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: at most one unknown-position Pauli fault with perfect readout of the four stabilizer generators

For this code: The no-error case and all fifteen nonidentity single-qubit Pauli faults have different syndromes, so the table is an exact inverse in this model. This statement does not include faults in the extraction circuit.

References: laflamme1996perfect, bennett1996mixed, divincenzo1996efficient

Lookup table lookup-table research-grade

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: flagged distance-three extraction with syndrome and flag outcomes from the cited circuit

For this code: Flags identify circuit faults that can spread into dangerous correlated data errors; the recovery table consumes the flag record and any required follow-up syndrome, not only the static four-bit syndrome.

References: chao2018twoextra, bhatnagar2023lowdepth

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: ordered repeated extraction with one ancilla and circular connectivity in the cited circuit model

For this code: Matching is applied to circuit-order-dependent detection events. It is not an intrinsic decoder for an isolated perfect syndrome and its noise weights do not transfer to an arbitrary extraction schedule.

References: higgott2022pymatching, antipov2023circular