Enhancement of radial basis function model via quantum kernel estimation

Abstract

The Radial Basis Function (RBF) model stands as a prominent method within the realm of Machine Learning (ML), showcasing remarkable performance in nonlinear high-dimensional modeling domains. However, the classical RBF model exhibits certain limitations in modeling speed and prediction accuracy when confronted with large-scale complex sample sets. To overcome the limitations mentioned above, we contemplate incorporating the quantum computing technology into the implementation of the classical RBF model to construct a quantum version of the RBF model. Presently, the quantum kernel estimation (QKE) stands as one of the highly regarded methods in the field of quantum computing, attracting significant scrutiny and attention. During the implementation of the QKE, we employ a specifically designed quantum feature map (QFM) circuit containing variational parameters to encode classical input data into quantum states (also known as quantum feature vectors) and generate a trainable quantum kernel. We also employ the quantum gradient descent (QGD) optimization algorithm to train the variational parameters of the quantum kernel, leading to an enhancement in its expressive capacity. Subsequently, we integrate the trained quantum kernel with the classical RBF model, obtaining the quantum version of the RBF model envisioned in this study, referred to as a quantum kernel estimation-based Radial Basis Function (QKE-RBF) model. To substantiate the efficacy of the QKE-RBF model, three numerical experiments are performed in this study. The results of the experiments suggest that our proposed model demonstrates superior prediction accuracy in comparison to the classical RBF model.