# Machine Learning Approaches to Decoding Topological Quantum Codes

arXiv: https://arxiv.org/abs/2608.15760 · HTML: https://mlsanity.com/paper/2608.15760/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 98 references that are in the map.
- First posted on arXiv 16 Aug 2026.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [HiPPO: Recurrent Memory with Optimal Polynomial Projections](https://mlsanity.com/paper/2008.07669/) (2020)
- [The Modern Mathematics of Deep Learning](https://mlsanity.com/paper/2105.04026/) (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)
- [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)
- [A scalable and real-time neural decoder for topological quantum codes](https://mlsanity.com/paper/2512.07737/) (2025)
- [Neural Network Decoders for Large-Distance 2D Toric Codes](https://mlsanity.com/paper/1809.06640/) (2018)
- [A scalable and fast artificial neural network syndrome decoder for surface codes](https://mlsanity.com/paper/2110.05854/) (2021)
- [Efficient and Universal Neural-Network Decoder for Stabilizer-Based Quantum Error Correction](https://mlsanity.com/paper/2502.19971/) (2025)
- [The END: An Equivariant Neural Decoder for Quantum Error Correction](https://mlsanity.com/paper/2304.07362/) (2023)
- [Decoding Quantum LDPC Codes Using Graph Neural Networks](https://mlsanity.com/paper/2408.05170/) (2024)
- [Scalable Neural Decoders for Practical Fault-Tolerant Quantum Computation](https://mlsanity.com/paper/2604.08358/) (2026)
- [Scalable Neural Decoders for Practical Real-Time Quantum Error Correction](https://mlsanity.com/paper/2510.22724/) (2025)
- [Learning to Decode in Parallel: Self-Coordinating Neural Network for Real-Time Quantum Error Correction](https://mlsanity.com/paper/2601.09921/) (2026)

## Built on by (most cited first, 1 of 1)

- [When Quantum Meets AI: Quantum Methods for Machine Learning and Machine Learning Methods for Quantum Systems](https://mlsanity.com/paper/2609.25641/) (2026)

## Abstract (arXiv)

Decoding is an essential component of quantum error correction (QEC), translating stabilizer measurement outcomes into corrective actions that suppress logical errors and preserve logical quantum information. Building fault-tolerant architectures requires increasing the code distance, which in turn places growing demands on decoding accuracy, scalability, and practical deployability. While a wide range of decoding algorithms have been proposed and demonstrated, achieving reliable, scalable, and real-time decoding remains a significant challenge. Machine-learning (ML) approaches are particularly well suited to this setting, as quantum error decoding is fundamentally a problem of processing large volumes of classical data with complex spatiotemporal correlations. This chapter surveys ML-based methods for quantum error decoding, with a focus on topological codes and an emphasis on architectural principles, practical performance, and real-time considerations. We first frame decoding as a learning problem and outline key paradigms, including discriminative, generative, and reinforcement-learning formulations. We then introduce the neural network building blocks that underpin most contemporary neural decoders and discuss how these components can be integrated to balance expressivity, scalability, and latency. Building on this architectural perspective, we review recent progress and benchmarks in neural decoding for memory experiments, and discuss real-time decoding, open challenges, and future directions toward scalable fault-tolerant quantum computing.