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Midgley, Stuart. "Quantum waveguide theory." University of Western Australia. School of Physics, 2003. http://theses.library.uwa.edu.au/adt-WU2004.0036.
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The study of nano-electronic devices is fundamental to the advancement of the semiconductor industry. As electronic devices become increasingly smaller, they will eventually move into a regime where the classical nature of the electrons no longer applies. As the quantum nature of the electrons becomes increasingly important, classical or semiclassical theories and methods will no longer serve their purpose. For example, the simplest non-classical effect that will occur is the tunnelling of electrons through the potential barriers that form wires and transistors. This results in an increase in noise and a reduction in the device?s ability to function correctly. Other quantum effects include coulomb blockade, resonant tunnelling, interference and diffraction, coulomb drag, resonant blockade and the list goes on. This thesis develops both a theoretical model and computational method to allow nanoelectronic devices to be studied in detail. Through the use of computer code and an appropriate model description, potential problems and new novel devices may be identified and studied. The model is as accurate to the physical realisation of the devices as possible to allow direct comparison with experimental outcomes. Using simple geometric shapes of varying potential heights, simple devices are readily accessible: quantum wires; quantum transistors; resonant cavities; and coupled quantum wires. Such devices will form the building blocks of future complex devices and thus need to be fully understood. Results obtained studying the connection of a quantum wire with its surroundings demonstrate non-intuitive behaviour and the importance of device geometry to electrical characteristics. The application of magnetic fields to various nano-devices produced a range of interesting phenomenon with promising novel applications. The magnetic field can be used to alter the phase of the electron, modifying the interaction between the electronic potential and the transport electrons. This thesis studies in detail the Aharonov-Bohm oscillation and impurity characterisation in quantum wires. By studying various devices considerable information can be added to the knowledge base of nano-electronic devices and provide a basis to further research. The computational algorithms developed in this thesis are highly accurate, numerically efficient and unconditionally stable, which can also be used to study many other physical phenomena in the quantum world. As an example, the computational algorithms were applied to positron-hydrogen scattering with the results indicating positronium formation.
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Foerster, Alexander [Verfasser]. "Theory of semiconductor quantum-dot microcavity lasers : computational modeling and significance for experimental realization / Alexander Foerster." Magdeburg : Universitätsbibliothek, 2017. http://d-nb.info/1145018106/34.
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Santos, Samantha Fonseca dos. "Theoretical and computational studies of dissociative recombination of H₃⁺ with low kinetic energy electrons time-independent and time-dependent approach /." Orlando, Fla. : University of Central Florida, 2009. http://purl.fcla.edu/fcla/etd/CFE0002668.
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Dinescu, Adriana. "Metals in Chemistry and Biology: Computational Chemistry Studies." Thesis, University of North Texas, 2007. https://digital.library.unt.edu/ark:/67531/metadc3678/.
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Numerous enzymatic reactions are controlled by the chemistry of metallic ions. This dissertation investigates the electronic properties of three transition metal (copper, chromium, and nickel) complexes and describes modeling studies performed on glutathione synthetase. (1) Copper nitrene complexes were computationally characterized, as these complexes have yet to be experimentally isolated. (2) Multireference calculations were carried out on a symmetric C2v chromium dimer derived from the crystal structure of the [(tBu3SiO)Cr(µ-OSitBu3)]2 complex. (3) The T-shaped geometry of a three-coordinate β-diketiminate nickel(I) complex with a CO ligand was compared and contrasted with isoelectronic and isosteric copper(II) complexes. (4) Glutathione synthetase (GS), an enzyme that belongs to the ATP-grasp superfamily, catalyzes the (Mg, ATP)-dependent biosynthesis of glutathione (GSH) from γ-glutamylcysteine and glycine. The free and reactant forms of human GS (wild-type and glycine mutants) were modeled computationally by employing molecular dynamics simulations, as these currently have not been structurally characterized.
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Wang, Jiaqi. "The Impact of Computational Methods on Transition Metal-containing Species." Thesis, University of North Texas, 2015. https://digital.library.unt.edu/ark:/67531/metadc822795/.
