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: For this fixed distance-three block, a finite coset table maps the perfect syndrome to a minimum-weight correction and corrects every single-qubit Pauli error. The block has no intrinsic asymptotic threshold: as of 2026-08-02, threshold claims require a concatenated protocol or a growing Reed–Muller family.

References: steane1996quantumrm

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 logical-state preparation

For this code: The decision rule consumes flag bits and preparation-check outcomes in addition to the final block syndrome. Those side-information bits keep correlated data faults propagated by a small preparation circuit distinguishable from ordinary single-qubit faults.

References: chamberland2019flagmagic

BP + ordered-statistics bp-osd research-grade

Uses belief propagation for soft error estimates, then ordered-statistics post-processing to repair failures caused by short cycles and degeneracy.

Type: bp-osd · Noise setting: code-capacity Pauli noise with perfect syndrome on quantum Reed–Muller blocks

For this code: The cited comparison uses BP-OSD as a baseline and improves belief propagation by decoding symmetry-permuted versions of the syndrome. These code-capacity results do not transfer to flagged preparation or code-switching circuits without a separate circuit-level benchmark.

References: roffe2020decoding, koutsioumpas2025autdec

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 during syndrome-conditioned Steane/Reed–Muller code conversion, including the measured conversion-check history

For this code: The decision rule uses the conversion syndromes to choose a Pauli-frame update for the target block. This is not the same table as perfect memory decoding: the measured checks and dangerous propagated faults depend on the conversion circuit, and device-level comparisons must retain preparation, verification, repetition, and postselection rules.

References: anderson2014conversion, butt2024switching