BP + OSD-CS
B1 · B3Belief propagation + ordered-statistics post-processing (information-set inversion).
Source · Roffe 2020 · Bravyi 2024
== Roffe’s ldpc to 99.8% / <0.4σ on the gross code; reproduces the toric threshold.
pre-1.0 · research-grade
Decode the quantum error-correction frontier.
Glean is a high-performance, open-source library for decoding quantum error-correcting codes — the “solver” companion to Stim. A fast Rust core with an ergonomic Python API. Stim simulates the noise; Glean infers the most likely error and how to correct it.
Build from source: maturin develop --release
import glean
code = glean.toric_code(4) # [[32, 2, 4]] toric code
error = [0] * code.n; error[5] = 1 # one X error
syndrome = code.hz_syndrome(error)
correction = code.decode(syndrome, p=0.05) # BP + OSD-CS-10
assert code.hz_syndrome(correction) == syndromeCorrect
A wrong guess corrupts the computation. Every decoder, code, and noise model reproduces a specific published benchmark — the Iron Rule.
Fast
A zero-dependency Rust core with opt-in rayon parallelism under an ergonomic Python API. The performance-critical inner loops stay microsecond-fast.
qLDPC-ready
Built for the frontier that slashes qubit overhead: the bivariate-bicycle [[144, 12, 12]] gross code, decoded circuit-level — not just surface codes.
Three decoder paradigms
One DEM, three ways to solve it.
Glean spans three distinct decoder families, all validated on the same gross-code circuit-level detector error model.
relay-BP
B4Disordered-memory min-sum BP + relaying + ensembling. OSD-free and real-time.
Source · Müller 2025
== the authors’ relay_bp crate (<0.95σ); real-time iteration budget met (p90 212 < 600).
BP + OTF
B7Belief propagation + Ordered Tanner Forest (graph-acyclication). Inversion-free, O(n log n).
Source · deMarti iOlius 2024
== Glean’s validated BP + OSD-0 oracle (0.33σ) on the gross-code DEM.
Rare-event estimators
Reach 10⁻⁷ without 10⁹ shots.
The deepest published logical-error rates are infeasible by direct Monte-Carlo. Glean ships two decoder-agnostic importance-sampling tools that reuse the same checks, observables, priors, and batched decode.
glean.dss
Dynamical Subset Sampling · Heußen 2024
Stratify faults by weight and sum the contributing classes analytically — the weight probabilities are exact and decoder-independent.
Unbiased on Glean’s pipeline (0.0σ vs direct Monte-Carlo).
glean.splitting
Splitting + Bennett acceptance ratio · Bravyi–Vargo 2013 · Mayer 2025
A telescoping product of Metropolis-sampled ratios with no resolution wall at depth — the deep-number pin.
Unbiased vs direct MC two decades into the rare regime; pins the gross-code deep point.
The moat
Validated against published numbers.
Each row reproduces a published number on the identical problem the source paper
used. Rerun the whole suite in one command: python benchmarks/run_all.py.
| ID | What | Result |
|---|---|---|
B1 | Toric BP+OSD threshold (Roffe 2020, 9.9 ± 0.2%) | ≈10.0–10.1% crossing — in-band |
B3 | Gross-code [[144,12,12]] circuit-level vs ldpc (Bravyi 2024) | == ldpc 99.8% / <0.4σ; 0.8% threshold bracketed |
B4 | relay-BP vs reference crate (Müller 2025) | == ref crate; “factor of three” reproduced; p90 212 < 600 |
B5 | Decode speed vs ldpc / relay_bp | on par with relay_bp; out-runs ldpc; rayon 4–5× on 10 cores |
B7 | BP+OTF vs BP+OSD-0 oracle (deMarti iOlius 2024) | ensemble BP+OTF == BP+OSD-0, 0.33σ |
B9/B10 | Deep point pL ≈ 2×10⁻⁷ @ p=10⁻³ (Bravyi Nature) | reproduced within convention + extrapolation uncertainty |
Honesty. Glean reproduces these numbers; it does not claim to beat them. The deep Nature point is consistent with — slightly below — the headline once normalized to the paper’s per-cycle convention; relay-BP’s separation over BP+OSD tops out near 7× for XZ-decoding. Each write-up states what reproduces and what is deferred.
Grounded in the literature.
No code without a citation: every decoder and code traces to a peer-reviewed source and ships with a benchmark reproducing that source’s published numbers.