Decoding topological XYZ ² codes with reinforcement learning based on attention mechanisms

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 in the paper, it is implemented on a hexagonal lattice of qubits and 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.In this paper, 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, which can reach 83.27% under the depolarising noise model, and we have measured thresholds of 0.18856 and 0.19043 for XYZ$^{2}$ codes at code spacing of 3 to 7 and 7 to 11, respectively. our study provides directions and ideas for the application of decoding schemes combining reinforcement learning attention mechanisms to other topological quantum error-correcting codes.