HyperNQ: A Hypergraph Neural Network Decoder for Quantum LDPC Codes

TL;DR

HyperNQ introduces a Hypergraph Neural Network decoder for Quantum LDPC codes to overcome Belief Propagation limitations caused by short cycles. By modeling stabilizers as hyperedges and employing a two-stage node↔hyperedge message passing, it captures higher-order correlations that improve decoding accuracy, particularly near the pseudo-threshold. The framework demonstrates up to 84% lower logical error rate than BP and 50% lower than GNN baselines on a Hypergraph Product code, with linear-scaling inference. This approach offers a scalable, expressive decoder for QLDPC codes, potentially enabling more efficient quantum error correction in fault-tolerant quantum computing.

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.

Figures (4)

• Figure 1: (a) represents the Tanner Graph and (b) is its Hypergraph Representation with weight (connected nodes) 4. Both graphs consist of $2n$ variable nodes (one per X- and Z-component of each qubit) and $m$ check nodes (stabilizers).
• Figure 2: Illustration of the two-stage Node–Hyperedge–Node message passing mechanism. In the Node$\to$Hyperedge pass, hyperedge features are updated by aggregating with corresponding node features. In the Hyperedge$\to$Node pass, the updated hyperedge features are propagated back to update node features, ensuring effective modeling of multi-qubit parity constraints.
• Figure 3: Block-level overview of Algorithm \ref{['alg:node2hyperedge']} and \ref{['alg:hyperedge2node']} showing the 4-step process in both stages of the message-passing scheme.
• Figure 4: Performance comparison of our proposed HyperNQ versus other approaches across different physical error rates for decoding the HGP code, [[n, k]] = [[129, 28]]).