Year: 2012
Type: dissertation
Abstract: The goal of this thesis is to present evolutionary algorithms, and demonstrate their applicability in quantum computing.As an introduction to evolutionary algorithms, it is applied to the simple but still challenging (from a computational viewpoint) Travelling Salesman Problem (TSP).This example is used to illustrate the effect of various parameters like selection method, and maximum population size on the accuracy and efficiency of the evolutionary algorithms.For the sample problem, the 48 continental state capitals of the USA, solutions are evolved and compared to the known optimal solution.From this investigation tournament selection was shown to be the most effective selection method, and that a population of 200 individuals per generation gave the most effective convergence rates.In the next part of the thesis, evolutionary algorithms are applied to the generation of optimal quantum circuits for the following cases:• The identity transformation : Picked for its simplicity as a test of the correct implementation of the evolutionary algorithm.The results of this investigation showed that the solver program functions correctly and that evolutionary algorithms can indeed find valid solutions for this kind of problem.• The work by Ding et al. [16] on optimal circuits for the two-qubit entanglement gate, controlled-S gate as well as the three qubit entanglement gate are solved by means of EA and the results compared.In all cases similar circuits are produced in fewer generations than the application of Ding et al. [16].The three qubit quantum Fourier transform gate was also attempted, but no convergence was attained.• The quantum teleportation algorithm is also investigated.Firstly the nature of the transformation that leads to quantum teleportation is considered.Next an effective circuit is sought using evolutionary algorithms.The best result is one gate longer than Brassard [11], and seven gates longer than Yabuki [61].iii
Author: Markus Gustav Kruger
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2109325892