Improving Gaussian process with quantum kernel estimation

Abstract

Gaussian process (GP), as a pivotal offshoot of machine learning (ML), has garnered significant attention in recent years due to its exceptional advantages in tackling high-dimensional and nonlinear regression quandaries. However, when confronted with large-scale datasets, the classical GP model often encounters dual challenges of modeling speed and prediction accuracy. To effectively tackle these challenges, we consider introducing the quantum kernel estimation (QKE) method into the implementation of the classical GP, and we propose a quantum kernel estimation-based Gaussian process (QKE-GP) model. The proposed QKE-GP model employs a quantum feature map (QFM) circuit containing two suitable variational parameters to generate the trainable quantum kernel. Moreover, we utilize the quantum gradient descent (QGD) optimization algorithm to bolster the expressive capacity of the trainable quantum kernel, thus improving the prediction accuracy of model when dealing with large-scale datasets. Following this, we utilize the trained quantum kernel to replace the classical kernel function within the GP model, obtaining the quantum version of the GP model for predicting new data points. To validate the effectiveness of the proposed model, three numerical experiments are carried out in this study. The findings demonstrate that the prediction accuracy of the QKE-GP model outperforms that of the classical GP model in all three scenarios.