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Quantum decoder design for subsystem surface code based on multi-head graph attention and edge weighting |
| Nai-Hua Ji(纪乃华)1,†, Hui-Qian Sun(孙汇倩)1, Bo Xiao(肖博)1, Ping-Li Song(宋平俐)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 |
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Abstract Quantum error-correcting codes are essential for fault-tolerant quantum computing, as they effectively detect and correct noise-induced errors by distributing information across multiple physical qubits. The subsystem surface code with three-qubit check operators demonstrates significant application potential due to its simplified measurement operations and low logical error rates. However, the existing minimum-weight perfect matching (MWPM) algorithm exhibits high computational complexity and lacks flexibility in large-scale systems. Therefore, this paper proposes a decoder based on a graph attention network (GAT), representing error syndromes as undirected graphs with edge weights, and employing a multi-head attention mechanism to efficiently aggregate node features and enable parallel computation. Compared to MWPM, the GAT decoder exhibits linear growth in computational complexity, adapts to different quantum code structures, and demonstrates stronger robustness under high physical error rates. The experimental results demonstrate that the proposed decoder achieves an overall accuracy of 89.95% under various small code lattice sizes $(L = 2, 3, 4, 5)$, with the logical error rate threshold increasing to 0.0078, representing an improvement of approximately 13.04% compared to the MWPM decoder. This result significantly outperforms traditional methods, showcasing superior performance under small code lattice sizes and providing a more efficient decoding solution for large-scale quantum error correction.
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Received: 25 October 2024
Revised: 16 December 2024
Accepted manuscript online: 20 December 2024
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PACS:
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03.67.-a
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(Quantum information)
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87.64.Aa
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(Computer simulation)
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03.67.Pp
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(Quantum error correction and other methods for protection against decoherence)
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| Fund: Project supported by the Natural Science Foundation of Shandong Province, China (Grant No. ZR2021MF049), 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). |
Corresponding Authors:
Nai-Hua Ji, Hong-Yang Ma
E-mail: 13964863452@126.com;hongyang_ma@aliyun.com
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Cite this article:
Nai-Hua Ji(纪乃华), Hui-Qian Sun(孙汇倩), Bo Xiao(肖博), Ping-Li Song(宋平俐), and Hong-Yang Ma(马鸿洋) Quantum decoder design for subsystem surface code based on multi-head graph attention and edge weighting 2025 Chin. Phys. B 34 020309
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