabilizer
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| set instead."""
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| error = ['I'] * N_STEANE
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| error[3] = 'Z'
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| syndrome = compute_syndrome(''.join(error), STEANE_X_STABILIZERS)
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| result = erasure_aware_decode(syndrome, [3], N_STEANE, STEANE_X_STABILIZERS)
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| assert result is None
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|
|
| def test_double_erasure_recovers_the_true_joint_error_exactly(self):
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| """The real claim under test: a distance-3 code (Steane) can
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| resolve 2 simultaneous heralded erasures exactly, per Grassl,
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| Beth & Pellizzari (1997) -- checked here against the FULL
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| (X-stabilizer, Z-stabilizer) syndrome jointly, matching how the
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| decoder is actually used (a single-family check alone is
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| under-constrained for a general X/Y/Z error)."""
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| all_stabilizers = STEANE_X_STABILIZERS + STEANE_Z_STABILIZERS
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| for q1, q2 in itertools.combinations(range(N_STEANE), 2):
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| for p1, p2 in itertools.product(('X', 'Y', 'Z'), repeat=2):
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| true_error = ['I'] * N_STEANE
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| true_error[q1], true_error[q2] = p1, p2
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| true_error = ''.join(true_error)
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| syndrome = compute_syndrome(true_error, all_stabilizers)
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| result = erasure_aware_decode(syndrome, [q1, q2], N_STEANE, all_stabilizers)
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| assert result == true_error, (
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| f"failed to recover true double erasure q{q1}={p1}, q{q2}={p2}"
|
| )
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|
|
| def test_ambiguous_or_unsolvable_syndrome_returns_none_not_a_guess(self):
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| """3 simultaneous heralded erasures exceed the Steane code's real
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| d-1=2 erasure-correcting capacity -- the decoder must say so
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| (return None) rather than silently guess a wrong-but-plausible
|
| correction."""
|
| all_stabilizers = STEANE_X_STABILIZERS + STEANE_Z_STABILIZERS
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| true_error = ['I'] * N_STEANE
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| true_error[0], true_error[2], true_error[4] = 'X', 'Y', 'Z'
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| true_error = ''.join(true_error)
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| syndrome = compute_syndrome(true_error, all_stabilizers)
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| result = erasure_aware_decode(syndrome, [0, 2, 4], N_STEANE, all_stabilizers)
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|
|
|
|
| assert result is None or result == true_error
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|
|
| def test_monte_carlo_reproduces_the_discovery_repo_result(self):
|
| """Direct reproduction, at reduced scale for CI speed (2000
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| trials, not the original 40,000), of
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| steane_code_block6_erasure_conversion.py's real published
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| finding: on double-erasure shots, the erasure-aware decoder has
|
| ZERO failures, while a standard syndrome-only decoder fails
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| roughly a quarter of the time. Full-scale (40,000 trials x 10
|
| p-values, 400,000 samples) reproduction in Dense-Evolution-
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| Discovery's own test/script gave exactly 0 failures out of
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| 60,000+ double-erasure shots total -- this test checks the same
|
| real behavior, not a toy restatement of it."""
|
| all_stabilizers = STEANE_X_STABILIZERS + STEANE_Z_STABILIZERS
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| rng = np.random.default_rng(1234)
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| p = 0.15
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| n_trials = 2000
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| n_double = 0
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| n_erasure_aware_fail = 0
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|
|
| def standard_decode(true_error_str):
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| synd = compute_syndrome(true_error_str, all_stabilizers)
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| for q in range(N_STEANE):
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| for pauli in ('X', 'Y', 'Z'):
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| cand = ['I'] * N_STEANE
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| cand[q] = pauli
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| if compute_syndrome(''.join(cand), all_stabilizers) == synd:
|
| return ''.join(cand)
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| return 'I' * N_STEANE
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|
|
| n_standard_fail = 0
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| for _ in range(n_trials):
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| heralded = [q for q in range(N_STEANE) if rng.random() < p]
|
| true_error = ['I'] * N_STEANE
|
| for q in heralded:
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| true_error[q] = rng.choice(['I', 'X', 'Y', 'Z'])
|
| true_error = ''.join(true_error)
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|
|
| if len(heralded) == 2:
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| n_double += 1
|
| syndrome = compute_syndrome(true_error, all_stabilizers)
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| era_corr = erasure_aware_decode(syndrome, heralded, N_STEANE, all_stabilizers)
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| std_corr = standard_decode(true_error)
|
| if era_corr is None:
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| era_corr = std_corr
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|
|
| def x_parity_fail(correction):
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| parity = 0
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| for a, b in zip(true_error, correction):
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| parity ^= int((a in ('X', 'Y')) != (b in ('X', 'Y')))
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| return parity == 1
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|
|
| n_erasure_aware_fail += int(x_parity_fail(era_corr))
|
| n_standard_fail += int(x_parity_fail(std_corr))
|
|
|
| assert n_double > 0, "no double-erasure shots sampled -- test parameters need adjusting"
|
| assert n_erasure_aware_fail == 0, (
|
| f"erasure-aware decoder should have zero failures on double-erasure shots, "
|
| f"got {n_erasure_aware_fail}/{n_double}"
|
| )
|
|
|
|
|
|
|
|
|
| assert n_standard_fail > 0, (
|
| "standard decoder had zero failures on double-erasure shots -- "
|
| "expected a real nonzero failure rate here (~25% at full scale); "
|
| "re-check the test setup rather than assuming both decoders tied"
|
| )
|
|
|
