# Efficient and Universal Neural-Network Decoder for Stabilizer-Based Quantum Error Correction

arXiv: https://arxiv.org/abs/2502.19971 · HTML: https://mlsanity.com/paper/2502.19971/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 57 references that are in the map.
- First posted on arXiv 27 Feb 2025.

## Builds on (most cited first, 11 of 11)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [On Layer Normalization in the Transformer Architecture](https://mlsanity.com/paper/2002.04745/) (2020)
- [Gated Delta Networks: Improving Mamba2 with Delta Rule](https://mlsanity.com/paper/2412.06464/) (2024)
- [Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) Network](https://mlsanity.com/paper/1808.03314/) (2018)
- [Parallelizing Linear Transformers with the Delta Rule over Sequence Length](https://mlsanity.com/paper/2406.06484/) (2024)
- [Learning to Decode the Surface Code with a Recurrent, Transformer-Based Neural Network](https://mlsanity.com/paper/2310.05900/) (2023)
- [Deep neural decoders for near term fault-tolerant experiments](https://mlsanity.com/paper/1802.06441/) (2018)
- [Advantages of versatile neural-network decoding for topological codes](https://mlsanity.com/paper/1802.08680/) (2018)
- [qecGPT: decoding Quantum Error-correcting Codes with Generative Pre-trained Transformers](https://mlsanity.com/paper/2307.09025/) (2023)

## Built on by (most cited first, 7 of 7)

- [A scalable and real-time neural decoder for topological quantum codes](https://mlsanity.com/paper/2512.07737/) (2025)
- [Learning to Decode in Parallel: Self-Coordinating Neural Network for Real-Time Quantum Error Correction](https://mlsanity.com/paper/2601.09921/) (2026)
- [Maximum Likelihood Decoding of Quantum Error Correction Codes](https://mlsanity.com/paper/2605.17230/) (2026)
- [Efficient foundation decoders for fault-tolerant quantum computing](https://mlsanity.com/paper/2606.27119/) (2026)
- [Machine Learning Approaches to Decoding Topological Quantum Codes](https://mlsanity.com/paper/2608.15760/) (2026)
- [Data-Driven Learnability Transition of Measurement-Induced Entanglement](https://mlsanity.com/paper/2512.01317/) (2025)
- [When AI meets quantum information: A comprehensive review](https://mlsanity.com/paper/2607.00365/) (2026)

## Abstract (arXiv)

Scaling quantum computing to practical applications necessitates reliable quantum error correction. Although numerous correction codes have been proposed, the overall correction efficiency critically limited by the decode algorithms. We introduce GraphQEC, a code-agnostic decoder leveraging machine-learning on the graph structure of stabilizer codes with linear time complexity. GraphQEC demonstrates unprecedented accuracy and efficiency across all tested code families, including surface codes, color codes, and quantum low-density parity-check (QLDPC) codes. For instance, on a distance-12 QLDPC code, GraphQEC achieves a logical error rate of 9.55 × 10-5, an 18-fold improvement over the previous best specialized decoder's 1.74 × 10-3 under p=0.005 physical error rates, while maintaining 157μs/cycle decoding speed. Our approach represents the first universal solution for real-time quantum error correction across arbitrary stabilizer codes.