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 rectangular blocks with perfect two-qubit gauge outcomes under stochastic Pauli noise

For this code: The exact-small decision rule factorizes into repetition-style parity inference along rows and columns; it may be implemented by majority logic instead of literally storing a table. The optimum rectangle is a property of the X/Z noise bias and objective, not a code-only constant.

References: aliferis2007subsystem, napp2013optimal

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: circuit faults in repeated low-weight gauge extraction or encoded-ancilla Steane extraction on fixed small blocks

For this code: Here the input includes a protocol-specific history of gauge outcomes, flags, or encoded-ancilla checks. Repeating gauge measurements and using a Steane ancilla are different syndrome objects, so their logical-error comparisons cannot be transferred to an unspecified static decoder.

References: cross2009comparative, escobar2025improved

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: uniform circuit-level noise on the period-four Floquet–Bacon–Shor descendant

For this code: Matching consumes constant-weight spacetime detectors built from the scheduled circuit. This row is intentionally variant-scoped: it does not establish a conventional threshold for the static rectangular family. No extraction-independent threshold for plain static stabilizer products was found in the stated searches as of 2026-08-02.

References: higgott2022pymatching, alam2025board, gidney2023less