Feinstein, Natasha;
(2025)
Targeted catalysts for quantum annealing.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
Quantum annealing is a quantum algorithm for combinatorial optimisation that operates by evolving a system towards a Hamiltonian whose ground state encodes the optimal solution to a problem. The run-time needed to reach a given ground-state fidelity is dictated by the size of the minimum gap that appears between the ground- and first excited-states in the associated energy spectrum. A particular problem for the algorithm is the appearance of so-called perturbative crossings that form as a result of highly competitive local optima and result in gap minima that close exponentially with system size. The associated exponential run-time scaling has consequences for the efficiency of the algorithm and places infeasible demands on qubit coherence times. We explore the use of a targeted XX-catalyst Hamiltonian that aims to circumvent this bottleneck. We use perturbation theory to elucidate the relationship between the structure of the problem Hamiltonian and the effects of different coupling choices. Through this, we motivate particular choices of XX-couplings that could be identified through knowledge of local optima which the algorithm is likely to return. We explore the effectiveness of these catalysts numerically, utilising a problem graph construction that allows us to controllably produce annealing spectra featuring perturbative crossings with varying properties. Overall we find that the catalysts perform well, being able to remove perturbative crossings in a range of instances with the number of couplings present in the catalyst scaling linearly with the system size. In some cases we observe additional catalyst effects which complicate the outcome. In these cases we consider when and how they could be exploited in diabatic quantum annealing. Furthermore, we find that the theoretical framework that we have used to understand the effects of XX-catalysts extends well to other coupling choices, potentially proving a useful tool in the design of catalyst Hamiltonians more generally.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | Targeted catalysts for quantum annealing |
| 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 > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Electronic and Electrical Eng UCL |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10211122 |
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