Decoders

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: code-capacity Pauli noise with perfect syndrome on a three-color triangular boundary

For this code: Projection or restriction turns each color-pair sector into a surface-code matching problem, then a lifting step reconciles the correlated projections into one color-code correction. Boundary connected components are part of the algorithm; applying the closed-surface lifting rule unchanged can reduce the effective distance.

References: higgott2022pymatching, delfosse2014projection, chamberland2020triangular

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: perfect-syndrome Pauli noise on the standard triangular patch with all three color boundaries retained in one nonorientable matching graph

For this code: Möbius matching folds the three boundary sectors into a single graph so that a pairing can cross the seam instead of choosing three independent color projections. Its numerical performance is decoder- and noise-model-specific, so this entry does not attach a bare threshold to the check matrix.

References: higgott2022pymatching, sahay2022mobius

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: repeated circuit-level syndrome extraction with detector events, correlated faults, and a specified measurement schedule

For this code: Circuit-level matching must be built from the actual detector error model. Flag outcomes, superdense or middle-out extraction, and the reconciliation rule change the graph and its weights; results for one circuit are not an extraction-independent property of the 6.6.6 family.

References: higgott2022pymatching, chamberland2020triangular, gidney2023color, lee2025colordecoder