Physics
https://researchspace.ukzn.ac.za/handle/10413/6599
2019-08-24T21:02:36ZMagnetic cluster formation in Al₂O₃.
https://researchspace.ukzn.ac.za/handle/10413/16246
Magnetic cluster formation in Al₂O₃.
Abstract available in PDF file.
Master of Science in Chemistry and Physics. University of KwaZulu-Natal, Durban, 2017.
2017-01-01T00:00:00ZSynthesis, structural and magnetic characterization of spinel nanoparticle ferrites with applications for electrochemical sensors.
https://researchspace.ukzn.ac.za/handle/10413/16245
Synthesis, structural and magnetic characterization of spinel nanoparticle ferrites with applications for electrochemical sensors.
Abstract available in PDF file.
Doctor of Philosophy in Physics. University of KwaZulu-Natal, Durban, 2015.
2015-01-01T00:00:00ZQuantum machine learning for supervised pattern recognition.
https://researchspace.ukzn.ac.za/handle/10413/15748
Quantum machine learning for supervised pattern recognition.
Humans are experts at recognising patterns in past experience and applying them to new tasks.
For example, after seeing pictures of a face we can usually tell if another image contains the
same person or not. Machine learning is a research discipline at the intersection of computer
science, statistics and mathematics that investigates how pattern recognition can be performed
by machines and for large amounts of data. Since a few years machine learning has come
into the focus of quantum computing in which information processing based on the laws of
quantum theory is explored. Although large scale quantum computers are still in the first stages
of development, their theoretical description is well-understood and can be used to formulate
`quantum software' or `quantum algorithms' for pattern recognition. Researchers can therefore
analyse the impact quantum computers may have on intelligent data mining. This approach is
part of the emerging research discipline of quantum machine learning that harvests synergies
between quantum computing and machine learning.
The research objective of this thesis is to understand how we can solve a slightly more specific
problem called supervised pattern recognition based on the language that has been developed
for universal quantum computers. The contribution it makes is twofold: First, it presents a
methodology that understands quantum machine learning as the combination of data encoding into
quantum systems and quantum optimisation. Second, it proposes several quantum algorithms for
supervised pattern recognition. These include algorithms for convex and non-convex optimisation,
implementations of distance-based methods through quantum interference, and the preparation of
quantum states from which solutions can be derived via sampling. Amongst the machine learning
methods considered are least-squares linear regression, gradient descent and Newton's method,
k-nearest neighbour, neural networks as well as ensemble methods. Together with the growing
body of literature, this thesis demonstrates that quantum computing offers a number of interesting
tools for machine learning applications, and has the potential to create new models of how to learn
from data.
Doctor of Philosophy in Physics. University of KwaZulu-Natal, Durban 2017.
,
2017-01-01T00:00:00ZQuantum simulation of open quantum systems.
https://researchspace.ukzn.ac.za/handle/10413/15733
Quantum simulation of open quantum systems.
Over the last two decades the field of quantum simulations has experienced incredible
growth, which, coupled with progress in the development of controllable quantum
platforms, has recently begun to allow for the realisation of quantum simulations of a
plethora of quantum phenomena in a variety of controllable quantum platforms. Within
the context of these developments, we investigate within this thesis methods for the
quantum simulation of open quantum systems.
More specically, in the first part of the thesis we consider the simulation of Markovian
open quantum systems, and begin by leveraging previously constructed universal
sets of single-qubit Markovian processes, as well as techniques from Hamiltonian simulation,
for the construction of an efficient algorithm for the digital quantum simulation
of arbitrary single-qubit Markovian open quantum systems. The algorithm we provide,
which requires only a single ancillary qubit, scales slightly superlinearly with respect
to time, which given a recently proven no fast-forwarding theorem for Markovian dynamics,
is therefore close to optimal. Building on these results, we then proceed to
explicitly construct a universal set of Markovian processes for quantum systems of any
dimension. Specifically, we prove that any Markovian open quantum system, described
by a one-parameter semigroup of quantum channels, can be simulated through coherent
operations and sequential simulations of processes from the universal set. Under the assumption
that these universal Markovian processes can be efficiently implemented, this
allows us to propose an efficient algorithm for a wide class of Markovian open quantum
systems, while simultaneously providing a tool for combining and exploiting existing
simulation methods.
In the second part of this thesis we then consider the simulation of many-body non-
Markovian open quantum systems. In particular, we develop an algorithmic procedure
for the quantum simulation of system propagators which are not completely positive
maps, which allows us to provide an explicit algorithm for the digital quantum simulation
of many-body locally-indivisible non-Markovian open quantum systems described by
time-dependent master equations. Finally we construct generalised Suzuki-Lie-Trotter
theorems which allow us to analyse the efficiency of our method, which is expected to
be experimentally achievable for a variety of interesting cases.
Doctor of Philosophy n Physics, University of KwaZulu-Natal, Westville, 2016.
2016-01-01T00:00:00Z