SAQ: Stabilizer-Aware Quantum Error Correction Decoder
David Zenati, Eliya Nachmani
TL;DR
This work introduces SAQ-Decoder, a unified quantum error-correction decoder that blends transformer-based learning with constraint-aware post-processing to achieve near-ML accuracy while scaling linearly with syndrome size. It employs a dual-stream transformer with asymmetric attention to separately process local syndrome constraints and global logical degeneracy, coupled with a differentiable logical-centric loss and a constraint-projected nullspace descent to enforce syndrome consistency. Across toric, rotated surface, color, and repetition codes under multiple noise models, SAQ-Decoder attains near-ML thresholds and consistently outperforms both neural and classical baselines, with strong parameter efficiency and scalability. The approach promises practical fault-tolerant quantum computing by delivering high decoding performance at realistic computational costs.
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 polynomial complexity, while tensor network decoders achieve high accuracy but at prohibitively high computational cost. Recent neural decoders reduce complexity 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 computational scalability with respect to the syndrome size. Our approach combines a dual-stream transformer architecture that processes syndromes and logical information with asymmetric attention patterns, and a novel differentiable 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 efficiency, addressing key requirements for practical fault-tolerant quantum computing systems.