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Quantum Algorithm for K-Nearest Neighbors Classification Based on the Categorical Tensor Network States

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Abstract

The quantum K-nearest neighbor algorithm is superior to the classical K-nearest neighbor algorithm in terms of classification efficiency and accuracy. We utilize a graphical data structure called categorical tensor network states to describe the quantum K-nearest neighbors algorithm. Compared with the quantum K-nearest neighbor algorithm described by quantum circuit, it can make the complex core structures of the algorithm more intuitive, clear and readable while keeping the computation efficient. In addition, compared with the performance of the classical K-nearest neighbor algorithm, it can realize an exponential speed-up in terms of the time logarithmic in both the number of vectors and their dimension.

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Acknowledgements

J. Zhang thanks K. He and R.-F. Ma for valuable discussion. This work was supported by the National Natural Science Foundation of China, (Grant Nos.11771011,11901421) and the Natural Science Foundation of Shanxi Province, China (Grant Nos.201801D221032,201801D221019) and Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (Grant No. 2019L0178) and Youth Foundation of Taiyuan University of technology (No.2017QN13).

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Authors and Affiliations

  1. College of Data Science, Taiyuan University of Technology, 030024, Taiyuan, China

    Yan-zhu Ma, Hong-fei Song & Jun Zhang

  2. College of Mathematics, Institute of Mathematics, Taiyuan University of Technology, 030024, Taiyuan, China

    Jun Zhang

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  1. Yan-zhu Ma
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  2. Hong-fei Song
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  3. Jun Zhang
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Correspondence to Jun Zhang.

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Ma, Yz., Song, Hf. & Zhang, J. Quantum Algorithm for K-Nearest Neighbors Classification Based on the Categorical Tensor Network States. Int J Theor Phys 60, 1164–1174 (2021). https://doi.org/10.1007/s10773-021-04742-y

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