Pellegrino, D.
(2019)
Strong zero Modes in Generalized
Spin chains and Topological
Quantum Computation.
PhD thesis, National University of Ireland Maynooth.
Abstract
Part of the interest in topological phases of matter stems from their potentially revolutionary
technological applications. One of the most exciting possibilities would
be the ability to store and manipulate quantum information in topological degrees
of freedom. This information would be intrinsically protected from some local error
processes and there are now significant efforts being made to harness this property
in scalable quantum devices. In this context, we numerically investigate the dynamical
evolution of a topological memory that consists of two p-wave superconducting
wires separated by a non-topological junction. We consider a closed system and
do not consider general types of errors that may arise from the interaction of the
system with an external environment. We therefore consider the best case scenario
apt to quantum computation and expand upon existing knowledge on the subject.
We find that non-adiabatic effects associated with processing and storing quantum
information, might be relevant as a source of errors in spite of the topological protection
of the quantum qubit. In particular we focus on the primary source of errors
(i.e., qubit-loss) and on secondary errors (bit and phase-
ip) and provide physical
reasoning behind how these types of errors may take place.
Further we consider model for more exotic quantum wires, the so-called ZN
parafermionic clock models that are also expected, in varying degrees, to possess
topological protection. We analyze in detail when this protection might take place
and provide an iterative construction of the associated zero-energy parafermionic
modes. The method, outlined in this thesis, summarizes and generalizes existing
methods for constructing zero modes in spin chains and enlightens common surprising
features of these types of constructions. This opens up the way for future
research on the subject.
Item Type: |
Thesis
(PhD)
|
Keywords: |
Strong zero Modes; Generalized;
Spin chains; Topological
Quantum Computation; |
Academic Unit: |
Faculty of Science and Engineering > Theoretical Physics |
Item ID: |
12563 |
Depositing User: |
IR eTheses
|
Date Deposited: |
09 Mar 2020 17:15 |
URI: |
|
Use Licence: |
This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available
here |
Repository Staff Only(login required)
![View Item View Item](/style/images/action_view.png) |
Item control page |
Downloads per month over past year
Origin of downloads