Thesis
Variational quantum algorithms : a noisy landscape
- Creator
- Rights statement
- Awarding institution
- University of Strathclyde
- Date of award
- 2025
- Thesis identifier
- T17520
- Person Identifier (Local)
- 201978756
- Qualification Level
- Qualification Name
- Department, School or Faculty
- Abstract
- Quantum computing is an alternative paradigm of computation to the classical Boolean logic based systems, leveraging the laws of quantum mechanics. There is ample evidence that a large-scale, error-corrected quantum computer would be able to outperform classical computers for specific problems. However, current technology is not yet capable of realising such systems, meaning that the computers of present day are too small and too prone to errors (also known as quantum noise). Furthermore, the problems for which we have convincing proof of quantum advantage are mostly of academic interest. Thus over the past two decades the scientific community has been actively searching for novel algorithms that can be run on current devices, and that may be of commercial interest. A class of quantum algorithms that has received much attention in recent times is variational quantum algorithms, which are the focus on this Thesis. These algorithms include a feedback loop between a parameterised quantum circuit and a classical optimiser, the latter receiving input in the form of a cost value. The overarching topic of investigation in this Thesis is whether variational quantum algorithms are inherently resilient to noise, a question of paramount importance since these algorithms are intended to be applicable to quantum devices that lack error correction. The problem is approached by examining, analytically and numerically, how noise affects optimisation, with a particular focus on how the cost function (or energy) landscape is modified by various types and rates of errors. On the way to answering this guiding question, new perspectives and theoretical tools are developed. These include a linearised model for the impact of noise on optimisation, symmetries in the cost function landscape that are sensitive to certain types of noise, a generic theory of the exponential accumulation of errors, and a variety of methods based on Fourier analysis to distinguish the disparate effects of hardware noise on the cost function. These tools in turn reveal new phenomena including noise thresholds for optimisation and simulatability, noise-induced barren plateaus, and different impact on optimisation of different error models. The results overall paint a mixed picture. While there appears to be some inherent noise resilience in the optimisation process, and in some cases noise may give rise to larger gradients, under mild assumptions on the noise and the quantum circuit it can be shown that noise frequently acts as an impediment to optimisation. From the energy landscape point of view, noise generically appears to have a smoothing effect leading to vanishing gradients for deep circuits. This phenomenon also manifests as a dampening of high-frequency Fourier modes, making the noisy landscape classical simulatable on average. The evidence suggests that further advances are needed before such algorithms can deliver advantage over classical methods.
- Advisor / supervisor
- Kupke, C. (Clemens)
- Resource Type
- DOI
Relations
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T17520.pdf | 2026-06-05 | Public | Download |