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

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.