Abstract
This thesis proposes a novel framework for finding high-quality solutions to combinatorial optimisation problems, via an alternating series of quantum walks and solution-quality-dependent phase shifts. We demonstrate how problem constraints can be encoded through choice of graph structure, and derive efficient quantum circuits to implement the framework. The scheme is shown to have improved performance for real-world problems such as financial portfolio optimisation. We also apply the framework to the spatial database search problem, demonstrating improved success probability and runtime compared to previous techniques. Finally, we explore the power of nonlinear quantum mechanics applied to solving combinatorial optimisation problems.
Original language | English |
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Qualification | Doctor of Philosophy |
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Award date | 30 Oct 2021 |
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Publication status | Unpublished - 2021 |