Quantum toric code decoding method based on syndrome-preliminary error fusion module and ResNet architecture

doi:10.1088/1674-1056/ae1818

中国物理B ›› 2026, Vol. 35 ›› Issue (6): 60303-060303.doi: 10.1088/1674-1056/ae1818

Quantum toric code decoding method based on syndrome-preliminary error fusion module and ResNet architecture

Nai-Hua Ji(纪乃华)¹, Ping-Li Song(宋平俐)¹, Wei Wang(王伟)¹, Hui-Qian Sun(孙汇倩)¹, and Hong-Yang Ma(马鸿洋)^2,†

1 School of Information and Control Engineering, Qingdao University of Technology, Qingdao 266033, China;
2 School of Sciences, Qingdao University of Technology, Qingdao 266033, China

收稿日期:2025-05-15 修回日期:2025-10-25 接受日期:2025-10-28 发布日期:2026-06-15
通讯作者: Hong-Yang Ma E-mail:mahongyang@qut.edu.cn
基金资助:
Project supported by the Joint Fund of the Natural Science Foundation of Shandong Province, China (Grant Nos. ZR2022LLZ012 and ZR2021LLZ001) and the Key Research and Development Program of Shandong Province, China (Grant No. 2023CXGC010901).

Quantum toric code decoding method based on syndrome-preliminary error fusion module and ResNet architecture

Nai-Hua Ji(纪乃华)¹, Ping-Li Song(宋平俐)¹, Wei Wang(王伟)¹, Hui-Qian Sun(孙汇倩)¹, and Hong-Yang Ma(马鸿洋)^2,†

1 School of Information and Control Engineering, Qingdao University of Technology, Qingdao 266033, China;
2 School of Sciences, Qingdao University of Technology, Qingdao 266033, China

Received:2025-05-15 Revised:2025-10-25 Accepted:2025-10-28 Published:2026-06-15
Contact: Hong-Yang Ma E-mail:mahongyang@qut.edu.cn
Supported by:
Project supported by the Joint Fund of the Natural Science Foundation of Shandong Province, China (Grant Nos. ZR2022LLZ012 and ZR2021LLZ001) and the Key Research and Development Program of Shandong Province, China (Grant No. 2023CXGC010901).

摘要/Abstract

摘要： Quantum error correction technology is based on the principle of redundant encoding, encoding logical quantum information into multiple physical qubits to provide important support for the stable operation of quantum computers. To address the issues of low decoding accuracy and limited feature extraction in quantum error correction, this paper proposes a toric code decoder based on a syndrome-preliminary error fusion module (SPEFM) and a ResNet architecture. This decoder takes full advantage of the correlations between $X$ and $Z$ errors. In the SPEFM, the syndrome and preliminary error predictions are deeply fused, while a unidirectional Swin transformer architecture is incorporated to extract global error features from the syndrome data, significantly improving both decoding accuracy and computational efficiency. In addition, this paper further extracts local error features from the fused features using the deep residual structure of ResNet, enhancing the decoder's ability to capture quantum error patterns. Experimental results show that the decoder is applicable to different code distances (${d}=4, 6, 8, 10$) under the depolarizing noise model. Its bit error rate is lower than that of the minimum weight perfect matching (MWPM) algorithm, and its logical error rate is lower than both the MWPM algorithm and the ResNet18 decoder. Furthermore, the decoding threshold is increased to 0.163, representing a 3.82% improvement over the MWPM algorithm threshold of 0.157.

关键词: quantum error correction, toric code, ResNet, Swin transformer

Abstract: Quantum error correction technology is based on the principle of redundant encoding, encoding logical quantum information into multiple physical qubits to provide important support for the stable operation of quantum computers. To address the issues of low decoding accuracy and limited feature extraction in quantum error correction, this paper proposes a toric code decoder based on a syndrome-preliminary error fusion module (SPEFM) and a ResNet architecture. This decoder takes full advantage of the correlations between $X$ and $Z$ errors. In the SPEFM, the syndrome and preliminary error predictions are deeply fused, while a unidirectional Swin transformer architecture is incorporated to extract global error features from the syndrome data, significantly improving both decoding accuracy and computational efficiency. In addition, this paper further extracts local error features from the fused features using the deep residual structure of ResNet, enhancing the decoder's ability to capture quantum error patterns. Experimental results show that the decoder is applicable to different code distances (${d}=4, 6, 8, 10$) under the depolarizing noise model. Its bit error rate is lower than that of the minimum weight perfect matching (MWPM) algorithm, and its logical error rate is lower than both the MWPM algorithm and the ResNet18 decoder. Furthermore, the decoding threshold is increased to 0.163, representing a 3.82% improvement over the MWPM algorithm threshold of 0.157.

Key words: quantum error correction, toric code, ResNet, Swin transformer

中图分类号: (Quantum error correction and other methods for protection against decoherence)

03.67.Pp

03.67.-a (Quantum information)

Nai-Hua Ji(纪乃华), Ping-Li Song(宋平俐), Wei Wang(王伟), Hui-Qian Sun(孙汇倩), and Hong-Yang Ma(马鸿洋). Quantum toric code decoding method based on syndrome-preliminary error fusion module and ResNet architecture[J]. 中国物理B, 2026, 35(6): 60303-060303.

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Quantum toric code decoding method based on syndrome-preliminary error fusion module and ResNet architecture

Quantum toric code decoding method based on syndrome-preliminary error fusion module and ResNet architecture

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