关键词: quantum error correction, $XZZX$ code, biased noise, graph neural network

Abstract: Quantum error correction is a technique that enhances a system's ability to combat noise by encoding logical information into additional quantum bits, which plays a key role in building practical quantum computers. The $XZZX$ surface code, with only one stabilizer generator on each face, demonstrates significant application potential under biased noise. However, the existing minimum weight perfect matching (MWPM) algorithm has high computational complexity and lacks flexibility in large-scale systems. Therefore, this paper proposes a decoding method that combines graph neural networks (GNN) with multi-classifiers, the syndrome is transformed into an undirected graph, and the features are aggregated by convolutional layers, providing a more efficient and accurate decoding strategy. In the experiments, we evaluated the performance of the $XZZX$ code under different biased noise conditions (${\rm bias} = 1$, 20, 200) and different code distances ($d=3$, 5, 7, 9, 11). The experimental results show that under low bias noise (${\rm bias} = 1$), the GNN decoder achieves a threshold of 0.18386, an improvement of approximately 19.12% compared to the MWPM decoder. Under high bias noise (${\rm bias} = 200$), the GNN decoder reaches a threshold of 0.40542, improving by approximately 20.76%, overcoming the limitations of the conventional decoder. They demonstrate that the GNN decoding method exhibits superior performance and has broad application potential in the error correction of $XZZX$ code.

Key words: quantum error correction, $XZZX$ code, biased noise, graph neural network