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: one fixed block under a single-qubit Pauli fault, perfect readout of the eight stabilizers, and correction modulo stabilizer degeneracy

For this code: Decode an X component from the two adjacent-pair Z syndromes inside its block, then decode a Z component from the two long X syndromes between blocks; a Y component triggers both decisions. The rule may be stored as a finite syndrome table or executed as two nested repetition decisions. It is not an asymptotic threshold claim. Under coherent correlated idling, stabilizer-sector interference changes the likelihood model, so the independent-Pauli table is not a model-free decoder.

References: shor1995scheme, gottesman1997stabilizer, debroy2021optimizing