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 finite HGP CSS matrix with perfect X- and Z-syndrome bits; free variables are fixed algebraically without a likelihood model
For this code: This deterministic solver applies to the exported matrix but exploits no HGP logical shape, degeneracy, factor distance, or noise statistics. It is a reproducible baseline, not evidence that arbitrary HGP factors are efficiently decodable.
References: tillich2009quantum
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: sparse finite HGP checks under code-capacity Pauli noise with perfect syndrome and implementation-specific message-passing settings
For this code: BP-OSD is a generic qLDPC benchmark whose post-processing can repair short-cycle failures. Performance on selected HGP matrices does not transfer a threshold, tuning, or asymptotic guarantee to every factor pair.
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: arbitrary binary factor pairs with repeated noisy syndrome extraction, routing faults, correlated data faults, and no expansion or erasure side-information assumption
For this code: No uniform construction-wide decoder for this combined regime was found in the primary-source search completed on 2026-08-10. ReShape, erasure, Viderman-style, iterative, and BP-OSD results remain available only under their separate hypotheses.
References: quintavalle2021reshape, connolly2024erasure, krishna2023viderman, pradhan2025linear