Analysis and synthesis of feature map for kernel-based quantum classifier
- PDF / 2,246,714 Bytes
- 9 Pages / 595.224 x 790.955 pts Page_size
- 101 Downloads / 202 Views
RESEARCH ARTICLE
Analysis and synthesis of feature map for kernel-based quantum classifier Yudai Suzuki1 · Hiroshi Yano2 · Qi Gao3,5 · Shumpei Uno3,6 · Tomoki Tanaka3,7 · Manato Akiyama4 · Naoki Yamamoto3,8 Received: 25 October 2019 / Accepted: 21 May 2020 © Springer Nature Switzerland AG 2020
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. Keywords Quantum computing · Support vector machine · Kernel method · Feature map
1 Introduction Over the last 20 years, the unprecedented improvements in the cost-effectiveness ration of computer, together with improved
Y. Suzuki, H. Yano: Equally contributing authors. Yudai Suzuki
[email protected] Naoki Yamamoto [email protected] 1
Department of Mechanical Engineering, Keio University, Hiyoshi 3-14-1, Kohoku, Yokohama 223-8522, Japan
2
Department of Information and Computer Science, Keio University, Hiyoshi 3-14-1, Kohoku, Yokohama 223-8522, Japan
3
Quantum Computing Center, Keio University, Hiyoshi 3-14-1, Kohoku, Yokohama 223-8522, Japan
4
Department of Biosciences and Informatics, Keio University, Hiyoshi 3-14-1, Kohoku, Yokohama 223-8522, Japan
5
Mitsubishi Chemical Corporation Science, Innovation Center, 1000, Kamoshida-cho, Aoba-ku, Yokohama 227-8502, Japan
6
Mizuho Information, Research Institute, Inc., 2-3 Kanda-Nishikicho, Chiyoda-ku, Tokyo 101-8443, Japan
7
Mitsubishi UFJ Financial Group, Inc. and MUFG Bank, Ltd., 2-7-1 Marunouchi, Chiyoda-ku, Tokyo 100-8388, Japan
8
Department of Applied Physics and Physico-Informatics, Keio University, Hiyoshi 3-14-1, Kohoku, Yokohama 223- 8522, Japan
computational techniques, make machine learning widely applicable in every aspect of our lives such as education, healthcare, games, finance, transportation, energy, business, science, and engineering (Hastie et al. 2009; Alpaydin 2016). Among numerous developed machine learning methods, support vector machine (SVM) is a very established one which has become an overwhelmingly popular choice for data analysis (Boser and Guyon 1992). In SVM method, a nonlinear dataset is transformed via a feature map to another dataset and is separated by a hyperplane in the feature space, which can be effectively performed using the kernel trick. In particular, the Gaussian kernel is often used. Quantum computing is expected to speed-up the performance of machine learning through exploiting quantum mechanical properties including superposition, interference, and entanglement. As for the quantum classifier, a renaissance began in the past few years, w
Data Loading...
