Utilizing Non Linear Functions Based Quantum Kernels to Categorize Small Datasets

Quantum computing is the application of Quantum mechanical resources to solve computational problems more precisely, quickly, and effectively than classical computers. Machine learning is all about discovering patterns and relationships in data. Quantum Machine Learning (QML) blends Machine Learning (ML) and Quantum Computing (QC) technologies. QML approaches may be utilized efficiently for data classification problems. Quantum Feature Maps (QFMs) are used for transferring non-linear classical data from lower input space to higher dimensional Hilbert space. Calculating the inner product between data points for classification purposes is exceedingly costly when Hilbert Space is vast. Quantum Kernel Techniques, which are immediate results of QFMs, are used to overcome this problem. In general, we cannot claim that QFMs are superior than Classical Feature Maps (CFMs); yet, there are datasets for which QFMs perform better while CFMs are less effective. It gives us the motivation behind using QFM for classification. In this paper, we proposed two new non-linear encoding functions based quantum kernels for data classification in the range [0, 2π]. The make_moons and make_circles datasets are utilized in this article to perform binary classifications using Qiskit and Sklearn. Construction of quantum kernels is performed, and Support Vector Machines (SVM) are then applied for classification. We have compared the results of our two newly proposed non-linear encoding functions to those mentioned in the literature. Our classifier's performance is approximately comparable or in some cases better to that of existing classifiers in literature.