【作者】 陈波涛；

【导师】 王红军；

【作者基本信息】 西南交通大学 ， 计算机技术（专业学位）， 2019， 硕士

【摘要】 本文首先回顾了量子计算和量子机器学习的发展历史并介绍了量子机器学习的发展现状。然后介绍了量子计算的概念,包括量子力学基本原理以及量子计算的基本元素,还对量子计算的硬件实现予以简单说明。介绍了量子计算的几个基本算法,其中重点介绍了量子线性判别分析,这一算法为本文的工作提供了重要的基础。本文的主要工作是给出量子典范相关分析的算法,在这一算法中,首先利用一种新的技巧来构造两组多维随机变量的互协方差矩阵。然后使用构造算符链式乘积的方法构造了互协方差矩阵和类内散布矩阵的指数函数乘积,最后使用相位分析方法获得典型变量和典型相关系数。假设两组变量的维度分别是n和m,且假设两组变量之间具有线性相关,则量子典范相关分析算法的时间复杂度为O(log（N（n+m））K_eff^3.5/∈³),其中N是变量对的个数,∈为构造链式乘积期望达到的且由链式乘积矩阵函数形式决定的精度,Keff是在构造链式乘积的过程中预定义的一个统一的针对所有参与链式乘积的矩阵适用的有效条件数且K_eff=O（1/∈）,n和m是两组变量的维度。另外,本文给出了一种针对两组变量的综合的互协方差矩阵对应的幺正演化的实施方法,与trotter公式及在其基础上改进的相似的算法相比,该方法的复杂度有指数式的降低。更多还原

【Abstract】 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.更多还原