Research On Quantum Machine Learning Algorithms

Quantum computing takes advantage of the linear superposition of quantum states and has the natural parallel computing capability,which shows great advantages over classical computing.The design of quantum algorithms determines whether quantum computing can be effectively accelerated and is the core field of quantum computing.The machine learning algorithms have the advantages of high adaptability and self-learning ability,which makes it widely used in the field of cyberspace security.At the same time,the application of quantum technology further improves the ability of machine learning to process massive data,thus it is of great significance to carry out research on quantum machine learning algorithms.This paper focuses on three aspects of quantum machine learning: principal component analysis,support vector machine and quantum-inspired algorithms.The research results are as follows:1.Research on quantum principal component analysis algorithm.Principal component analysis(PCA)is a common dimensionality reduction algorithm in machine learning and the key step is matrix decomposition.The measurement result of original quantum principal component analysis(QPCA)algorithm cannot guarantee the target singular value and the corresponding singular vector.In this paper,the quantum matrix low-rank approximation algorithm is proposed,which can be used as the preprocessing step of some quantum algorithms.This algorithm is used to further process the result of the original quantum principal component analysis algorithm,so that the measurement result can obtain the target singular values and the corresponding singular vectors can be obtained with the success rate of 1.When the singular value of the matrix is relatively uniform and the same target singular values can be obtained,the running times numbers of the new algorithm are can be reduced.2.Research on quantum support vector machine algorithm.The least square support vector machine(LSSVM)is a common machine learning algorithm for binary classification problems and the key step is the inversion of matrix.On the one hand,the original quantum support vector machine algorithm using full discrete variables for the process of information processing.There are requires a large number of qubits to store eigenvalues information and the storage complexity is higher.On the other hand,the original algorithm need to runs the algorithm for many times to estimate the predicted value of the new data.A full quantum method consumes a lot of quantum storage resources.In this paper,two algorithms are proposed to solve these two problems.Firstly,continuous variables are used to encode the eigenvalues in the continuous state,which eliminates the extra additional storage resources in the information processing process and greatly reduces the storage complexity of the algorithm.Secondly,the parameter vector iscompressed to the equivalent "sparse" vector by through matrix transformation.And the classical results are measured and stored,so as to reduce the quantum storage resources of parameter vector during the procedure of algorithm.In addition,for a class of nonlinear models,a new approach is proposed to estimate the quantum gaussian kernel mapping.3.Application research of quantum-inspired algorithm.XL algorithm is an important method for solving nonlinear equations.This paper combines the quantum-inspired algorithm with XL algorithm and designs the quantum-inspired XL algorithm.Under certain conditions,the time complexity can be reduced to O(7)ploy(log MN)(8).Compared with the existing XL algorithm,the exponential acceleration can be realized.