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Analysis and synthesis of feature map for kernel-based quantum classifier

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Abstract

A method for analyzing the feature map for the kernel-based quantum classifier is developed; that is, we give a general formula for computing a lower bound of the exact training accuracy, which helps us to see whether the selected feature map is suitable for linearly separating the dataset. We show a proof of concept demonstration of this method for a class of 2-qubit classifier, with several 2-dimensional datasets. Also, a synthesis method, which combines different kernels to construct a better-performing feature map in a lager feature space, is presented.

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Funding

This work was supported by MEXT Quantum Leap Flagship Program Grant Number JPMXS0118067285 and Cabinet Office PRISM.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Keio University, Hiyoshi 3-14-1, Kohoku, Yokohama, 223-8522, Japan

    Yudai Suzuki

  2. Department of Information and Computer Science, Keio University, Hiyoshi 3-14-1, Kohoku, Yokohama, 223-8522, Japan

    Hiroshi Yano

  3. Quantum Computing Center, Keio University, Hiyoshi 3-14-1, Kohoku, Yokohama, 223-8522, Japan

    Qi Gao, Shumpei Uno, Tomoki Tanaka & Naoki Yamamoto

  4. Department of Biosciences and Informatics, Keio University, Hiyoshi 3-14-1, Kohoku, Yokohama, 223-8522, Japan

    Manato Akiyama

  5. Mitsubishi Chemical Corporation Science, Innovation Center, 1000, Kamoshida-cho, Aoba-ku, Yokohama, 227-8502, Japan

    Qi Gao

  6. Mizuho Information, Research Institute, Inc., 2-3 Kanda-Nishikicho, Chiyoda-ku, Tokyo, 101-8443, Japan

    Shumpei Uno

  7. Mitsubishi UFJ Financial Group, Inc. and MUFG Bank, Ltd., 2-7-1 Marunouchi, Chiyoda-ku, Tokyo, 100-8388, Japan

    Tomoki Tanaka

  8. Department of Applied Physics and Physico-Informatics, Keio University, Hiyoshi 3-14-1, Kohoku, Yokohama, 223- 8522, Japan

    Naoki Yamamoto

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  1. Yudai Suzuki
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  2. Hiroshi Yano
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  3. Qi Gao
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  4. Shumpei Uno
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  5. Tomoki Tanaka
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  6. Manato Akiyama
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  7. Naoki Yamamoto
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Correspondence to Yudai Suzuki.

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Y. Suzuki, H. Yano: Equally contributing authors.

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Suzuki, Y., Yano, H., Gao, Q. et al. Analysis and synthesis of feature map for kernel-based quantum classifier. Quantum Mach. Intell. 2, 9 (2020). https://doi.org/10.1007/s42484-020-00020-y

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  • DOI: https://doi.org/10.1007/s42484-020-00020-y

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