Decoding Quantum LDPC Codes Using Graph Neural Networks

2024/08/09 by Vukan Ninković, Ognjen Kundačina, Ninkovic, Vukan +7 · 6 citations
Computer Science · Engineering · #Quantum Computing Algorithms and Architecture #Error Correcting Code Techniques #Molecular Communication and Nanonetworks

paper · pdf · doi:10.48550/arxiv.2408.05170

Abstract

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.

Cited by

• Scalable Neural Decoders for Practical Fault-Tolerant Quantum Computation
• HyperNQ: A Hypergraph Neural Network Decoder for Quantum LDPC Codes
• Quantum Low-Density Parity-Check Codes
• Toward Uncertainty-Aware and Generalizable Neural Decoding for Quantum LDPC Codes
• Accelerating BP-based decoders for QLDPC Codes with Local Syndrome-Based Preprocessing
• Adaptive Learned Belief Propagation for Decoding Error-Correcting Codes

Related

• Graph Neural Networks for Enhanced Decoding of Quantum LDPC Codes
• HyperNQ: A Hypergraph Neural Network Decoder for Quantum LDPC Codes
• Neural Belief Propagation Decoding of Quantum LDPC Codes Using Overcomplete Check Matrices
• Machine Learning Message-Passing for the Scalable Decoding of QLDPC Codes
• Data-driven decoding of quantum error correcting codes using graph neural networks