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Clustering using matrix product states
Shi, Xiao1,2; Shang, Yun1,3; Guo, Chu1,4,5,6
2022-05-18
Source PublicationPHYSICAL REVIEW A
ISSN2469-9926
Volume105Issue:5Pages:8
AbstractThe 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.
DOI10.1103/PhysRevA.105.052424
Indexed BySCI
Language英语
Funding ProjectNational 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 Research AreaOptics ; Physics
WOS SubjectOptics ; Physics, Atomic, Molecular & Chemical
WOS IDWOS:000804520400004
PublisherAMER PHYSICAL SOC
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/61497
Collection数学所
Corresponding AuthorShang, Yun
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, NCMIS, MDIS, Beijing 100190, 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
Recommended Citation
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.
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