Continuous-time quantum optimisation

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Continuous-time quantum optimisation

Banks, Robert James; (2025) Continuous-time quantum optimisation. Doctoral thesis (Ph.D), UCL (University College London). Green open access

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Abstract

The adiabatic theorem presents a clear bottleneck on adiabatic quantum optimisation. Even given access to a coherent quantum system, the time required to remain adiabatic is typically too long to be reached when solving a large combinatorial optimisation problem. This necessitates operating the device non-adiabatically. Continuous-time quantum walks, multi-stage quantum walks, and reverse-quantum annealing all present attempts to use the same hardware, while dropping the adiabatic requirement. Since these approaches operate far from adiabaticity, the adiabatic theorem cannot be used to motivate their use in tackling combinatorial optimisation problems. Continuous-time quantum walks have been shown to perform well numerically on some optimisation problems. However, the mechanism behind quantum walks for optimisation has not been well understood. By establishing a connection between continuous-time quantum walks and the eigenstate thermalisation hypothesis, this dissertation explores the mechanism behind continuous-time quantum walks as well as how they can be optimised. By appealing to pure-state statistical physics more generally, it is shown how a variety of time-dependent approaches, such as multi-stage quantum walks, can be motivated. This is done by using the physically motivated assumption, termed Planck's Principle, that work cannot be extracted from a cyclic process in an isolated system. This is sometimes referred to as Kelvin's formulation of the second law of thermodynamics. This work also explores a different design mantra, away from adiabatic inspired approaches, based on optimal state transfer. This provides insight on how continuous-time quantum algorithms might be designed away from conventional approaches. It is shown that the optimal state transfer approaches can outperform current conventional quantum approaches.

Type:	Thesis (Doctoral)
Qualification:	Ph.D
Title:	Continuous-time quantum optimisation
Open access status:	An open access version is available from UCL Discovery
Language:	English
Additional information:	Copyright © The Author 2025. Original content in this thesis is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) Licence (https://creativecommons.org/licenses/by-nc/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request.
UCL classification:	UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Physics and Astronomy
URI:	https://discovery.ucl.ac.uk/id/eprint/10204863