Global Optimization: Software and Applications
Date
2018-04-17
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
ORCID
0000-0002-3265-977X
Type
Thesis
Degree Level
Masters
Abstract
Mathematical models are a gateway into both theoretical and experimental understand-
ing. However, sometimes these models need certain parameters to be established in order to
obtain the optimal behaviour or value. This is done by using an optimization method that
obtains certain parameters for optimal behaviour, as described by an objective function that
may be a minimum (or maximum) result. Global optimization is a branch of optimization
that takes a model and determines the global minimum for a given domain. Global opti-
mization can become extremely challenging when the domain yields multiple local minima.
Moreover, the complexity of the mathematical model and the consequent lengths of calcu-
lations tend to increase the amount of time required for the solver to find the solution. To
address these challenges, two software packages were developed to aid a solver in optimizing a
black box objective function. The first software package is called Computefarm, a distributed
local-resource computing software package that parallelizes the iteration step of a solver by
distributing objective function evaluations to idle computers. The second software package is
an Optimization Database that is used to monitor the global optimization process by storing
information on the objective function evaluation and any extra information on the objective
function. The Optimization Database is also used to prevent data from being lost during a
failure in the optimization process.
In this thesis, both Computefarm and the Optimization Database are used in the context
of two particular applications. The first application is quantum error correction gate design.
Quantum computers cannot rely on software to correct errors because of the quantum me-
chanical properties that allow non-deterministic behaviour in the quantum bit. This means
the quantum bits can change states between (0, 1) at any point in time. There are various
ways to stabilize the quantum bits; however, errors in the system of quantum bits and the sys-
tem to measure the states can occur. Therefore, error correction gates are designed to correct
for these different types of errors to ensure a high fidelity in the overall circuit. A simulation
of a quantum error correction gate is used to determine the properties of components needed
to correct for errors in the circuit of the qubit system. The gate designs for the three-qubit
and four-qubit systems are obtained by solving a feasibility problem for the intrinsic fidelity
ii(error-correction percentage) to be above the prescribed 99.99% threshold. The Optimization
Database is used with the MATLAB ’s Global Search algorithm to obtain the results for the
three-qubit and four-qubit systems. The approach used in this thesis yields a faster high-
fidelity (≤ 99.99%) three-qubit gate time than obtained previously, and obtained a solution
for a fast high-fidelity four-qubit gate time. The second application is Rational Design of
Materials, in which global optimization is used to find stable crystal structures of chemical
compositions. To predict crystal structures, the enthalpy that determines the stability of
the structure is minimized. The Optimization Database is used to store information on the
obtained structure that is later used for identification of the crystal structure and Compute-
farm is used to speed up the global optimization process. Ten crystal structures for carbon
and five crystal structures for silicon-dioxide are obtained by using Global Convergence Par-
ticle Swarm Optimization. The stable structures, graphite (carbon) and cristobalite (silicon
dioxide), are obtained by using Global Convergence Particle Swarm Optimization. Achieving
these results allows for further research on the stable and meta-stable crystal structures to
understand various properties like hardness and thermal conductivity.
Description
Keywords
Global Optimizaition, quantum error correction, crystal structure perdiction
Citation
Degree
Master of Science (M.Sc.)
Department
Computer Science
Program
Computer Science