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Quantum chemistry methodologies can be used to address a wide variety of chemical problems. Key to the success of quantum chemistry methodologies, however, is the selection of suitable methodologies for specific problems of interest, which often requires significant assessment. To gauge a number of methodologies, the utility of density functionals (BLYP, B97D, TPSS, M06L, PBE0, B3LYP, M06, and TPSSh) in predicting reaction energetics was examined for model studies of C-O bond activation of methoxyethane and methanol. These species provide excellent representative examples of lignin degradation via C-O bond cleavage. PBE0, which performed better than other considered DFT functionals, was used to investigate late 3d (Fe, Co, and Ni), 4d (Ru, Rh, and Pd), and 5d (Re, Os, and Ir) transition metal atom mediated Cβ -O bond activation of the β–O–4 linkage of lignin. Additionally, the impact of the choice of DFT functionals, basis sets, implicit solvation models, and layered quantum chemical methods (i.e., ONIOM, Our Own N-layered Integrated molecular Orbital and molecular Mechanics) was investigated for the prediction of pKa for a set of Ni-group metal hydrides (M = Ni, Pd, and Pt) in acetonitrile. These investigations have provided insight about the utility of a number of theoretical methods in the computation of thermodynamic properties of transition metal hydrides in solution. As single reference wavefunction methods commonly perform poorly in describing molecular systems that involve bond-breaking and forming or electronic near-degeneracies and are typically best described with computationally costly multireference wavefunction-based methods, it is imperative to a priori analyze the multireference character for molecular systems so that the proper methodology choice is applied. In this work, diagnostic criteria for assessing the multireference character of 4d transition metal-containing molecules was investigated. Four diagnostics were considered in this work, including the weight of the leading configuration of the CASSCF wavefunction, C02; T1, the Frobenius norm of the coupled cluster amplitude vector related to single excitations and D1, the matrix norm of the coupled cluster amplitude vector arising from coupled cluster calculations; and the percent total atomization energy, %TAE. This work demonstrated the need to have different diagnostic criteria for 4d molecules than for main group molecules.
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Acheampong, Edward. "Computational Quantum Chemistry Studies of the Interactions of Amino Acids Side Chains with the Guanine Radical Cation." Digital Commons @ East Tennessee State University, 2018. https://dc.etsu.edu/etd/3489.
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Guanine is generally accepted as the most easily oxidized DNA base when cells are subjected to ionizing radiation, photoionization or photosensitization. At pH 7, the midpoint reduction potential is on the order of 0.2 – 0.3 V higher than those of the radicals of e.g. tyrosine, tryptophan cysteine and histidine, so that the radical “repair” (or at least, a thermodynamically favorable reaction) involving these amino acids is feasible. Computational quantum studies have been done on tyrosine, tryptophan, cysteine and histidine side chains as they appear in histones. Density functional theory was employed using B3LYP/6-31G+ (d, p) basis set to study spin densities on these amino acids side chains as they pair with the guanine radical cation. The amino acid side chains are positioned so as not to disrupt the Watson-Crick base pairing. Our results indicate that, these side chains of amino acid with reducing properties can repair guanine radical cation through electron transfer coupled with proton transfer.
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Ringer, Ashley L. "From small to big." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/28089.
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Thesis (M. S.)--Chemistry and Biochemistry, Georgia Institute of Technology, 2009.Committee Chair: Sherrill, C. David; Committee Member: Bredas, Jean-Luc; Committee Member: El-Sayed, Mostafa A.; Committee Member: Harvey, Stephen C; Committee Member: Hernandez, Rigoberto.
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Romero, Rivera Adrian. "Computational studies of enzymatic and biomimetic catalysts." Doctoral thesis, Universitat de Girona, 2018. http://hdl.handle.net/10803/666175.
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Enzymes are the most efficient biocatalysts in Nature. However, biocatalysts in general are not capable of catalyzing reactions for industrial purposes. Hence, biocatalysts need to be engineered by introducing mutations in the active site or at distal positions in the enzyme, thereby inducing changes in the conformational dynamics of enzymes. In this thesis an analysis of conformational dynamics of several enzymes has been developed by using computational tools for understanding how their conformational dynamics affect the enzyme function.
