wai-quantum 0.3.30: qLDPC memory at circuit level, re-derived from the circuit up #150

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2026-10-04

Transaction Science

wai-quantum 0.3.30: qLDPC memory at circuit level, re-derived from the circuit up ...

quantum_ldpc re-derives the logical failure rates of bivariate-bicycle
memories (arXiv:2308.07915) from scratch:

- Codes from their two polynomials: check matrices, k by GF(2) rank, a basis
  of logical operators. Presets [[72,12,6]], [[90,8,10]], [[108,8,10]],
  [[144,12,12]] and [[288,12,18]] all come out with their published k.
- The depth-8 syndrome cycle as circuit text: the published CNOT order, X and
  Z checks interleaved, circuit-level depolarizing noise on every CNOT, idle,
  preparation and measurement, two noiseless closing cycles, observables from
  the logical basis. quantum_frame samples it and derives its error model.
- BP-OSD: min-sum belief propagation in the log domain with adaptive scaling
  1 - 2^-t, then ordered statistics on non-convergence (information set in
  posterior order, combination sweep of order 7, cost sum ln(1/p)), in f64
  with in-crate logarithms.
- Memory experiments in fixed 64-shot chunks across threads (one on wasm32);
  the tally does not depend on the thread count.

Checked against the source's own Apache-2.0 simulation software:
- the error model for [[72,12,6]] (six cycles, p = 0.003) has its columns
  exactly, 2,268 X-fault and 2,232 Z-fault; half the probabilities agree to
  1e-13, the largest gap is 0.94% (merged faults: sums vs independent);
- on identical syndromes and error model, its decoder makes the same
  decision as BpOsd on 1,500 of 1,500 shots;
- failure rates per run on [[72,12,6]]: 0.028/0.090/0.230 here vs
  0.034/0.086/0.209 at p = 0.003/0.004/0.005 (halves combined as
  independent; the source's halves fail together 2.9% vs 1.3%);
- half by half at p = 0.005 the Z-type agrees (0.122 vs 0.118); the X-type is
  0.121 here (20,000 shots) vs 0.111 (9,000 runs), 2.3 sigma. Priors make no
  difference (476 vs 478 of 4,000) and both samplers match the exact detector
  rates, so the residual is in sampling and is documented as open;
- [[144,12,12]] per run 0.034 / 0.180 vs 0.039 / 0.193 at p = 0.004 / 0.005;
  per cycle on the published fit (2.90e-3 vs 3.15e-3, 1.64e-2 vs 1.54e-2).

CLI: wai-quantum ldpc [--code --p --cycles --shots --basis --max-iter
--osd-order --threads --seed --json] and ldpc --circuit. Example:
ldpc_memory. Pinned bit for bit natively and under wasm32-wasip2 (15 pins);
CLI output byte-identical across the two, including threaded vs not.

Co-Authored-By: Claude Opus 5.5 <[email protected]>

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