Several fitness functions and entanglement gates in quantum kernel generation

Quantum machine learning (QML) represents a promising frontier in the quantum technologies. In this pursuit of quantum advantage, the quantum kernel method for support vector machine has emerged as a powerful approach. Entanglement, a fundamental concept in quantum mechanics, assumes a central role in quantum computing. In this paper, we investigate the optimal number of entanglement gates in the quantum kernel feature maps by a multi-objective genetic algorithm. We distinct the fitness functions of genetic algorithm for non-local gates for entanglement and local gates to gain insights into the benefits of employing entanglement gates. Our experiments reveal that the optimal configuration of quantum circuits for the quantum kernel method incorporates a proportional number of non-local gates for entanglement. The result complements the prior literature on quantum kernel generation where non-local gates were largely suppressed. Furthermore, we demonstrate that the separability indexes of data can be leveraged to estimate the number of non-local gates required for the quantum support vector machine's feature maps. This insight can be helpful in selecting appropriate parameters, such as the entanglement parameter, in various quantum programming packages like https://qiskit.org/ based on data analysis. Our findings offer valuable guidance for enhancing the efficiency and accuracy of quantum machine learning algorithms.