Biomimetic chemistry seeks to design novel efficient metal-based organocatalysts mimicking the structure-function from the enzyme’s active site. In this thesis detailed mechanism pathways for EUK-8 salen ligand have been proposed through computational tools. 57Fe Mössbauer spectroscopy is a technique that provides information about the chemical nature of Iron systems, regardless of its spin and oxidation states. Since the Mössbauer spectra is not always straightforward to analyze, this new computational analysis performed will support experimental Mössbauer data for helping to characterize Fe-based systems.Els enzims són els catalitzadors més eficients que existeixen a la Natura. No obstant, en general no són capaços de catalitzar reaccions importants per a propòsits industrials. Per tant, calen ser modificats introduint mutacions en el centre actiu o en posicions llunyanes, alterant així la seva dinàmica conformacional. En aquesta tesi s'ha realitzat un anàlisi centrat en la dinàmica conformacional de diferents enzims fent servir eines computacionals. La química biomimètica cerca dissenyar nous organocatalitzadors eficients imitant la funció estructural del centre actiu de l’enzim. En aquesta tesi es presenta el mecanisme detallat pel lligand EUK-8 salen per tal de poder-ne millorar la seva activitat catalasa. L’espectroscòpia Mössbauer de 57Fe és una tècnica que proporciona informació sobre la naturalesa química dels sistemes de Ferro, respecte els estat d’espín i d’oxidació. Com que els espectres de Mössbauer no sempre són fàcils d’analitzar, el nou mètode desenvolupat ajudarà a analitzar les dades experimentals de Mössbauer i també a caracteritzar les diferents espècies de Fe.
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Odell, Anders. "Quantum transport and geometric integration for molecular systems." Doctoral thesis, KTH, Tillämpad materialfysik, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-26780.
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Molecular electronics is envisioned as a possible next step in device miniaturization. It is usually taken to mean the design and manufacturing of electronic devices and applications where organic molecules work as the fundamental functioning unit. It involves the measurement and manipulation of electronic response and transport in molecules attached to conducting leads. Organic molecules have the advantages over conventional solid state electronics of inherent small sizes, endless chemical diversity and ambient temperature low cost manufacturing. In this thesis we investigate the switching and conducting properties of photoswitching dithienylethene derivatives. Such molecules change their conformation in solution when acted upon by light. Photochromic molecules are attractive candidates for use in molecular electronics because of the switching between different states with different conducting properties. The possibility of optically controlling the conductance of the molecule attached to conducting leads may lead to new device implementations. The switching reaction is investigated with potential energy calculations for different values of the reaction coordinate between the closed and the open isomer. The electronic and atomic structure calculations are performed with Density Functional Theory (DFT). The potential energy barrier separating the open and closed isomer is investigated, as well as the nature of the excited states involved in the switching. The conducting properties of the molecule inserted between gold, silver and nickel leads is calculated within the Non Equilibrium Green Function theory (NEGF). The molecule is found to be a good conductor in both conformations, with the low-bias current for the closed one being about 20 times larger than that of the open in the case of gold contacts, and over 30 times larger in the case of silver contacts. For the Ni leads the current for the closed isomer is almost 40 times larger than that of the open. Importantly, the current-voltage characteristics away from the linear response is largely determined by molecular orbital re-hybridization in an electric field, in close analogy to what happens for Mn12 molecules. However in the case of dithienylethene attached to Au and Ag such a mechanism is effective also in conditions of strong electronic coupling to the electrodes. In reality these molecules are in constant motion, and the dynamical properties has to be considered. In this thesis such a line of work is initiated. In order to facilitate efficient and stable dynamical simulations of molecular systems the extended Lagrangian formulation of Born-Oppenheimer molecular dynamics have been implemented in two different codes. The extended Lagrangian framework enables the geometric integration of both the nuclear and electronic degrees of freedom. This provides highly efficient simulations that are stable and energy conserving even under incomplete and approximate self-consistent field (SCF) convergence. In the density functional theory code FreeON, different symplectic integrators up to the 6th order have been adapted and optimized. It is shown how the accuracy can be significantly improved compared to a conventional Verlet integration at the same level of computational cost, in particular for the case of very high accuracy requirements. Geometric integration schemes, including a weak dissipation to remove numerical noise, are developed and implemented in the self-consistent tight-binding code LATTE. We find that the inclusion of dissipation in the symplectic integration methods gives an efficient damping of numerical noise or perturbations that otherwise may accumulate from finite arithmetics in a perfect reversible dynamics. The modification of the integration breakes symplecticity and introduces a global energy drift. The systematic driftin energy and the broken symplecticity can be kept arbitrarily small without significant perturbations of the molecular trajectories.QC 20101202
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Tekin, Emine Deniz. "Investigation Of Biologically Important Small Molecules: Quantum Chemical And Molecular Dynamics Calculations." Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612343/index.pdf.
