Year: 2018
Type: dissertation
Abstract: Mathematical models are a gateway into both theoretical and experimental understand-\ning. However, sometimes these models need certain parameters to be established in order to\nobtain the optimal behaviour or value. This is done by using an optimization method that\nobtains certain parameters for optimal behaviour, as described by an objective function that\nmay be a minimum (or maximum) result. Global optimization is a branch of optimization\nthat takes a model and determines the global minimum for a given domain. Global opti-\nmization can become extremely challenging when the domain yields multiple local minima.\nMoreover, the complexity of the mathematical model and the consequent lengths of calcu-\nlations tend to increase the amount of time required for the solver to find the solution. To\naddress these challenges, two software packages were developed to aid a solver in optimizing a\nblack box objective function. The first software package is called Computefarm, a distributed\nlocal-resource computing software package that parallelizes the iteration step of a solver by\ndistributing objective function evaluations to idle computers. The second software package is\nan Optimization Database that is used to monitor the global optimization process by storing\ninformation on the objective function evaluation and any extra information on the objective\nfunction. The Optimization Database is also used to prevent data from being lost during a\nfailure in the optimization process.\nIn this thesis, both Computefarm and the Optimization Database are used in the context\nof two particular applications. The first application is quantum error correction gate design.\nQuantum computers cannot rely on software to correct errors because of the quantum me-\nchanical properties that allow non-deterministic behaviour in the quantum bit. This means\nthe quantum bits can change states between (0, 1) at any point in time. There are various\nways to stabilize the quantum bits; however, errors in the system of quantum bits and the sys-\ntem to measure the states can occur. Therefore, error correction gates are designed to correct\nfor these different types of errors to ensure a high fidelity in the overall circuit. A simulation\nof a quantum error correction gate is used to determine the properties of components needed\nto correct for errors in the circuit of the qubit system. The gate designs for the three-qubit\nand four-qubit systems are obtained by solving a feasibility problem for the intrinsic fidelity\nii(error-correction percentage) to be above the prescribed 99.99% threshold. The Optimization\nDatabase is used with the MATLAB ’s Global Search algorithm to obtain the results for the\nthree-qubit and four-qubit systems. The approach used in this thesis yields a faster high-\nfidelity (≤ 99.99%) three-qubit gate time than obtained previously, and obtained a solution\nfor a fast high-fidelity four-qubit gate time. The second application is Rational Design of\nMaterials, in which global optimization is used to find stable crystal structures of chemical\ncompositions. To predict crystal structures, the enthalpy that determines the stability of\nthe structure is minimized. The Optimization Database is used to store information on the\nobtained structure that is later used for identification of the crystal structure and Compute-\nfarm is used to speed up the global optimization process. Ten crystal structures for carbon\nand five crystal structures for silicon-dioxide are obtained by using Global Convergence Par-\nticle Swarm Optimization. The stable structures, graphite (carbon) and cristobalite (silicon\ndioxide), are obtained by using Global Convergence Particle Swarm Optimization. Achieving\nthese results allows for further research on the stable and meta-stable crystal structures to\nunderstand various properties like hardness and thermal conductivity.
Author: Marina Schmidt
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2802363943