Decoders

Lookup table lookup-table standard

Exhaustively maps each syndrome to a correction for one fixed, small code and noise model; exact lookup becomes impractical as the syndrome space grows.

Type: exact-small · Noise setting: finite one-shot chain with independent protected-sector data flips, perfect final data readout, and no measurement faults

For this code: Maximum likelihood reduces to majority inference for the symmetric independent model. Calling the rule “majority vote” is not enough to extend it to repeated noisy syndrome extraction: that setting has a different observation object and fault equivalence.

References: gottesman1997stabilizer, chen2021repetitive

Minimum-weight perfect matching mwpm standard

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 projective parity rounds with stochastic data and measurement faults represented by a calibrated planar spacetime detection graph

For this code: Matching pairs detection events using edge weights derived from the admitted circuit model. Leakage, long-range correlations, and ambiguous multi-fault mechanisms require graph augmentation or a different decoder; no threshold is transferred to an unspecified circuit here.

References: higgott2022pymatching, kelly2015preservation, chen2021repetitive

Tensor-network maximum-likelihood decoder tensor-network-mld research-grade

Compares logical-class probabilities by exact free-fermion methods for restricted noise or by approximate tensor-network contraction for more general channels.

Type: tensor-network · Noise setting: planar circuit-level repetition model whose logical sectors admit exact partition-function evaluation

For this code: Exact maximum-likelihood decoding retains circuit correlations that an independently weighted matching graph can discard. Its exactness is scoped to the planar model and boundary conditions in the cited work, not to arbitrary leakage or correlated hardware noise.

References: bravyi2014efficient, cao2025exactrepetition