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 physical-qubit Pauli error with perfect X- and Z-stabilizer syndromes

For this code: Read each nonzero four-bit syndrome as one of the fifteen Hamming columns. The Z-check syndrome locates an X component, the X-check syndrome locates a Z component, and simultaneous addresses identify a Y error. This exact finite rule is not a threshold claim; noisy extraction and concatenation require a circuit- or hierarchy-specific decoder.

References: gottesman1997stabilizer, steane1996simple