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Quantum kernel estimation-based quantum support vector regression

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Abstract

Quantum machine learning endeavors to exploit quantum mechanical effects like superposition, entanglement, and interference to enhance the capabilities of classical machine learning methods. One of the most researched quantum machine learning methodologies presently is the quantum support vector machine (QSVM). Researchers have now developed quantum support vector classifiers and substantiated their potential for accelerating computation and enhancing classification accuracy in practical contexts through experimentation. Nevertheless, the utility of QSVM in regression tasks remains a relatively uncharted territory. In light of this, we introduce a quantum kernel estimation-based quantum support vector regression (QKE-QSVR) model for completing regression tasks. Within this proposed model, classical inputs are encoded as quantum feature vectors using the designed quantum feature map circuit with a variable parameter. The inner product between quantum feature vectors give rise to a trainable quantum kernel, which is subject to optimization through our proposed quantum kernel alignment-based regression (QKAR) algorithm, thereby bolstering the model's predictive accuracy when applied to a specific dataset. Subsequently, the trained quantum kernel is incorporated into the classical support vector regression process to construct the decision function and provide predictions for new data points. In this study, we validate the efficacy of the proposed model using three illustrative examples. Experimental findings underscore that, in comparison to the classical support vector machine model, our proposed model demonstrates superior predictive accuracy.

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Data availability

The datasets analyzed during the current study can be obtained from the corresponding author upon reasonable request.

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Acknowledgements

The funding provided for this study by the National Natural Science Foundation of China under Grant No.71872088, 71904078 and 71401080, the Social Science Foundation of Jiangsu under Grant No.17GLB016, Postgraduate Research & Practice Innovation Program of Jiangsu Province (Grant number: KYCX22_0881 and KYCX23_0934), the State Scholarship Fund of China under Grant No.201508320059, 1311 Talent Fund of NJUPT, the Science Foundation of Jiangsu under Grant No.BK20190793, the Project of Philosophy and Social Science Research in Colleges and Universities in Jiangsu Province under Grant No. 2018SJA0263 and Social Science Foundation of NJUPT under Grant No.NY218064 are gratefully acknowledged.

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  1. Department of Management, Nanjing University of Posts and Telecommunications, Nanjing, China

    Xiaojian Zhou, Jieyao Yu & Junfan Tan

  2. School of Information Engineering, Nanjing University of Finance and Economics, Nanjing, China

    Ting Jiang

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Zhou, X., Yu, J., Tan, J. et al. Quantum kernel estimation-based quantum support vector regression. Quantum Inf Process 23, 29 (2024). https://doi.org/10.1007/s11128-023-04231-7

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