A High-Performance List Decoding Algorithm for Surface Codes with Erroneous Syndrome

Quantum error-correcting codes (QECCs) are necessary for fault-tolerant quantum computation. Surface codes are a class of topological QECCs that have attracted significant attention due to their exceptional error-correcting capabilities and easy implementation. In the decoding process of surface codes, the syndromes are crucial for error correction, though they are not always correctly measured. Most of the existing decoding algorithms for surface codes are not equipped to handle erroneous syndrome information or need additional measurements to correct syndromes with errors, which implies a potential increase in inference complexity and decoding latency. In this paper, we propose a high-performance list decoding algorithm for surface codes with erroneous syndromes. More specifically, to cope with erroneous syndrome information, we incorporate syndrome soft information, allowing the syndrome to be listed as well. To enhance the efficiency of the list decoding algorithm, we use LCOSD, which can significantly reduce the average list size in classical error correction compared with the conventional ordered statistics decoding (OSD). Numerical results demonstrate that our proposed algorithm significantly improves the decoding performance of surface codes with erroneous syndromes compared to minimum-weight perfect matching (MWPM) and BP decoders.