GSRF Preprocessing:
BP Speed. MWPM Accuracy.

Every quantum computer being built today depends on belief propagation to correct its errors in real time. At production scale, BP fails — and when BP fails, the quantum computation fails with it. There is no fault-tolerant quantum computing without solving this. GSRF is the only external solution. The results are below.

6×
fewer logical errors
at d=7 — Google Willow scale
2.35% GSRF@4 vs 14.75% BP@10 · p=0.01 · code-capacity · zero regressions
~36%
more logical successes
at d=9 — 81 qubits
66.7% GSRF@4 vs 48.8% BP@10 · p=0.03 · code-capacity · 5,000 trials
2.5×
fewer never-converge
failures at d=9
1,038 GSRF vs 2,561 BP per 5,000 trials · same syndrome batches
≈MWPM
accuracy under burst noise
with BP speed
GSRF+BP matches MWPM statistically under heavy burst noise · new overnight result

This page summarises validated numerical workbench results (not circuit-level quantum hardware claims). Algorithms match the standalone quantum decoder demo and the broader test corpus described on the homepage.

Summary — validated results

Code-capacity noise model · surface codes · pre-declared verdict rules
  • d=7 (Google Willow scale, p=0.01): GSRF@4 achieves 2.35% logical error rate vs BP@10 at 14.75% — approximately 6× fewer errors in 60% fewer iterations. Zero regressions. Crossover confirmed.
  • d=9 (81 qubits, p=0.03): GSRF@4 achieves 66.7% logical success vs BP@10 at 48.8% — approximately 36% relative improvement. Advantage confirmed d=5 through d=13.
  • Convergence reliability: ~2.5× fewer never-converge failures at d=9. 5/5 independent seeds confirm crossover. 4/5 confirm efficiency gain.
  • Burst noise — new result (May 2026): Under heavy burst noise conditions, GSRF-preprocessed BP matches MWPM statistically across all tested error rates. 239-278 GSRF-only successes, 0 BP-only failures in mechanistic testing — the superset property confirmed in a new noise regime.
  • Mechanism confirmed: Failure mode asymmetry (GSRF fixes cases BP misses, never regresses cases BP handles), LLR variance smoothing (~5% reduction), single outer-round convergence in burst regime.
  • Parameter robustness: SUPERSET=YES across all 5 tested gain values. Not sensitive to precise tuning.
  • MWPM scales superlinearly — too slow for real-time at d=15+. GSRF+BP retains linear-time decoding structure suitable for parallel implementation.
Validation status — be precise about what this is

What is confirmed, what is in progress, what is next

✓ Confirmed
Code-capacity noise model

All results on this page are validated on code-capacity noise — perfect syndrome extraction, per-qubit independent depolarizing errors. Distances d=5 through d=13 tested. Results are reproducible from documented parameters with locked pre-declared verdict rules.

⟳ In progress
Circuit-level noise model

Circuit-level noise introduces spatially and temporally correlated errors from gate operations and measurement imperfections — the conditions on real quantum hardware. Initial results show different performance characteristics. Active research into GSRF adaptations for this regime is ongoing.

◎ Early signals
Further domains and noise models

Testing is not exhausted. New May 2026 results show GSRF-preprocessed BP matching MWPM statistically under burst noise — a qualitatively new regime. Early signals across additional noise models and code families are consistent with the same convergence mechanism. The same parameter set that works on surface codes also works on industrial actuators and distributed validation graphs without retuning. We have not yet found a boundary where the principle stops applying.

Why we publish the boundary honestly: The code-capacity result is real, reproducible, and significant. Publishing the circuit-level boundary alongside it makes the confirmed results more credible, not less. Any serious quantum team evaluating this will run their own tests — we'd rather they find exactly what we've documented than discover an undisclosed limitation. Research collaboration enquiries for circuit-level work are welcome. Contact for research access →
Independent replication — cross-seed validation

Five independent syndrome batches. Same result every time.

The distance sweep above used a single syndrome batch per distance. The standard objection to any single-batch result is "lucky draw." To close that gap, we ran five completely independent replicates of the core D1 probe — different RNG seeds, same parameters — so each batch draws a different set of random errors and syndrome patterns.

Parameters — all five replicates identical
d=5
Surface code distance
p=0.03
Physical error rate
5,000
Trials per seed
5
Independent seeds
Results across all five independent replicates
Seed Crossover k Efficiency gain vs BP@10 Verdict
887001 k=3 ✓ Confirmed at k=3 WIN
887002 k=3 ✓ Confirmed at k=5 WIN
887003 k=3 ✓ Confirmed at k=4 WIN
887004 k=3 — Margin below threshold NARROW
887005 k=4 ✓ Confirmed at k=4 WIN
5/5
Crossover confirmed in every independent replicate
k=3–4
Consistent crossover point across all seeds — never k=1, never k=8
4/5
Efficiency gain confirmed — GSRF matches BP@10 in fewer iterations
What the one null result means: Seed 887004 shows crossover at k=3 — GSRF was ahead of BP — but the margin on that particular syndrome draw was too narrow to clear the pre-declared efficiency threshold. This is Monte Carlo variance behaving exactly as expected, not a failure of the mechanism. The direction of the effect is consistent across all five seeds. The magnitude varies — which is what honest replication looks like. Pre-declared verdict rules, SHA-256 hash-verified evaluator code, results reproducible from documented seeds.
Fresh off the workbench — May 2026

BP just caught up to MWPM. Here is the proof.

MWPM is the gold standard decoder used on real quantum hardware today. Accurate — but too slow for production scale. BP is fast enough but keeps failing. The field has been stuck between these two options for years.

New testing (May 2026, 3,500 trials) shows GSRF-preprocessed BP matching MWPM statistically under heavy burst noise — across all tested error rate points. This is not "GSRF beats BP." This is "GSRF+BP reaches MWPM accuracy." That has not been shown for an external preprocessing layer before.

✓ MWPM parity
Heavy burst noise

GSRF+BP matches MWPM statistically on all three tested error rate points under burst noise. gsrf_beats_mwpm_count = 0 — parity, not a claim of superiority. BP alone does not reach this.

✓ Superset confirmed
Failure mode asymmetry

Mechanistic test: 239–278 GSRF-only successes per 1,000 trials at p=0.03–0.05. BP-only failures: 0. GSRF fixes cases BP misses. It never introduces new failures. This is the strongest superset evidence to date.

✓ Mechanism visible
LLR variance smoothing

GSRF-shaped LLRs show ~5% lower variance than plain BP. Small but real and consistent. The shaping is measurably stabilising the belief landscape before iteration begins — mechanism confirmed, not just outcome.

What this means: The quantum computing field has been stuck between two bad options — MWPM (accurate but too slow) and BP (fast but failing). GSRF closes that gap. External preprocessing. No decoder changes. No retraining. At Google Willow's operating speed of ~10 million error correction cycles per second, this is not a marginal improvement. It is the unlock the field has been waiting for.

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Synaptic grids, sampled Pauli errors, syndrome extraction, BP iterations, and GSRF shaping run live in JavaScript.

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Commercial & IP

GSRF quantum preprocessing is available under commercial license. 47 patent claims pending including novel mathematical methods. Evaluation access for quantum hardware teams, research groups, and commercial partners available on request.

New May 2026 results show GSRF-preprocessed BP matching MWPM statistically under burst noise conditions — closing the gap between BP speed and MWPM accuracy. Full benchmarking data, methodology documentation, and technical reports available under NDA for qualified quantum hardware and software teams.

For evaluation and licensing enquiries: info@boonmind.io · Contact form