Title: SAQ: Stabilizer-Aware Quantum Error Correction Decoder
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
Keywords: Deep learning, Quantum Information, Error Correcting Codes

Abstract: Quantum Error Correction (QEC) decoding faces a fundamental accuracy-
efficiency tradeoff. Classical methods like Minimum Weight Perfect Matching
(MWPM) exhibit variable performance across noise models and suffer from poly-
nomial complexity, while tensor network decoders achieve high accuracy but
at prohibitively high computational cost. Recent neural decoders reduce com-
plexity but lack the accuracy needed to compete with computationally expensive
classical methods. We introduce SAQ-Decoder, a unified framework combining
transformer-based learning with constraint aware post-processing that achieves
both near Maximum Likelihood (ML) accuracy and linear scalability. Our ap-
proach combines a dual-stream transformer architecture that processes syndromes
and logical information with asymmetric attention patterns, and a novel differ-
entiable logical loss that directly optimizes Logical Error Rates (LER) through
smooth approximations over finite fields. SAQ-Decoder achieves near-optimal
performance, with error thresholds of 10.99% (independent noise) and 18.6%
(depolarizing noise) on toric codes that approach the ML bounds of 11.0% and
18.9% while outperforming existing neural and classical baselines in accuracy,
complexity, and parameter efficiency. Our findings establish that learned decoders
can simultaneously achieve competitive decoding accuracy and computational ef-
ficiency, addressing key requirements for practical fault-tolerant quantum com-
puting systems.