关键词: quantum error correction, topological quantum stabilizer code, reinforcement learning, attention mechanism

Abstract: Quantum error correction, a technique that relies on the principle of redundancy to encode logical information into additional qubits to better protect the system from noise, is necessary to design a viable quantum computer. For this new topological stabilizer code-$XYZ^{2}$ code defined on the cellular lattice, it is implemented on a hexagonal lattice of qubits and it encodes the logical qubits with the help of stabilizer measurements of weight six and weight two. However topological stabilizer codes in cellular lattice quantum systems suffer from the detrimental effects of noise due to interaction with the environment. Several decoding approaches have been proposed to address this problem. Here, we propose the use of a state-attention based reinforcement learning decoder to decode $XYZ^{2}$ codes, which enables the decoder to more accurately focus on the information related to the current decoding position, and the error correction accuracy of our reinforcement learning decoder model under the optimisation conditions can reach 83.27\% under the depolarizing noise model, and we have measured thresholds of 0.18856 and 0.19043 for $XYZ^{2}$ codes at code spacing of 3-7 and 7-11, respectively. our study provides directions and ideas for applications of decoding schemes combining reinforcement learning attention mechanisms to other topological quantum error-correcting codes.

Key words: quantum error correction, topological quantum stabilizer code, reinforcement learning, attention mechanism