# Decoding Quantum LDPC Codes Using Graph Neural Networks

arXiv: https://arxiv.org/abs/2408.05170 · HTML: https://mlsanity.com/paper/2408.05170/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 25 references that are in the map.
- First posted on arXiv 9 Aug 2024.

## Builds on (most cited first, 6 of 6)

- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Deep Learning Methods for Improved Decoding of Linear Codes](https://mlsanity.com/paper/1706.07043/) (2017)
- [Neural Enhanced Belief Propagation on Factor Graphs](https://mlsanity.com/paper/2003.01998/) (2020)
- [Graph Neural Networks for Channel Decoding](https://mlsanity.com/paper/2207.14742/) (2022)
- [Graph Neural Networks on Factor Graphs for Robust, Fast, and Scalable Linear State Estimation with PMUs](https://mlsanity.com/paper/2304.14680/) (2023)

## Built on by (most cited first, 5 of 5)

- [Scalable Neural Decoders for Practical Fault-Tolerant Quantum Computation](https://mlsanity.com/paper/2604.08358/) (2026)
- [Toward Uncertainty-Aware and Generalizable Neural Decoding for Quantum LDPC Codes](https://mlsanity.com/paper/2510.06257/) (2025)
- [HyperNQ: A Hypergraph Neural Network Decoder for Quantum LDPC Codes](https://mlsanity.com/paper/2511.01741/) (2025)
- [Machine Learning Approaches to Decoding Topological Quantum Codes](https://mlsanity.com/paper/2608.15760/) (2026)
- [When AI meets quantum information: A comprehensive review](https://mlsanity.com/paper/2607.00365/) (2026)

## Abstract (arXiv)

In this paper, we propose a novel decoding method for Quantum Low-Density Parity-Check (QLDPC) codes based on Graph Neural Networks (GNNs). Similar to the Belief Propagation (BP)-based QLDPC decoders, the proposed GNN-based QLDPC decoder exploits the sparse graph structure of QLDPC codes and can be implemented as a message-passing decoding algorithm. We compare the proposed GNN-based decoding algorithm against selected classes of both conventional and neural-enhanced QLDPC decoding algorithms across several QLDPC code designs. The simulation results demonstrate excellent performance of GNN-based decoders along with their low complexity compared to competing methods.