Weaving, Timothy John; (2025) Contextual Subspace Chemistry: Practical Approaches to Quantum Computing for Electronic Structure. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

Quantum computers are expected to be a transformative technology for many domains of science. They promise to bring the most pressing questions of scientific discovery into focus, where the inherent limitations of conventional computing approaches fall short. One domain that should be an early beneficiary of quantum computation is quantum chemistry, which is concerned with resolving the electronic structure of molecular systems. The wavefunction describing a quantum many-body system lives within an exponentially vast vector space and direct treatment is typically intractable for classical platforms. By contrast, the state of a quantum computer describes a many-body system and is therefore a better representation of the problems we aim to solve. While the theoretical value of quantum computation is clear, there is still a staggering amount of progress to make before we see this novel computing paradigm providing solutions to problems of a sufficient scale to be considered scientifically relevant. Today, quantum hardware is very noisy, and the period of time over which we are able to sustain its fragile quantum state - the coherence time - is remarkably short. To extract useful information from current and near-term devices, the field of quantum error mitigation has seen rapid expansion with the goal of distilling utility from these noisy devices. Furthermore, to alleviate the burden on quantum hardware, hybrid algorithms leveraging the strengths of both quantum and classical resources have been developed which, alongside subspace techniques, extends the reach of current quantum computers. This thesis presents novel work at the intersection of these fields, with the development of improved hybrid algorithms, subspace techniques and error mitigation strategies, complemented by practical implementations that validate the methodology developed herein. We suggest that this approach reveals a path towards quantum advantage as hardware matures in the coming years, providing solutions to vital questions in chemistry.

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