HyperNQ: A Hypergraph Neural Network Decoder for Quantum LDPC Codes

2025-11-03

AI Summary

Conventional belief propagation (BP) decoding of quantum low-density parity-check (QLDPC) codes suffers from poor convergence due to short cycles in Tanner graphs, while existing graph neural network (GNN)-based decoders are limited by pairwise message passing and thus unable to effectively capture high-order stabilizer constraints. Method: This work introduces hypergraph neural networks (HGNNs) into QLDPC decoding for the first time. By representing multi-variable joint constraints via hyperedges and designing a two-stage message-passing mechanism over the Tanner graph structure, the framework enables end-to-end learnable decoding. Contribution/Results: Experiments demonstrate that, below the pseudo-threshold, the proposed HGNN decoder reduces logical error rates by up to 84% compared to BP and by up to 50% relative to GNN baselines. The method significantly improves both decoding performance and robustness, offering a principled solution to modeling higher-order quantum constraints.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Quantum computing requires effective error correction strategies to mitigate noise and decoherence. Quantum Low-Density Parity-Check (QLDPC) codes have emerged as a promising solution for scalable Quantum Error Correction (QEC) applications by supporting constant-rate encoding and a sparse parity-check structure. However, decoding QLDPC codes via traditional approaches such as Belief Propagation (BP) suffers from poor convergence in the presence of short cycles. Machine learning techniques like Graph Neural Networks (GNNs) utilize learned message passing over their node features; however, they are restricted to pairwise interactions on Tanner graphs, which limits their ability to capture higher-order correlations. In this work, we propose HyperNQ, the first Hypergraph Neural Network (HGNN)- based QLDPC decoder that captures higher-order stabilizer constraints by utilizing hyperedges-thus enabling highly expressive and compact decoding. We use a two-stage message passing scheme and evaluate the decoder over the pseudo-threshold region. Below the pseudo-threshold mark, HyperNQ improves the Logical Error Rate (LER) up to 84% over BP and 50% over GNN-based strategies, demonstrating enhanced performance over the existing state-of-the-art decoders.

Problem

• Decoding quantum LDPC codes with hypergraph neural networks
• Overcoming poor convergence of belief propagation in short cycles
• Capturing higher-order correlations beyond pairwise graph interactions

Innovation

• Hypergraph Neural Network for QLDPC decoding
• Two-stage message passing scheme for hyperedges
• Higher-order stabilizer constraints for enhanced performance