量子典型相关分析算法

doi:10.3969/j.issn.1007-5461.2023.01.014

量子电子学报 ›› 2023, Vol. 40 ›› Issue (1): 120-126.doi: 10.3969/j.issn.1007-5461.2023.01.014

量子典型相关分析算法

王庆乐1,2,3 , 薛雪1 , 李元诚1∗

( 1 华北电力大学控制与计算机工程学院, 北京 102206; 2 北京邮电大学网络与交换技术国家重点实验室, 北京 100876; 3 中国科学技术大学量子信息重点实验室, 安徽合肥 230026 )

收稿日期:2021-04-06 修回日期:2021-05-10 出版日期:2023-01-28 发布日期:2023-01-28
通讯作者: E-mail: ncepua@163.com E-mail:E-mail: ncepua@163.com
作者简介:王庆乐 ( 1987 - ), 女, 山东临沂人, 博士, 副教授, 主要从事量子密码、量子信息论、量子计算方面的研究。 E-mail: wqle519@gmail.com
基金资助:
国家自然科学基金 (61801126), 北京邮电大学网络与交换技术国家重点实验室开放项目 (SKLNST-2021-1-05), 中国科学技术大学中国科学院量子信息重点实验室开放项目 (KQI201902), 信息网络安全公安部重点实验室开放课题 (C21605), 中央高校基本科研业务 (2020MS014)

Quantum canonical correlation analysis algorithm

WANG Qingle 1,2,3 , XUE Xue 1 , LI Yuancheng 1∗

( 1 School of Control and Computer Engineering, North China Electric Power University, Beijing 102206, China; 2 State key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China; 3 CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China )

Received:2021-04-06 Revised:2021-05-10 Published:2023-01-28 Online:2023-01-28

摘要/Abstract

摘要： 典型相关分析是一种重要的数据处理方法, 用于处理随机向量之间的相互依赖关系。然而, 经典的典型相关分析算法的复杂度对数据维度是多项式依赖的, 致使该类算法并不适用于分析在大数据时代下规模呈指数增长的数据。针对经典的典型相关分析算法的这种缺陷, 提出了一种量子典型相关分析算法。该算法把典型相关分析所涉及的优化问题转化为适合用量子计算技术处理的代数问题, 并采用量子主成分分析技术进行求解, 从而降低了典型相关分析算法的复杂度。在特定的参数条件下, 所提算法可实现在数据维度上的指数加速, 符合当今实际数据处理对该算法的需求。

关键词: 量子算法, 量子主成分分析, 相关分析, 指数加速

Abstract: Canonical correlation analysis is an important data processing method for dealing with the interdependence of random vectors. However, the complexity of the classical canonical correlation analysis algorithm is polynomial dependent on the data dimension, making this type of algorithm not suitable for analyzing the data whose scale is growing exponentially in the era of big data. Aiming at the defect of classical canonical correlation analysis algorithm, a quantum canonical correlation analysis algorithm was proposed. The algorithm transformes the optimization problems involved in canonical correlation analysis into algebraic problems suitable for quantum computing technology, and uses quantum principal component analysis technology to solve it, thereby reducing the cost of canonical correlation analysis algorithms. Under certain parameter conditions, the proposed algorithm can achieve exponential acceleration in the data dimension, which meets the requirements of this algorithm for today’s actual data processing.

Key words: quantum algorithm, quantum principal component analysis, correlation analysis; exponential acceleration

中图分类号:

O413

王庆乐, , 薛雪 , 李元诚∗. 量子典型相关分析算法[J]. 量子电子学报, 2023, 40(1): 120-126.

WANG Qingle , , XUE Xue , LI Yuancheng ∗. Quantum canonical correlation analysis algorithm[J]. Chinese Journal of Quantum Electronics, 2023, 40(1): 120-126.

参考文献

[1]SHOR P W.Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer[J].SIAM J Comput, 1997, 26(5):1484-509 [2] GROVER L K.A fast quantum mechanical algorithm for database search [M]. Proceedings of the twenty-eighth annual ACM symposium on Theory of Computing. Philadelphia, Pennsylvania, USA; Association for Computing Machinery. 1996: 212–9. [3]HARROW A W, HASSIDIM A, LLOYD S.Quantum algorithm for linear systems of equations[J].Phys Rev Lett, 2009, 103(15):150502- [4]WOSSNIG L, ZHAO Z, PRAKASH A.Quantum Linear System Algorithm for Dense Matrices[J].Phys Rev Lett, 2018, 120(5):050502- [5] CLADER B D, JACOBS B C, SPROUSE C R.Preconditioned Quantum Linear System Algorithm [J].Physical Review Letters, 2013, 110(25):- [6]REBENTROST P, MOHSENI M, LLOYD S.Quantum support vector machine for big data classification[J].Phys Rev Lett, 2014, 113(13):130503- [7]LIANG J-M, SHEN S-Q, LI M, et al.Variational quantum algorithms for dimensionality reduction and classification[J].Physical Review A, 2020, 101(3):032323- [8]WANG G.Quantum algorithm for linear regression[J].Physical Review A, 2017, 96(1):012335- [9]HOTELLING H.Relations Between Two Sets of Variates[J].Biometrika, 1936, 28(34):321-77 [10]HARDOON D R, SZEDMAK S, SHAWE-TAYLOR J.Canonical Correlation Analysis: An Overview with Application to Learning Methods[J].Neural Computation, 2004, 16(12):2639-64 [11]Sun Quansen, Zeng Shenggen, Wang Pingan, et al.The Theory of Canonical Correlation Analysis and Its Application to Feature Fusion[J].Chinese Journal of Computers, 2005, 28(9):1524-33 [12]孙权森, 曾生根, 王平安, 等.典型相关分析的理论及其在特征融合中的应用[J].计算机学报, 2005, 28(9):1524-33 [13] CONG I, DUAN L.Quantum discriminant analysis for dimensionality reduction and classification [J].New Journal of Physics, 2016, 18(7):- [14]LLOYD S, MOHSENI M, REBENTROST P.Quantum principal component analysis[J].Nature Physics, 2014, 10(9):631-3

量子典型相关分析算法

Quantum canonical correlation analysis algorithm

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