Belief propagation Archives - IEEE Transactions on Quantum Engineering

Improved Belief Propagation Decoding Algorithms for Surface Codes

June 6, 2025Jiahan Chen; Zhengzhong Yi; Zhipeng Liang; Xuan WangUncategorizedAccuracy, Belief propagation, Codes, Complexity theory, Error correction, Maximum likelihood decoding, Noise, Qubit, Silicon, Time complexity

Abstract: Quantum error correction is crucial for universal fault-tolerant quantum computing. Highly accurate and low-time-complexity decoding algorithms play an indispensable role in ensuring quantum error correction works effectively. Among existing decoding algorithms, belief propagation (BP) is notable for its nearly linear time complexity and general applicability to stabilizer codes. However, BP’s decoding accuracy without postprocessing […]

Log-Domain Decoding of Quantum LDPC Codes Over Binary Finite Fields

A quantum stabilizer code over GF(q) corresponds to a classical additive code over GF(q2) that is self-orthogonal with respect to a symplectic inner product. We study the decoding of quantum low-density parity-check (LDPC) codes over binary finite fields GF(q = 2l) by the sum-product algorithm, also known as belief propagation (BP). Conventionally, a message in a nonbinary BP for quantum codes […]