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: memoryless Pauli errors with one perfect X/Z syndrome

For this code: Each nonzero three-bit syndrome is one column of the Hamming parity matrix, so X and Z components are corrected by two seven-entry address tables. The fixed [[7,1,3]] block has no intrinsic asymptotic threshold; threshold statements require concatenation or a growing code family.

References: steane1996multiple, gottesman1997stabilizer

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: single circuit faults during flagged syndrome extraction

For this code: The decision table consumes both syndrome and flag outcomes. A flag separates dangerous correlated data faults propagated by the extraction ancilla from ordinary single-qubit faults; the circuit schedule and available ancillas are therefore part of the decoder specification.

References: chao2018twoextra, reichardt2020few