HyperNQ: A Hypergraph Neural Network Decoder for Quantum LDPC Codes

TL;DR

HyperNQ introduces a hypergraph neural network decoder for quantum LDPC codes, capturing higher-order correlations and significantly improving error correction performance over traditional and GNN-based decoders.

Contribution

It is the first hypergraph neural network-based decoder for QLDPC codes, enabling better decoding by modeling higher-order stabilizer constraints.

Findings

HyperNQ reduces Logical Error Rate by up to 84% compared to BP.

HyperNQ outperforms GNN-based strategies by 50% in error correction.

Decoding performance is evaluated over the pseudo-threshold region.

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.