量子核判别分析算法  

Quantum Kernel Discriminant Analysis Algorithm

作　　者：康榕乘 余凯[1,2] 张新 林崧[1] 郭躬德[1] KANG Rongcheng;YU Kai;ZHANG Xin;LIN Song;GUO Gongde(College of Computer and Cyber Security,Fujian Normal University,Fuzhou 350117,China;Digital Fujian Environmental Monitoring Internet of Things Laboratory,Fujian Normal University,Fuzhou 350117,China;College of Mathematics and Statistics,Fujian Normal University,Fuzhou 350117,China)

机构地区：[1]福建师范大学计算机与网络空间安全学院,福建福州350117 [2]福建师范大学数字福建环境监测物联网实验室,福建福州350117 [3]福建师范大学数学与统计学院,福建福州350117

出　　处：《郑州大学学报（理学版）》2025年第1期61-66,共6页Journal of Zhengzhou University:Natural Science Edition

基　　金：国家自然科学基金项目(62171131,61976053,61772134);福建省自然科学基金项目(2022J01186,2023J01533)。

摘　　要：核判别分析法通过核函数扩展了线性判别分析对非线性数据的处理能力,成为模式识别领域中一个重要的分支。然而,随着数据的指数增长,经典核判别分析算法在提取特征时会消耗大量计算资源。针对这一问题,利用量子叠加性和并行性提出了一种量子核判别分析算法。首先,借助量子随机存储器技术与控制旋转操作构造需要的类间矩阵和类内矩阵所对应的密度算子;然后,融入线性方程的求解思路并行获取特征态。理论分析表明,所提算法与经典算法相比具有指数级加速。Kernel discriminant analysis was an important branch in the field of pattern recognition which aimed to expand the ability of linear discriminant analysis to process nonlinear data by kernel function.However,with the exponential growth of data,the classical kernel discriminant analysis algorithm consumed a lot of computing resources in extracting features.To solve this problem,a quantum kernel discriminant analysis algorithm was proposed based on quantum superposition and parallelism.Firstly,the density operators corresponding to the desired between-class scatter matrix and within-class scatter matrix were constructed with quantum random access memory technology and controlled rotation operation.Then,the eigenstates were obtained in parallel by incorporating the solution idea of linear equation.Theoretical analysis showed that the algorithm could achieve exponential acceleration compared with the classical algorithm.

关 键 词：量子机器学习 非线性判别分析 核函数 特征提取 量子厄米特链积 相位估计 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]