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Quantum low-density parity-check (QLDPC) codes are promising candidates forerror correction in quantum computers. One of the major challenges inimplementing QLDPC codes in quantum computers is the lack of a universaldecoder. In this work, we first propose to decode QLDPC codes with a beliefpropagation (BP) decoder operating on overcomplete check matrices. Then, weextend the neural BP (NBP) decoder, which was originally studied for suboptimalbinary BP decoding of QLPDC codes, to quaternary BP decoders. Numericalsimulation results demonstrate that both approaches as well as theircombination yield a low-latency, high-performance decoder for several short tomoderate length QLDPC codes.

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