Quaternary Neural Belief Propagation Decoding of Quantum LDPC Codes with Overcomplete Check Matrices

TL;DR

This paper introduces a novel quaternary neural belief propagation decoder for quantum LDPC codes using overcomplete check matrices, achieving low-latency and high-performance error correction in quantum computing.

Contribution

It proposes the first quaternary neural BP decoder for QLDPC codes with overcomplete check matrices, enhancing decoding performance.

Findings

Decoders show improved error correction performance in simulations.

Combination of approaches yields low-latency decoding.

Effective for short to moderate length QLDPC codes.

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.