Maximum likelihood decoding 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 […]

Trellis Decoding for Qudit Stabilizer Codes and Its Application to Qubit Topological Codes

Trellis decoders are a general decoding technique first applied to qubit-based quantum error correction codes by Ollivier and Tillich in 2006. Here, we improve the scalability and practicality of their theory, show that it has strong structure, extend the results using classical coding theory as a guide, and demonstrate a canonical form from which the […]