# Construction of Unitary Matrices and Bounding Minimal Quantum Gate Fidelity Using Genetic Algorithms

 Title: Construction of Unitary Matrices and Bounding Minimal Quantum Gate Fidelity Using Genetic Algorithms Gregor, Connor Department of Mathematics and Statistics Mathematics and Statistics Kribs, DavidAshlock, Dan In this thesis a novel representation of a unitary matrix intended to act as a quantum program generated by evolutionary programming shall be presented. The representation consists of a number of $2 \times 2$ matrices being evolved and combined such that a unitary matrix capable of carrying out a predetermined function on a pure quantum state is generated. In this thesis the algorithm will demonstrate proficiency at performing tasks such as cloning a quantum state or creating order amidst a quantum state in superposition. Furthermore, in the field of quantum information, quantum channels are implemented in order to either perform quantum operations to a quantum state or for one to transmit a quantum state from a sender to a recipient. When this happens, the physical implementation of a quantum channel will often differ from the intended quantum channel that was to be implemented. In cases such as these, the quantum gate fidelity is calculated in order to determine how decoherent the resulting state is from what it should have been. In this thesis a procedure that uses a genetic algorithm to place an upper bound on minimal quantum gate fidelity will be presented. http://hdl.handle.net/10214/14743 2018-09 Attribution-NonCommercial 4.0 International All items in the Atrium are protected by copyright with all rights reserved unless otherwise indicated.
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