Research On Topological Quantum Error-correcting Codes Against Noise Based On Deep Reinforcement Learning

The emergence of quantum communication and topological quantum error correction codes brings new vitality to social progress and the development of science and technology.As one of the important research contents,topological quantum error correction codes are widely used in different fields because of their unique properties that do not affect the whole world because of local errors.Especially,they play an important role in solving problems related to channel communication and information transmission,such as optimization and correction.In addition,the joint research of topological quantum error correcting codes and machine learning also plays a key role,so more and more researchers devote themselves to the joint research of topological quantum error correcting codes and machine learning.To solve the problems of low error correction accuracy and poor performance of machine learning decoder experiments.Therefore,this paper uses vertex operators and palquette operators to construct topological Toric codes and topological Semion codes to optimize the existing decoders,to achieve the purpose high error correction accuracy,good performance of the decoder,and perfect threshold.The main content of this paper includes the following parts: based on topological quantum Toric codes,a novel deep reinforcement learning decoder optimization of topological quantum semion codes is realized,which proves the feasibility of the deep reinforcement learning decoder of Semion codes.A deep Q network decoder for Toric codes is proposed for the first part.Firstly,the original and dual lattice is constructed according to the vertex operator and palquette operator of the Toric code.To locate the error faster when the error occurs,find out the corresponding correction operator and complete the error correction work.Secondly,the decoder designed by the MWPM algorithm is changed,and the depth Q network improved by depth Q learning is used to design the error correction code decoder.The purpose is to change the limitation of the MWPM algorithm in detecting the correlation between errors,and the error correction accuracy can not achieve the optimal effect.Finally,through the experiments of the test set and experimental set,the relationship between logic error rate,physical error rate,and different code distance is obtained,and the threshold of Toric code is calculated and analyzed,which lays the groundwork and provides design ideas for the design of depth Q network decoder of Semion code.For the second part,the deep Q network decoder of Semion codes is proposed.Compared with more studied Toric codes,a novel Semion code is proposed,which opens up the field of vision for the research of topological quantum error correction codes and machine learning.Firstly,the hexagonal lattice is constructed according to the vertex operator and palquette operator of Semion code,and the string operator,self-crossover path,and self-overlapping path are studied to improve the error correction work and find out the corresponding correction operator.Secondly,to better design the decoder,the Semion code of the hexagonal lattice is embedded into the torus to get the mapped square image,which is convenient for the follow-up decoding work.Finally,through the experiments of the test set and experimental set,the relationship between logical error rate,physical error rate,and different code distance is obtained,the threshold of the Semion code is calculated and analyzed,and the logical quantum gate overhead of the decoding process experiments.Compare the original overhead and the logical overhead of using a depth Q network under different thresholds.The decoder experiments of Semion codes prove the feasibility of deep reinforcement learning in the implementation of Semion code decoders and contribute to the subsequent research of topological quantum error correction codes and machine learning.