O'Connor, Daniel T.; (2024) Computational Methods in Quantum Annealing. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

Quantum annealing is a non-universal sub-field of quantum computing used for solving combinatorial optimisation problems found in industries such as telecommunications, supply-chain networks, and finance. However, whether current quantum annealers can provide additional commercial value compared to state-of-the-art classical optimization algorithms is still an open question, given that some of the quantum nature of the computation is lost to noise sources plaguing modern qubits. The work presented addresses a range of problems faced when solving optimisation problems on quantum annealers, with experimental validation of the novel methods proposed where possible. We compare parameter setting methods, demonstrating that the choice of method is crucial to the success of minor-embedding, something which is typically overlooked in the literature when solving large-scale optimisation problems that cannot be directly embedded onto the quantum processing unit (QPU) topology. It is also shown how the mapping that exists between NP problems is useful in reducing qubit overheads in constrained optimisation problems, with the reduction of the graph-colouring problem into several maximal-independent set problems evaluated. Reverse-annealing for optimisation was explored for its potential as a localsearch algorithm that can improve existing suboptimal results. It was found that thermal effects on the QPU contribute to the performance of this algorithm, hinting that non-adiabatic algorithms can be successful in finding solutions on modern quantum annealers. The usefulness of thermally assisted computation is investigated using a Hamiltonian with tuneable hardness called the perturbed ferromagnetic chain, which was also used to demonstrate that the thermalization mechanisms observed on the QPU are distinctly different from classical thermalization mechanisms. Finally, the framework of the locally-suppressed transverse-field diabatic quantum annealing is extended to optimisation problems and compared to traditional adiabatic quantum annealing and classical analogues. The protocol is also adapted into an interferometer and used as a test of coherence for multi-qubit systems.

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