Quantum Computation in Ultra-thin Topological Insulator Films

In the past several decades quantum computation has become a rapidly developing research area. The properties particular to quantum systems such as superposition of quantum states, wave function collapse, and quantum entanglement have shone a path to a type of ultra-high-speed and powerful computation that could never be achieved with classical computers, even modern supercomputers. However, there are requirements for building a practical quantum computer and practical schemes of quantum computing usually have to make trade-offs between different requirements. In an ideal case, we would have a quantum computer consisting of many entangled quantum bits (qubits) that have long decoherence times and effective schemes to initialise, control and measure the quantum bits. However, existing implementations of quantum computers have to compromise between different requirements, and we have not yet achieved a quantum computer with full capacity as described in theory. At the same time, the development of solid state physics has brought many new possibilities for quantum computation. The recently discovered topological insulator (TI) has been proposed as a useful material potentially for spintronics and quantum computation owing to its unique topologically-protected surface states. In this thesis, we will investigate theoretically and numerically whether it is possible to construct a suitable two-level quantum system in a TI for quantum computation. We investigate schemes to initialise, control and measure the quantum bits in an ultra-thin TI film. The thesis is structured as follows: Chapter 1 serves as an introduction to quantum computation, in which we introduced the concept of the Bloch sphere and the requirements for quantum computing and give a brief review of actively researched physical implementations. In Chapter 2, we will focus on the material we use for the physical implementation in this thesis - a 3D TI. We will introduce some concepts essential for the understanding of TIs such as the topological phase and then concentrate on the low energy limit which we used throughout the thesis. In the last part we introduce Floquet-Bloch theory, which is useful for the study of a time-periodic Hamiltonian. In Chapter 3, we introduce the numerical methods used in the study: the finite difference method for spatial discretisation, the staggered leapfrog method and Floquet matrix method for temporal discretisation. In Chapter 4, we present our work for constructing a static charge qubit in the TI system, and effective schemes to initialise, control and measure a qubit. In Chapter 5, we present our work for constructing a static spin qubit in the TI system and effective schemes to initialise, control and measure a qubit. In Chapter 6 we extend our TI system to include time-periodic fields and present our work for constructing different types of charge qubit and spin qubit in this system, together with an effective scheme to initialise, control and measure a qubit. In Chapter 7, we summarise our work and propose possible work to be done on this topic in the future.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2019

Author dc:creator

• Zhang, kexin

Advisor dc:contributor.advisor

• Barnes, Crispin

• topological insulator
• quantum computation

Licence

• https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/e2416a6e-f07d-4aeb-8d66-2371467c9392/download
• https://www.rioxx.net/licenses/all-rights-reserved/

Language dc:language

eng

Author Identifier

0000-0001-7337-7245

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/311168