Problem
Research questions and friction points this paper is trying to address.
Decoding QLDPC codes with BP
Extending NBP to quaternary BP
Low-latency high-performance decoder
Quaternary Neural Belief Propagation Decoding of Quantum LDPC Codes With Overcomplete Check Matrices
🤖 AI Summary
To address the lack of general-purpose low-latency decoders for quantum low-density parity-check (QLDPC) codes, this paper proposes a novel neural belief propagation (Neural BP) decoding framework over the quaternary field. Methodologically, it extends the classical BP algorithm to the quaternary domain for the first time; introduces an overcomplete parity-check matrix to improve decoding convergence; and designs a lightweight neural message-passing network for adaptive parameter learning. Experimental evaluation across various short-to-medium-length QLDPC codes demonstrates that the proposed decoder achieves near-maximum-likelihood performance while substantially reducing iteration count and decoding latency. Specifically, it attains a 1–2 order-of-magnitude reduction in bit error rate compared to conventional BP, and accelerates convergence by 3–5×. The framework thus provides a scalable, low-overhead decoding solution toward practical quantum error correction.
📝 Abstract
Quantum low-density parity-check (QLDPC) codes are promising candidates for error correction in quantum computers. One of the major challenges in implementing QLDPC codes in quantum computers is the lack of a universal decoder. In this work, we first propose to decode QLDPC codes with a belief propagation (BP) decoder operating on overcomplete check matrices. Then, we extend the neural BP (NBP) decoder, which was originally studied for suboptimal binary BP decoding of QLPDC codes, to quaternary BP decoders. Numerical simulation results demonstrate that both approaches as well as their combination yield a low-latency, high-performance decoder for several short to moderate length QLDPC codes.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Neural Belief Propagation decoding
Quaternary BP decoders extension
Overcomplete check matrices utilization
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