# Neural Minimum Weight Perfect Matching for Quantum Error Codes

arXiv: https://arxiv.org/abs/2601.00242 · HTML: https://mlsanity.com/paper/2601.00242/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 73 references that are in the map.
- First posted on arXiv 1 Jan 2026.

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [On Layer Normalization in the Transformer Architecture](https://mlsanity.com/paper/2002.04745/) (2020)
- [Masked Label Prediction: Unified Message Passing Model for Semi-Supervised Classification](https://mlsanity.com/paper/2009.03509/) (2020)
- [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)
- [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)
- [Fusion Blossom: Fast MWPM Decoders for QEC](https://mlsanity.com/paper/2305.08307/) (2023)

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

- [Distance Prediction for Quantum Codes](https://mlsanity.com/paper/2610.18130/) (2026)

## Abstract (arXiv)

Realizing the full potential of quantum computation requires Quantum Error Correction (QEC). QEC reduces error rates by encoding logical information across redundant physical qubits, enabling errors to be detected and corrected. A common decoder used for this task is Minimum Weight Perfect Matching (MWPM) a graph-based algorithm that relies on edge weights to identify the most likely error chains. In this work, we propose a data-driven decoder named Neural Minimum Weight Perfect Matching (NMWPM). Our decoder utilizes a hybrid architecture that integrates Graph Neural Networks (GNNs) to extract local syndrome features and Transformers to capture long-range global dependencies, which are then used to predict dynamic edge weights for the MWPM decoder. To facilitate training through the non-differentiable MWPM algorithm, we formulate a novel proxy loss function that enables end-to-end optimization. Our findings on the toric code under depolarizing noise demonstrate thresholds of 17.9% and 10.95%, nearing the 18.9% and 11.0% maximum likelihood bounds, highlighting the advantage of hybrid decoders that combine the predictive capabilities of neural networks with the algorithmic structure of classical matching.