Horizons of Artificial Intelligence in Quantum Computation

Abstract

The potential emergence of practical quantum computers has guided research into their potential applications, particularly in the context of artificial intelligence. Motivated by the success of deep neural networks in classical machine learning, a prevailing hope is that such success will translate to so-called quantum variational algorithms or quantum neural networks inspired by their classical counterparts.

Contemporary deep learning algorithms are primarily developed using a series of heuristics, which often lack rigorous proofs to justify their efficacy. Due to the opaque nature of these algorithms, providing definitive assurances regarding their performance remains a formidable challenge. Though this complexity extends to the quantum analogues of deep learning, a growing body of literature has identified a set of theoretical tools to better understand the reasons why classical machine learning models are so effective in real-world tasks. We use these tools to investigate these quantum analogues in an effort to partially address the question of when and under what conditions we can anticipate success.

We primarily study the learnability of quantum machine learning algorithms via tools from statistical learning theory, quantum mechanics, random matrix theory, and group theory. Our findings indicate that careful consideration must be given to the design of quantum machine learning algorithms in order to achieve reasonable levels of success. In fact, some of our results reveal that random or unstructured methods in quantum machine learning are prone to various challenges, including issues related to trainability or the absence of significant advantages over the best classical algorithms. Throughout the thesis, we offer several examples of how to potentially introduce structure into these algorithms to partly remedy these issues.

Furthermore, we explore the reverse question of how quantum computing can inform and enhance classical machine learning. We investigate the incorporation of unitary matrices into classical neural networks, which leads to a more efficient design for these unitary neural networks.