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

TL;DR

This paper introduces a high-performance list decoding algorithm for surface codes that effectively handles erroneous syndromes by integrating soft information, reducing the need for extra measurements and improving decoding accuracy.

Contribution

The proposed algorithm combines belief propagation and ordered statistics decoding to recover qubits and syndromes without additional measurements, enhancing decoding performance for surface codes with errors.

Findings

Significantly improves decoding accuracy over existing methods.

Efficiently recovers erroneous syndromes without extra measurements.

Outperforms MWPM, BP, and original BP-OSD algorithms in simulations.

Abstract

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, however, they are not always correctly measured. Most of the existing decoding algorithms for surface codes need extra 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, where syndrome soft information is incorporated in the decoding, allowing qubits and syndrome to be recovered without needing extra measurements. Precisely, we first use belief propagation (BP) decoding for pre-processing with syndrome soft information, followed by ordered statistics decoding (OSD) for post-processing to list and recover both qubits and syndromes. Numerical results demonstrate that our proposed algorithm efficiently recovers erroneous syndromes and significantly improves the decoding performance of surface codes with erroneous syndromes compared to minimum-weight perfect matching (MWPM), BP and original BP-OSD algorithms.