# SAQ: Stabilizer-Aware Quantum Error Correction Decoder

arXiv: https://arxiv.org/abs/2512.08914 · HTML: https://mlsanity.com/paper/2512.08914/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 86 references that are in the map.
- First posted on arXiv 9 Dec 2025.

## Builds on (most cited first, 14 of 14)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Big Bird: Transformers for Longer Sequences](https://mlsanity.com/paper/2007.14062/) (2020)
- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [Quantum advantage in learning from experiments](https://mlsanity.com/paper/2112.00778/) (2021)
- [Learning to Decode the Surface Code with a Recurrent, Transformer-Based Neural Network](https://mlsanity.com/paper/2310.05900/) (2023)
- [Reinforcement Learning Decoders for Fault-Tolerant Quantum Computation](https://mlsanity.com/paper/1810.07207/) (2018)
- [CrossMPT: Cross-attention Message-Passing Transformer for Error Correcting Codes](https://mlsanity.com/paper/2405.01033/) (2024)
- [Deep Quantum Error Correction](https://mlsanity.com/paper/2301.11930/) (2023)
- [Advantages of versatile neural-network decoding for topological codes](https://mlsanity.com/paper/1802.08680/) (2018)
- [Piecewise-Velocity Model for Learning Continuous-time Dynamic Node Representations](https://mlsanity.com/paper/2212.12345/) (2022)
- [Quantum Artificial Intelligence: A Brief Survey](https://mlsanity.com/paper/2408.10726/) (2024)

## Abstract (arXiv)

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.