Machine learning applications for noisy intermediate-scale quantum computers

Quantum machine learning has proven to be a fruitful area in which to search for potential applications of quantum computers. This is particularly true for those available in the near term, so called noisy intermediate-scale quantum (NISQ) devices. In this Thesis, we develop and study three quantum machine learning applications suitable for NISQ computers, ordered in terms of increasing complexity of data presented to them. These algorithms are variational in nature and use parameterised quantum circuits (PQCs) as the underlying quantum machine learning model. The first application area is quantum classification using PQCs, where the data is classical feature vectors and their corresponding labels. Here, we study the robustness of certain data encoding strategies in such models against noise present in a quantum computer. The second area is generative modelling using quantum computers, where we use quantum circuit Born machines to learn and sample from complex probability distributions. We discuss and present a framework for quantum advantage for such models, propose gradient-based training methods and demonstrate these both numerically and on the Rigetti quantum computer up to 28 qubits. For our final application, we propose a variational algorithm in the area of approximate quantum cloning, where the data becomes quantum in nature. For the algorithm, we derive differentiable cost functions, prove theoretical guarantees such as faithfulness, and incorporate state of the art methods such as quantum architecture search. Furthermore, we demonstrate how this algorithm is useful in discovering novel implementable attacks on quantum cryptographic protocols, focusing on quantum coin flipping and key distribution as examples.Comment: PhD Thesis. Defended 26th November 2021, University of Edinburg