Decoders

Renormalization-group decoder renormalization-group research-grade

Coarse-grains syndrome and error distributions hierarchically, using local inference to retain degeneracy information that a single lightest-path calculation discards.

Type: renormalization-group · Noise setting: thermal or phenomenological local Pauli faults with perfect access to the violated cubic-code stabilizers

For this code: The decoder clusters defects over increasing length scales and locally neutralizes clusters compatible with bounded errors. Its reported memory behavior belongs to the specified thermal dynamics and canonical cubic family; it is not a circuit-level repeated-measurement threshold.

References: duclos2010fast, bravyi2011selfcorrection, haah2011local

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 represented only by the exported sparse binary CSS matrix

For this code: BP-OSD is a generic qLDPC matrix baseline, not a theorem about fracton syndrome geometry. Its performance and tuning cannot be transferred from unrelated sparse codes to this periodic family without a dedicated benchmark.

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 fully specified repeated syndrome-extraction circuit with data, measurement, leakage, and correlated hardware faults

For this code: No primary circuit-level threshold for exact CSS Code 1 was found in the dated search completed on 2026-08-09. The actionable scalable-decoder and benchmark gap is routed to wanted:decoders-3d-fracton.

References: haah2011local, bravyi2011selfcorrection