Generating quantum feature maps using multi-objective genetic algorithm

We present a novel approach for efficiently generating quantum feature maps for quantum-enhanced support vector machines, a kernel-based classifier, enabling access to high-dimensional Hilbert space. Our method employs a multi-objective genetic algorithm that simultaneously maximizes classification accuracy while minimizing both the local and non-local gate costs of the quantum feature map's circuit. To achieve this, we define distinct fitness functions for local gates and entanglement gates. Comparisons with classical classifiers are given in order to understand the advantages of using quantum machine learning. Surprisingly, 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, contrary to previous literature where non-local gates were largely suppressed. Furthermore, we demonstrate that the separability indexes of data can be effectively leveraged to determine the number of non-local gates required for the quantum support vector machine's feature maps. This insight can significantly aid in selecting appropriate parameters, such as the entanglement parameter, in various quantum programming packages like quiskit.org based on data analysis. Our findings offer valuable guidance for enhancing the efficiency and accuracy of quantum machine learning algorithms.