# A Symmetry-Integrated Approach to Surface Code Decoding

arXiv: https://arxiv.org/abs/2509.10164 · HTML: https://mlsanity.com/paper/2509.10164/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 15 references that are in the map.
- First posted on arXiv 12 Sep 2025.

## Builds on (most cited first, 3 of 3)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Transformer-QEC: Quantum Error Correction Code Decoding with Transferable Transformers](https://mlsanity.com/paper/2311.16082/) (2023)

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

- [USDs: A universal stabilizer decoder framework using symmetry](https://mlsanity.com/paper/2601.15361/) (2026)

## Abstract (arXiv)

Quantum error correction, which utilizes logical qubits that are encoded as redundant multiple physical qubits to find and correct errors in physical qubits, is indispensable for practical quantum computing. Surface code is considered to be a promising encoding method with a high error threshold that is defined by stabilizer generators. However, previous methods have suffered from the problem that the decoder acquires solely the error probability distribution because of the non-uniqueness of correct prediction obtained from the input. To circumvent this problem, we propose a technique to reoptimize the decoder model by approximating syndrome measurements with a continuous function that is mathematically interpolated by neural network. We evaluated the improvement in accuracy of a multilayer perceptron based decoder for code distances of 5 and 7 as well as for decoders based on convolutional and recurrent neural networks and transformers for a code distance of 5. In all cases, the reoptimized decoder gave better accuracy than the original models, demonstrating the universal effectiveness of the proposed method that is independent of code distance or network architecture. These results suggest that re-framing the problem of surface code decoding into a regression problem that can be tackled by deep learning is a useful strategy.