Decoders

BP + ordered-statistics bp-osd standard

Uses belief propagation for soft error estimates, then ordered-statistics post-processing to repair failures caused by short cycles and degeneracy.

Type: bp-osd · Noise setting: memoryless Pauli and phenomenological qLDPC benchmarks

For this code: Belief propagation supplies soft reliabilities and ordered-statistics postprocessing repairs many failures caused by degeneracy and short Tanner-graph cycles. Performance belongs to the stated channel and stopping/OSD settings, not to the bare check matrix.

References: roffe2020decoding, panteleev2021degenerate

BP + ordered-statistics bp-osd research-grade

Uses belief propagation for soft error estimates, then ordered-statistics post-processing to repair failures caused by short cycles and degeneracy.

Type: bp-osd · Noise setting: circuit detector model for the seven-CNOT-layer extraction schedule

For this code: The original end-to-end study reports a 0.8% circuit-level threshold for its BB memory family under the standard circuit-noise model, depth-seven extraction, and BP-OSD. It is not a decoder-independent threshold of every BB construction: changing the family, CNOT order, detector model, noise normalization, or postprocessing defines a different threshold experiment.

References: roffe2020decoding, bravyi2024bicycle

Minimum-weight perfect matching mwpm research-grade

Represents detection events as vertices of a weighted graph and pairs them by minimum total weight; the pairing determines a likely correction chain.

Type: matching · Noise setting: BB symmetry reduction to toric-code-like cylinders

For this code: A cylinder construction exposes matching subproblems and can be combined with BP and over-matching. Its certificate is the specific symmetry reduction; it does not turn every BB instance into independent toric codes.

References: higgott2022pymatching, sahay2026matching