Entry facet

Decoders

Algorithms, noise models, applicability, and performance notes.

Deterministic CSS pivot baseline css-pivot research-grade
Solves the X- and Z-syndrome linear systems by left-to-right GF(2) elimination with free variables fixed to zero; it scales polynomially but ignores likelihoods and degeneracy, so it is a reproducible baseline rather than a competitive decoder.
Type: algebraic-baseline · Noise setting: one exported finite CSS matrix with perfect X- and Z-syndrome bits; the deterministic algebraic solution ignores error likelihood and degeneracy
For this code: This is only a reproducible matrix baseline. It is not small-set flip and inherits none of the adversarial or random-error expansion guarantees. The family-specific algorithm is explained in the small-set-flip view; the current controlled decoder registry has no distinct benchmark adapter for it.
References: leverrier2015quantumexpander
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: code-capacity Pauli noise with perfect syndrome on a sparse binary HGP check matrix
For this code: BP-OSD is a generic qLDPC comparison point. Its finite-length behavior, tuning, and thresholds on other sparse families do not prove the expansion-conditioned small-set-flip theorem for this family.
References: roffe2020decoding, panteleev2021degenerate
No standard decoder known none-known none-known
Marks an honest algorithmic gap where the Atlas has no broadly accepted decoder for the stated code and noise setting.
Type: none · Noise setting: a complete repeated syndrome-extraction circuit with data, measurement, routing, leakage, and correlated hardware faults
For this code: No exact-family circuit-level threshold or repeated-syndrome experimental decoder was found in the primary-source search completed on 2026-08-09. This dated gap does not erase the perfect-syndrome small-set-flip theorem.
References: leverrier2015quantumexpander, delfosse2021measurement