Quantum-Classical Optimization in Machine Learning

Machine Learning (ML) is a driving force of innovation and a key technology of the future. At the same time, Quantum Computing (QC) is emerging as a technology that holds the potential of asymptotic speedups and efficient computation in exponentially large spaces. It also enables faster optimization, which lies at the core of ML, leading to ongoing efforts of utilizing QC to perform ML. However, QC is still in its infancy, and applications of quantum-based optimization and ML are severly limited by imperfect hardware. This thesis explores strategies of using QC to enhance ML on the one hand, and using classical optimization to enhance QC in its current restricted state on the other. To this end, a feature selection method based on a QUBO embedding is discussed, which is deployed on a quantum annealer. For Support Vector Machines, a classical ML model, two embeddings on quantum computers are shown, using both paradigms of adiabatic QC and gate-based QC. It is shown how evolutionary optimization can be used to jointly learn the structure and parameters of quantum circuits. Further, it is shown that low precision of QUBO weights can lead to loss of performance on quantum annealers, and strategies to mitigate this effect are presented, leading to higher-quality optimization results. Taken together, this thesis broadens the scope of quantum-classical computation by both adding to the toolkit of quantum-enhanced ML methods, and by improving the quality of near-term QC itself. Finally, this thesis demonstrates in a range of practical applications how quantum-classical optimization can be applied in a resource-aware fashion, employing various techniques to utilize near-term QC effectively.