Decoding Of Quantum Topological Codes Based On Convolutional Neural Network

Compared with classical computing,quantum computing has attracted the attention of many scholars due to its high efficiency in some difficult problems.But in the process of quantum computing,it is difficult to avoid the interference of quantum noise.In order to solve this problem,quantum error correction code technology came into being.Stabilizer codes are a class of quantum error correcting codes which are widely used and studied,but the decoding problem of stabilizer codes has always been a difficult problem.At present,the more active research fields are those codes with algebraic structure.Among them,the unique coding structure of topological codes makes the decoding problem a hot topic in stabilizer codes.Neural network is a data model which can simulate the structure and behavior of human brain nerve.It can actively detect the internal relationship between given data and give prediction results.It is widely used in various fields.The degenercy of stabilizer codes and the limitation of traditional decoding algorithms in error correlation detection make researchers turn their eyes to neural networks.This paper will study the decoding of topological codes based on neural network.Specifically including:First,a fully connected neural network decoder is built.In the depolarization channel model,given the syndrome of the toric code and the corresponding error train neural network to automatically detect the relationship between them,so that the model can predict the probability distribution of X and Z errors on the qubit when the neural network is given,and then the predicted errors are extracted by sampling to verify whether it can generate the same syndrome and calculate the proportion of correct decoding.At the same time,this paper compares and analyzes the MWPM decoding algorithms under the same channel model,finds that the neural network decoder can improve the performance under the same size of noise,and has a higher threshold than the MWPM decoding algorithm.Second,based on the pursuit of faster decoding speed,and more simplified network model.This paper improves the performance of the decoder based on convolutional neural network.The decoding simulation is carried out under the depolarization channel model.The comparison with MWPM decoding algorithm shows that convolutional neural network decoder can also break the limitation of the ability of MWPM decoder in the X and Z error correlation,improve the error correction ability of the decoder.In addition,the improvement of the decoder threshold also shows that the convolutional neural network decoder can improve its ability of noise resistance.Compared with the network model in(1),it has a better performance in training time.In addition,the model is trained under uncorrelated channel model and compared with MWPM decoding algorithm.It is found that convolutional neural network decoder can achieve similar decoding performance as MWPM decoder.It is proved that our decoding algorithm is also applicable.