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Clustering using matrix product states

文献类型：期刊论文

作者Shi, Xiao2,3; Shang, Yun1,2; Guo, Chu2,4,5,6
刊名PHYSICAL REVIEW A
出版日期2022-05-18
卷号105期号:5页码:8
ISSN号2469-9926
DOI10.1103/PhysRevA.105.052424
英文摘要The matrix product state has been demonstrated to be able to explore the most relevant portion of the exponentially large quantum Hilbert space and find accurate solutions for one-dimensional interacting quantum many-body systems. Inspired by this success, here we propose a clustering algorithm based on the matrix product state, which first maps the classical data into quantum states represented as matrix product states, and then minimizes the loss function using a variational matrix product states algorithm in the enlarged space. We demonstrate this algorithm by applying it to several commonly used machine learning data sets, showing that this algorithm could reach higher learning precision and that it is less likely to be trapped in local minima compared to the standard K-means algorithm. We also show that this algorithm can achieve state-of-the-art learning precision on popular computer vision data sets when used in combination with better initialization schemes.
资助项目National Natural Science Foundation of China[11805279] ; National Natural Science Foundation of China[61833010] ; National Natural Science Foundation of China[12074117] ; National Natural Science Foundation of China[12061131011] ; Program for Creative Research Group of the National Natural Science Foundation of China[61621003]
WOS研究方向Optics ; Physics
语种英语
WOS记录号WOS:000804520400004
出版者AMER PHYSICAL SOC
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/61496]  
专题数学所
通讯作者Shang, Yun
作者单位1.Chinese Acad Sci, Acad Math & Syst Sci, NCMIS, MDIS, Beijing 100190, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China
3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
4.Henan Key Lab Quantum Informat & Cryptog, Zhengzhou 450000, Henan, Peoples R China
5.Hunan Normal Univ, Key Lab Low Dimens Quantum Struct & Quantum Contr, Minist Educ, Dept Phys, Changsha 410081, Peoples R China
6.Hunan Normal Univ, Synerget Innovat Ctr Quantum Effects & Applicat, Changsha 410081, Peoples R China
推荐引用方式
GB/T 7714		 Shi, Xiao,Shang, Yun,Guo, Chu. Clustering using matrix product states[J]. PHYSICAL REVIEW A,2022,105(5):8.
APA Shi, Xiao,Shang, Yun,&Guo, Chu.(2022).Clustering using matrix product states.PHYSICAL REVIEW A,105(5),8.
MLA Shi, Xiao,et al."Clustering using matrix product states".PHYSICAL REVIEW A 105.5(2022):8.

入库方式： OAI收割

来源：数学与系统科学研究院

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