Category Theory, Artificial Intelligence and Interdisciplinary Quantum Structures

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Originally a branch of Pure Mathematics, Category Theory is attracting increasing attention for practical uses. Application areas are broad, including, but not limited to: Programming Language Design, Database Management, Fundamental Physics, Quantum Computing, Artificial Intelligence, Linguistics and intersections thereof. Category Theory is an expressive yet rigorous language, able to describe each of these phenomena in isolation, but also ideal for drawing connections between them by design. This owes to its historical use for relating seemingly disparate branches of Mathematics, which has since evolved into more interdisciplinary uses across fields such as Physics and Computer Science.An area this project potentially impacts is Quantum Computing. Recent research on Category Theory-based diagrammatic languages has been used to drastically reduce the size of Quantum Circuits. Further research in this direction may help produce more efficient Quantum Computers, accelerating the development of Quantum Computation at scale.Another potential impact is on Artificial Intelligence. Currently, mainstream Artificial Intelligence largely consists of 'black box' implementations: decision making procedures are frequently heuristics-based and often lack understanding and interpretability. Suitable for formalising abstract processes, Category Theory may allow for better understood Artificial Intelligence.Furthermore, at the intersection of Artificial Intelligence and Quantum Computing, recent developments have shown that by describing both language and Quantum circuits in terms of Category Theory, some Natural Language Processing tasks easily translate to Quantum circuits. This bodes well for future applications of Quantum Computers to a wider variety of Artificial Intelligence tasks.Aims and objectives include:Explore the applications of diagrammatic languages to Quantum Computation such as Quantum circuit optimization, Quantum software and Quantum algorithms.Devise expressive, yet formal Category-theoretic descriptions of both Classical and Quantum Artificial Intelligence algorithms that make them more amenable to human understanding.Devise Category Theory based methods for utilizing Quantum Computation in Artificial Intelligence applications.Further develop Mathematical formalisms to uncover connections between Mathematics, Computation, Fundamental Physics and Cognition.Ways in which this research is novel:Much of the current work concerning diagrammatic languages for Quantum circuits utilises a specific language called the ZX-Calculus. Despite this, other variations exist, such as 'ZW' and 'ZH'. Different languages may be more suitable for different applications. As such, this project is not limited in scope to ZX, but also seeks to explore novel use and development of other diagrammatic languages.Much Artificial Intelligence research is results-focused but lacks interpretability and understanding of the intelligent systems producing these results. This project takes an alternative approach, prioritizing a deeper understanding of why these systems work, why they perform as well as they do, and to seek a human-interpretable rationale behind the decisions and predictions they make.Quantum Artificial Intelligence is still limited to a narrow range of Machine Learning and Natural Language Processing applications. On the other hand, there is a wealth of sub-fields of Artificial Intelligence that have yet to be explored in the Quantum realm, such as Computer Vision and Reinforcement Learning. This project aims to extend the current scope of Quantum Artificial Intelligence tasks beyond its current limits, uncovering novel use cases.This project is interdisciplinary, addressing aspects of the EPSRC Mathematical Sciences research theme, the Artificial Intelligence Technologies research area, and the Quantum Technologies theme.