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This thesis investigates several broad areas related to the effective implementation of quantum information processing, from large scale quantum algorithms and error correction, through to system identification and characterization techniques, efficient designs for quantum computing architectures and the design of small devices which utilize quantum effects. The discussion begins with the introduction of a quantum circuit appropriate for implementing Shor’s factoring algorithm on Linear Nearest Neighbor qubit arrays such as the Kane phosphorus in silicon system. Detailed numerical sim- ulations are then presented, demonstrating the sensitivity of the circuit under coherent quantum errors. The concepts of Quantum Error Correction and Fault-tolerant computation are reviewed with original work carried out to show the relative robustness and practicality of Fault-tolerant computation for logical state preparation. Methods of intrinsic system identification and characterization are proposed. Protocols for characterizing both the confinement of a multi-level system to the qubit subspace and the Hamiltonian dynamics governing two-qubit interactions are presented as well as a brief review of characterization techniques already developed for single qubit dynamics. (For complete abstract open document)

Thesis--Leiden. / Curriculum vitae. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1951. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1952. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1954. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Neste trabalho, estudamos alguns aspectos da física de neutrinos, usando os formalismos de vetores de estado e de matriz densidade, com o objetivo de entender a evolução dos neutrinos no universo primordial. No primeiro formalismo, analisamos o fenômeno de oscilação de neutrinos no vácuo, o potencial induzido pela matéria e sua expressão como um índice de refração, e a influência de efeitos de temperatura finita em tal índice. Iniciamos o segundo formalismo com o estudo de sistemas oscilantes de dois níveis sujeitos à colisões com o meio. Deduzimos uma equação de evolução da matriz densidade que descreve um sistema de neutrinos no universo primordial. Para tanto, usamos uma abordagem simplificada e outra baseada em primeiros princípios. / In this work, we studied some aspects of neutrino physics, using the state vector and density matrix formalisms, with the goal of understanding the neutrino evolution in the primordial universe. In the rst approach, we analysed the phenomenum of neutrino oscillation in vacuum, the induced matter potential and its expression as a refraction index, and the influence of finite temperature efects in such index. We began the second formalism with the study of oscillating two levels systems subject to collisions with media. We derived an evolution equation for the density matrix that describes a neutrino system in the primordial universe. To that end, we used one simplified approach and another based on first principles.

No presente trabalho usamos técnicas de física de muitos corpos não relativísticas para generalizar o limite clássico de sistemas quânticos de forma a incorporar misturas estatísticas. Efeitos de temperatura finita são estudados em detalhe no contexto das versões integrável e não integrável do modelo de Lipkin-Meshkov-Glick. Os dois aspectos mais notáveis de nossa análise são: o surgimento de um novo grau de liberdade essencialmente conectado a efeitos térmicos, ocorrendo a temperaturas suficientemente altas e uma caracterização quantitativa do efeito da temperatura no volume caótico do sistema. Mostra-se que os efeitos térmicos sistematicamente compensam a parte de interação da dinâmica. Este é o caso tanto no contexto da termodinâmica quanto da dinâmica a temperatura finita e acreditamos que seja verdadeiro em geral. / In the present work we use techniques of nonrelativistic many body physics to generalize the classic limit of quantum systems in such a way as to incorporate statistical mixtures. Finite temperature effects are studied in detail in the context of the integrable and nonintegrable versions of the Lipkin-Meshkov-Glick Model. The most remarkable features of our analysis is twofold: the appearance of a new degree of freedom essentially connected to thermal effects i.e., for high enough temperatures and a quantitative characterization of the temperature on the chaotic volume of the system. Thermal effects can be shown to consistently counterbalance the interaction part of the dynamics. This is the case both in the context of thermodynamics and of the thermal dynamics of the system and we believe it to be true in general.

<P> Solving the electronic Schrodinger equation for the molecular wavefunction is the central problem in theoretical chemistry. From these wavefunctions (possibly with relativistic corrections), one may completely characterise the chemical reactivity and physical properties of atoms, molecules, and materials. Unfortunately, there are very few systematic approaches for obtaining highly-accurate molecular wavefunctions. The approaches that do exist suffer from the so-called curse of dimensionality: their computational cost grows exponentially as the number of particles increases. Furthermore, even after obtaining an accurate wavefunction, partitioning the molecule into atoms is not straightforward. This is because the kinetic energy operator is a differential operator in spatial coordinates. This is a source of ambiguity in the definition of an atom-in-a-molecule and the associated atomic properties. Even after selecting an appropriate definition of an atom and obtaining the atoms from the wavefunction, the atom's intrinsic reactivity cannot be completely characterised without considering every possible reaction partner. This is because each set of two molecules produces a new wavefunction that is more complicated than the products of the wavefunctions of the separate molecules. </p> <P> This thesis presents methods for addressing the three challenges raised in the previous paragraph: computing atomic properties (e.g. chemical reactivity), partitioning molecules into atoms, and computing accurate molecular wavefunctions. The first challenge is addressed by developing a general-purpose reactivity indicator to quantify the reactivity of an atom within a molecule. This indicator quantifies the reactivity of any point of the molecule using only the electrostatic potential and Fukui potential at that point. The key idea is to include only a vague description of an incoming molecule and compute an approximate interaction with the incoming object; this ensures that the general-purpose reactivity indicator is simple enough to be useful. Practically, this indicator is most useful when it is used to compute the reactivity of the atomic sites in the molecule of interest. </p> <P> Partitioning a molecule into atoms is not straightforward because of the inherent nonlocality of quantum mechanics. In the context of molecular electronic structure, this nonlocality arises from the nature of the kinetic energy operator. The quantum theory of atoms in molecules (QTAIM) is a popular method that partitions molecules into atoms. QT AIM resolves the problem of ambiguity for all permissible forms of the kinetic energy operator. In this thesis the characterisation of an atom provided by QT AIM is extended to include relativistic contributions in the zero-order regular approximation (ZORA). The intrinsic ambiguity arising from the kinetic energy operator is also examined in detail. </p> <P> Computing atomic or molecular properties (including computing the general-purpose reactivity indicator) almost always requires a wavefunction. For this reason, obtaining accurate wavefunctions is the central hurdle of quantum chemistry. This thesis proposes algorithms for finding high-accuracy molecular wavefunctions without exponentially exploding computational cost. To do this, tools for exploiting the smoothness of electronic wavefunctions are crafted. Computational methods that use these tools can break the curse of exponential scaling without sacrificing accuracy. Specifically, the computation cost of these new methods grows only as some polynomial of the electron number. The wavefunctions obtained from these methods are much simpler than those from conventional approaches of similar accuracy, and are therefore ideal for computing the electron density and atomic properties. </p> / Thesis / Doctor of Philosophy (PhD)

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