Research On Quantum Error Correcting Codes Based On Machine Learning

Nowadays,quantum science and technology has entered a new historical stage of deepening development and rapid breakthrough,which urgently requires close intersection of multiple disciplines and system integration of various key technologies.Its potential practical applications and significant scientific and theoretical implications will make it have a huge impact on the future of science and technology,and thus it has attracted attention of more and more researchers.For scaled-up quantum bit systems,ensuring correct operation of whole system through quantum error correction is a necessary requirement and a major challenge for a period of time.To exploit high-speed and accurate computing power of quantum computers and take advantage of confidentiality and security of quantum communications,quantum computers are still needed to improve many existing defects,such as impact of quantum noise perturbation and excessive cost overhead of resources required for large-scale quantum computing.Based on this,this paper proposes a machine learning-based topological error correction code scheme for efficient decoding by using CNNs and introducing dueling network optimization threshold in dual Q algorithm,this paper examines following aspects:(1)To address the problems of low error rate threshold and slow decoding speed in quantum error correction process,a Toric code error correction scheme based on machine learning decoding was proposed.First,in order to encode logical quantum bits in errorprone physical quantum bits with stabilizer form for finding error messages,a complex surface code on two-dimensional dyadic lattice was designed.Second,a decoder based on CNN network was designed with the aim of optimizing error rate threshold in decoding process to ensure error correction.The decoder can normalize eigenvector to ensure that quantum bit information is retrieved without gradient disappearance at the very end,avoiding problem of excessive error.Again,the training layers of decoder were deepened by using RestNet network structure in the CNN network,which improves training speed and iteration depth.Finally,the integrity and error of decoded information was verified and the latest threshold limit was generated.Experimental results show that convolution operation increases decoding rate and optimizes error rate threshold to 10.8%,achieving a low Toric code cost and high threshold.(2)To address the problem that error correction scheme is not unique and error tolerance is low in error correction process,a reinforcement learning-based quantum error correction scheme for surface codes was proposed.First,the scalability of topological error correction codes was exploited to extend surface codes to 3D lattices for achieving dimensional leap of quantum error correction codes to ensure stability of code,and then the error detection and correction were completed for stabilizer measurement.Second,since surface code is not self-correcting,error defects will occur when affected by noise.So errors must be proactively detected and corrected,decoding algorithm played an important role in this.Again,to solve spatial correlation problem of surface codes,a dueling network structure with reinforcement learning mechanism was used to find the optimal correction chain among non-unique error correction schemes.The neural network in the dual Q algorithm was improved to reduce decoder threshold by increasing the number of flipped bits in correction chain,which solves the problem of high optimization threshold,and improves training accuracy to 96.259%using Restnet21 while reducing training time.Compared to the more common MWPM algorithm,reinforcement learning decoder achieves better performance,increasing fault tolerance threshold of model from 0.0050 of MWPM to 0.0085.The mechanism of information transmission protection under high threshold was also studied,which improved low fidelity of quantum information during transmission.The fidelity of decoder was increased to 0.754 without adding additional quantum bit overhead,and demonstrate the feasibility of quantum information coding under quantum fault-tolerant systems at high thresholds.