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

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 propa...

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Vydáno v:	IEEE access Ročník 13; s. 25637 - 25649
Hlavní autoři:	Miao, Sisi, Schnerring, Alexander, Li, Haizheng, Schmalen, Laurent
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Piscataway IEEE 2025 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	Belief propagation Binary codes channel coding Codes Computers Correlation Decoders Decoding decoding algorithms Error correcting codes Error correction Iterative decoding neural networks Numerical simulation Quantum computers Quantum error correction quantum low-density parity-check codes Qubit Reviews Vectors
ISSN:	2169-3536, 2169-3536
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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.
AbstractList	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.
Author	Schmalen, Laurent Li, Haizheng Schnerring, Alexander Miao, Sisi
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SubjectTerms	Belief propagation Binary codes channel coding Codes Computers Correlation Decoders Decoding decoding algorithms Error correcting codes Error correction Iterative decoding neural networks Numerical simulation Quantum computers Quantum error correction quantum low-density parity-check codes Qubit Reviews Vectors
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Title	Quaternary Neural Belief Propagation Decoding of Quantum LDPC Codes With Overcomplete Check Matrices
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