Skyrmionic beams and quantum matched filtering

Gao, Sijia (2022) Skyrmionic beams and quantum matched filtering. PhD thesis, University of Glasgow.

Abstract

This thesis is comprised of two parts. In the first part we introduce a new category of structured beams: the paraxial skyrmionic beams. In the second part of this thesis we introduce a quantum algorithm analogous to the classical matched filtering algorithm for gravitational wave data analysis.

Structured light refers to the generation and application of a customised light field, including
intensity, phase and polarisation. In the first part of this thesis, we demonstrate that a specific class of structured beam possesses a topological property that derives both from the spatially varying amplitude of the field and also from its varying polarization. This type of beam is referred to as a skyrmionic beam. We are interested in skyrmionic beams mainly for three reasons: the mathematical appeal of this structure; the physical significance of this structure to link the spatial and polarisation component of structured beams; and the potential application of this property in modelling beam propagation.

There are three important aspects to the skyrmionic nature of paraxial beams: the skyrmion
number, the skyrmion field, and the skyrmion vector potential field. In Chapter. 4 we introduce the construction of the skyrmion beams and their associate skyrmion number with two specific examples. In Chapter. 5 we introduce the skyrmion field along with proving that it is divergenceless. We will then proceed to illustrate this property with two examples. Lastly, in Chapter. 6 we introduce the skyrmion vector potential field. Our discussion throught this chapter will revolve around the analogy between this field and the superfluid velocity and accompanied by two examples.

In Chapter. 7 we explore the relation between the skyrmionic beams and the more familiar
Poincare beams to highlight their differences. During the discussion, we introduce another typeof beam similar to the skyrmionic beam, namely the fractional skyrmionic beam, which lacks the topological robustness of its counterpart

It is also important to explore the experimental realisation of skyrmionic beams. In particular,
collaborating with the Optics group we wish to develop a method to extract the skyrmion number of arbitrary beams through experimental measurements. In Chapter. 8 we propose three candidate methods and discuss their current results and roadblocks, respectively.

The second part of thesis will focus on quantum algorithms. We propose a quantum algorithm
analogous to the classical matched filter algorithm in Chapter. 11. Comparing with its classical counterpart, our algorithm provides a square-root speed-up, which would make possible otherwise intractable searches. We will also demonstrate both a proof-of-principle quantum circuit implementation, and a simulation of the algorithm’s application to the detection of the first gravitational wave signal GW150914 as well as a discussion on the time complexity and space requirements.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Subjects: Q Science > QC Physics
• Colleges/Schools: College of Science and Engineering > School of Physics and Astronomy
• Supervisor's Name: Barnett, Professor Stephen
• Date of Award: 2022
• Depositing User: Theses Team
• Unique ID: glathesis:2022-83183
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 13 Oct 2022 14:36
• Last Modified: 13 Oct 2022 14:36
• Thesis DOI: 10.5525/gla.thesis.83183
• URI: https://theses.gla.ac.uk/id/eprint/83183

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