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by Chan Kwan Leung. / Parallel title in Chinese characters. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1992. / Includes bibliographical references (leaves 168-169). / by Chan Kwan Leung. / Acknowledgement --- p.i / Abstract --- p.ii / Chapter 1. --- Introduction / Chapter 1.1 --- Objective of our variational method --- p.2 / Chapter 1.2 --- Outline of the content --- p.5 / Chapter 2. --- Formulation of the new variational method / Chapter 2.1 --- Formulation --- p.14 / Chapter 2.2 --- Motivation --- p.15 / Chapter 3. --- The variational method applied to the anharmonic oscillator problem / Chapter 3.1 --- Formalism --- p.18 / Chapter 3.2 --- Relationship with usual variational method --- p.32 / Chapter 3.3 --- Relationship with W.K.B. approximation --- p.37 / Chapter 3.4 --- Perturbative corrections --- p.45 / Chapter 3.5 --- Diagonalization of non-orthogonal basis --- p.57 / Chapter 3.6 --- Perturbative corrections using the non-orthogonal basis --- p.72 / Chapter 3.7 --- Some previous works on the anharmonic oscillator problem --- p.85 / Chapter 4. --- The variational method applied to the helium-like atomic problem / Chapter 4.1 --- Previous work on the problem --- p.90 / Chapter 4.2 --- Formulation of the variational method on the problem --- p.95 / Chapter 4.3 --- Zeroth order results for atomic helium --- p.103 / Chapter 4.4 --- Diagonalization using the non-orthogonal basis --- p.109 / Chapter 4.5 --- Results for some helium-like ions --- p.136 / Chapter 4.6 --- Possibility of generalization to systems with more electrons --- p.140 / Chapter 5 --- Concluding remarks / Chapter 5.1 --- Range of applicability of our variational method --- p.164 / Chapter 5.2 --- Ground state problem --- p.165 / Chapter 5.3 --- Completeness of our 'basis' --- p.166 / References --- p.168

The exponential nature of Moore's law has inadvertently created huge data storage complexes that are scattered around the world. Data elements are continuously being searched, processed, erased, combined and transferred to other storage units without much regard to power consumption. The need for faster searches and power efficient data processing is becoming a fundamental requirement. Quantum computing may offer an elegant solution to speed and power through the utilization of the natural laws of quantum mechanics. Therefore, minimal cost quantum circuit implementation methodologies are greatly desired. This thesis explores the decomposition of group functions and the Walsh spectrum for implementing quantum canonical cascades with minimal cost. Three different methodologies, using group decomposition, are presented and generalized to take advantage of different quantum computing hardware, such as ion traps and quantum dots. Quantum square root of swap gates and fixed angle rotation gates comprise the first two methodologies. The third and final methodology provides further quantum cost reduction by more efficiently utilizing Hilbert spaces through variable angle rotation gates. The thesis then extends the methodology to realize a robust quantum circuit synthesis tool for single and multi-output quantum logic functions.

Understanding changes in materials properties as a function of size is crucial for both fundamental science development and technological applications. Size restriction results in quantum confinement effects that modify both energy level structures and electron dynamics of solid materials. This study investigates individual quantum states in a single nanocrystal. Single electron charging effects in gold and semiconductor nanocrystals are observed. Charging effects are found to be dominant in samples, where the nanocrystals are weakly coupled to the substrate. For nanocrystals strongly coupled to the substrate, nanocrystal-substrate tunneling rate is larger than tip-nanocrystal tunneling rate. Therefore, the resulting peaks in the dI/dV spectrum are attributed to tunneling through the energy levels of the nanocrystal. A newly developed nanocrystals BEES technique is used successfully to further explore quantized energy levels and electron dynamics in single gold nanocrystals. BEES samples were grown successfully by depositing $unit[10]{nm}$ thick gold on silicon substrates. Nanocrystals are chemically attached to the gold substrate using a self assembled monolayer (SAM) of xyelendithiol molecules. Immobile and single isolated nanocrystals were imaged at low temperature. A BEES turn-on voltage of $unit[0.84]{V}$ was found on nanocrystal-free region of the substrate. The BEES spectrum acquired on a single gold nanocrystal is found to be attenuated by a factor of 10 when compared with BEES acquired on the substrate. The attenuation is attributed to electron relaxation to lower energy states before tunneling out of the nanocrystal. The measured hot electron lifetimes from experimental data were found to be on the order of $unit[16]{picoseconds}$, which is a long time compared to lifetimes in bulk metals or large nanocrystals. The long measured lifetimes result from the molecular-like energy level structures of these small nanocrystals.

Thesis (Ph. D.)--University of Washington, 2003. / Vita. Includes bibliographical references (p. 208-215).

Thesis (M.S.)--Ohio University, August, 1997. / Title from PDF t.p.