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 triangular 4.8.8 patch whose three colored boundaries are included in each projection

For this code: Graphical or restriction decoding turns the colored syndrome into surface-code-like matching subproblems and then lifts their union back to a color-code correction. The projections are correlated, so solving them as unrelated graphs loses information; no threshold is attached here without the source's lattice, channel, and lifting rule.

References: higgott2022pymatching, wang2010graphical, stephens2014decoding

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 noisy syndrome extraction on triangular 4.8.8 patches, with spacelike data faults and timelike measurement faults derived from a specified measurement circuit

For this code: Each restricted graph is extended through time before matching. A circuit-level graph must include correlations introduced by the weight-four and weight-eight extraction circuits; a threshold for one schedule is not a schedule-independent property of this check matrix.

References: higgott2022pymatching, stephens2014decoding