Comparative investigation of quantum and classical kernel functions applied in support vector machine algorithms

Abstract

Quantum kernels in modern computational paradigms present a revolutionary approach to machine learning by harnessing the power of quantum mechanics to redefine how data is processed and analysed. This study examines the performance and applicability of quantum kernels in machine learning models by investigating their potential among different tasks and datasets against classical kernels. The study utilized the radial basis function (RBF), linear, polynomial, and sigmoid classical kernel functions besides quantum kernel and fidelity state vector quantum kernels. The classical support vector classifier (SVC) and quantum support vector classifier (QSVC) with classical and quantum kernels were employed to perform classification tasks on different datasets, namely Cleveland, Framingham, CHSL, Glass Identification, Obesity, and Academic Success. Additionally, support vector regressor (SVR) and quantum support vector regressor (QSVR), employing classical and quantum kernels, were applied for regression tasks using Concrete, Abalone, Aquatic Toxicity, Auto MPG, and Auction Verification datasets. The results of the study provided insights into the performance of quantum kernels when applied to both classical and quantum SVM models regarding classification and regression tasks. In classification tasks, the quantum kernels provided significant competitiveness in terms of accuracy, precision, recall, and F1 measure scores when compared to the classical kernels. Moreover, the quantum kernels have demonstrated promising outcomes in regression tasks, outperforming the classical kernels by achieving less mean squared error (MSE), mean absolute error (MAE), and superior R-squared scores.