Quantum decoder design for subsystem surface code based on multi-head graph attention and edge weighting  

作　　者：Nai-Hua Ji Hui-Qian Sun Bo Xiao Ping-Li Song Hong-Yang Ma 纪乃华;孙汇倩;肖博;宋平俐;马鸿洋

机构地区：[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

出　　处：《Chinese Physics B》2025年第2期165-176,共12页中国物理B(英文版)

基　　金：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);the Key Research and Development Program of Shandong Province,China(Grant No.2023CXGC010901)。

摘　　要：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 multihead 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.

关 键 词：quantum error correction graph attention network subsystem surface code circuit-level noise 

分 类 号：O15[理学—数学]