Quantum machine learning (QML) has proven to be a fruitful area in which to search for 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 QML algorithms in three application areas. We focus our attention towards heuristic algorithms of a variational (meaning hybrid quantum-classical) nature, using parameterised quantum circuits as the underlying quantum machine learning model. The variational nature of these models makes them especially suited for NISQ computers. We order these applications in terms of the increasing complexity of the data presented to them.
Firstly, we study a variational quantum classifier in supervised machine learning, and focus on how (classical) data, feature vectors, may be encoded in such models in a way that is robust to the inherent noise on NISQ computers. We provide a framework for studying the robustness of these classification models, prove theoretical results relative to some common noise channels, and demonstrate extensive numerical results reinforcing these findings.
Secondly, we move to a variational generative model called the Born machine, where the data becomes a (classical or quantum) probability distribution. Now, the problem falls into the category of unsupervised machine learning. Here, we develop new training methods for the Born machine which outperform the previous state of the art, discuss the possibility of quantum advantage in generative modelling, and perform a systematic comparison of the Born machine relative to a classical competitor, the restricted Boltzmann machine. We also demonstrate the largest scale implementation (28 qubits) of such a model on real quantum hardware to date, using the Rigetti superconducting platform.
Finally, for our third QML application, the data becomes purely quantum in nature. We focus on the problem of approximately cloning quantum states, an important primitive in the foundations of quantum mechanics. For this, we develop a variational quantum algorithm which can learn to clone such states, and show how this algorithm can be used to improve quantum cloning fidelities on NISQ hardware. Interestingly, this application can be viewed as either supervised or unsupervised in nature. Furthermore, we demonstrate how this can algorithm can be used to discover novel implementable attacks on quantum cryptographic protocols, focusing on quantum coin flipping and key distribution as examples. 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
