Quantum Fuzzy Support Vector Machine for Binary Classification  

作　　者：Xi Huang Shibin Zhang Chen Lin Jinyue Xia 

机构地区：[1]School of Cybersecurity,Chengdu University of Information Technology,Chengdu,610225,China [2]Sichuan Key Laboratory of Advanced Cryptography and System Security,Chengdu,610225,China [3]International Business Machines Corporation(IBM),New York,14201,USA

出　　处：《Computer Systems Science & Engineering》2023年第6期2783-2794,共12页计算机系统科学与工程（英文）

基　　金：supported by the National Natural Science Foundation of China(No.62076042);the Key Research and Development Project of Sichuan Province(No.2021YFSY0012,No.2020YFG0307,No.2021YFG0332);the Science and Technology Innovation Project of Sichuan(No.2020017);the Key Research and Development Project of Chengdu(No.2019-YF05-02028-GX);the Innovation Team of Quantum Security Communication of Sichuan Province(No.17TD0009);the Academic and Technical Leaders Training Funding Support Projects of Sichuan Province(No.2016120080102643).

摘　　要：In the objective world,how to deal with the complexity and uncertainty of big data efficiently and accurately has become the premise and key to machine learning.Fuzzy support vector machine(FSVM)not only deals with the classifi-cation problems for training samples with fuzzy information,but also assigns a fuzzy membership degree to each training sample,allowing different training samples to contribute differently in predicting an optimal hyperplane to separate two classes with maximum margin,reducing the effect of outliers and noise,Quantum computing has super parallel computing capabilities and holds the pro-mise of faster algorithmic processing of data.However,FSVM and quantum com-puting are incapable of dealing with the complexity and uncertainty of big data in an efficient and accurate manner.This paper research and propose an efficient and accurate quantum fuzzy support vector machine(QFSVM)algorithm based on the fact that quantum computing can efficiently process large amounts of data and FSVM is easy to deal with the complexity and uncertainty problems.The central idea of the proposed algorithm is to use the quantum algorithm for solving linear systems of equations(HHL algorithm)and the least-squares method to solve the quadratic programming problem in the FSVM.The proposed algorithm can deter-mine whether a sample belongs to the positive or negative class while also achiev-ing a good generalization performance.Furthermore,this paper applies QFSVM to handwritten character recognition and demonstrates that QFSVM can be run on quantum computers,and achieve accurate classification of handwritten characters.When compared to FSVM,QFSVM’s computational complexity decreases expo-nentially with the number of training samples.

关 键 词：Quantum fuzzy support vector machine(QFSVM) fuzzy support vector machine(FSVM) quantum computing 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]