Study Of Quantum Algorithm For Liner Analysis In Machine Learning

In this thesis,we introduce the current situation of development of the quantum computing and quantum machine learning first,and then the concept of quantum computing that include the basic principles of quantum mechanics and the basic elements of quantum computing,furthermore,we introduce the development of the hardware of quantum computing with few simple examples.After that,we introduce a few basic quantum algorithms that constitute part of the basis of quantum algorithm,among of them,quantum Linear Discriminant Analysis provides an important basis of the work of this thesisThe main work in this thesis is that we give the quantum version of Canonical Correlation Analysis,first,we use a new skill to construct the cross-covariance matrix of a pair set of multidimension random variables,then we use chain product method to construct the production of cross-covariance matrix and the within class scatter matrix exponential function,after that,phase analysis was used to get the canonical variables and canonical correlation coefficients.If we suppose the dimensions of the variable in two data sets are n and m,and suppose there is a linear correlation between two sets of variables,then the algorithm in this work takes a time complexity of O(log(N(n+m))K_eff^3.5/?³),where N is the number of variables in each data set,? is the desired accuracy of the construct of chain production which is decided by the style of the matrix function,Keff is a pre-defined condition number for all matrix in the process of the construct of chain production and K_eff=O(1/?).In comparison with the classical algorithm,the quantum algorithm makes exponential speedupAdditionally,this thesis give a method for the implementation of the unitary evolution of the corresponding cross-covariance matrix of two sets of input data.In comparison with the trotter formula,the quantum algorithm is exponential speedup.