Quantum computing (QC) has emerged as a disruptive technology, promising exponential speedups for certain computational problems. At the same time, machine learning (ML) continues its transformative journey across scientific domains with its ability to locate patterns within data. The intersection of both disciplines, Quantum Machine Learning (QML), offers efficiency and optimization speedups in certain learning tasks, captivating the interest of both researchers and business leaders. The power of QML lies in its ability to harness quantum properties, such as superposition and entanglement, to solve complex business problems more efficiently than classical algorithms. These quantum properties can be applied to ML in numerous ways, depending on the complexity of the problem.

This thesis delves into Quantum Kernel Support Vector Machines (QKSVMs), a specific QML technique that leverages quantum computing for supervised learning, particularly support vector machines (SVMs). The reason behind focusing on this technique specifically lies in the fact that quantum algorithms can map data points into a higher dimensional feature space. Through this process, quantum kernels aim to locate atypical patterns in data for classification tasks. The discrete logarithm problem (DLP) is a common mathematical problem widely used in cryptography due to its one-way-function nature and resistance to classical algorithms. It has been argued that the case of DLP is a scenario where quantum-inspired algorithms can enhance their classical counterparts in terms of accuracy and other machine learning performance metrics. Utilizing this mathematical problem as the distribution within a dataset could potentially prove quantum advantage, suggesting that using quantum algorithms in certain situations may be beneficial.

This thesis presents empirical evidence of quantum algorithms’ performance enhancements within the DLP framework. This work concludes that in specific scenarios like DLP-distributed datasets, even near-term quantum algorithms operating with fewer qubits can have an advantage over existing algorithms. Furthermore, the findings from this work offer valuable insights to researchers and business leaders interested in investing in the design and implementation of QML models in scenarios beyond DLP, where quantum algorithms have an advantage over classical algorithms.