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In this thesis, six small molecules (S-allylcysteine, S-allyl mercaptocysteine, allicin, methyl propyl disulfide, allyl methyl sulfide and dipropylsulfide) that are found in garlic and onion, and are known to be beneficial for human health were studied using molecular mechanics, semi-empirical methods, ab-initio (Restricted Hartree Fock), and density functional theory. Using the same methods, a synthetic pyrethroid pesticide molecule, called cyfluthrin, was also studied. Structural, vibrational and electronic properties of these molecules were found. These theoretical studies could clarify the role of these molecules on human health before they are commercially developed and used. In addition, unfolding dynamics of small peptide sequences (DDATKTFT and its variants) in immunoglobulin G-binding protein G was investigated. Protein folding and unfolding is one of the most important unsolved problems in molecular biology. Because of the large number of atoms involved in protein folding, it is a massive computational problem. The hope is that, one could understand this mechanism with the help of molecular dynamics simulation on small peptides. One of our findings is that the location of the hydrogen bonds is important for the stability of the peptide.
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Parameswaran, Sreeja. "Solar Energy Conversion in Plants and Bacteria Studied Using FTIR Difference Spectroscopy and Quantum Chemical Computational Methodologies." Digital Archive @ GSU, 2009. http://digitalarchive.gsu.edu/phy_astr_diss/32.
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This dissertation presents a study of the molecular mechanism underlying the highly efficient solar energy conversion processes that occur in the Photosystem I (PS I) reaction centers in plants and bacteria. The primary electron donor P700 is at the heart of solar energy conversion process in PS I and the aim is to obtain a better understanding of the electronic and structural organization of P700 in the ground and excited states. Static Fourier Transform Infra-Red (FTIR) difference spectroscopy (DS) in combination with site directed mutagenesis and Density Functional Theory (DFT) based vibrational frequency simulations were used to investigate how protein interactions such as histidine ligation and hydrogen bonding modulate this organization. (P700+-P700) FTIR DS at 77K were obtained from a series of mutants from the cyanobacterium Synechocystis sp. 6803 (S. 6803) where the amino acid residues near the C=O groups of the two chlorophylls of P700 where specifically changed. (P700+-P700) FTIR DS was also obtained for a set of mutants from C. reinhardtii where the axial ligand to A0-, the primary electron acceptor in PS I was modified. The FTIR DS obtained from these mutants provides information on the axial ligands, the hydrogen bonding status as well as the polarity of the environment of specific functional groups that are part of the chlorophyll molecules that constitute P700. Assignment of the FTIR bands to vibrational modes in specific types of environment is very difficult. In order to assist the assignment of the difference bands in experimental spectra DFT based vibrational mode frequency calculations were undertaken for Chl-a and Chl-a+ model molecular systems under different set of conditions; in the gas phase, in solvents using the Polarizable Continuum Model (PCM), in the presence of explicit solvent molecules using QM/MM methods, and in the presence of axial ligands and hydrogen bonds. DFT methods were also used to calculate the charge, spin and redox properties of Chl-a/Chl-a’ dimer models that are representative of P700, the primary electron donor in PS I.
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Grilo, Alex Bredariol 1987. "Computação quântica e teoria de computação." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/275508.
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Orientador: Arnaldo Vieira MouraDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Computação
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Resumo: A Computação Quântica é um tópico relativamente recente e pouco conhecido, principalmente no meio da Computação. Seu estudo surgiu na tentativa de físicos simularem sistemas regidos pela Mecânica Quântica por computadores clássicos, o que se conjecturou inviável. Portanto, um novo modelo computacional que utiliza a estrutura quântica da matéria para computar foi teorizado para suprir estas deficiências. Este trabalho tem como objetivo principal estudar as influências da Computação Quântica na Teoria da Computação. Para atingir tal objetivo, primeiramente são expostos os conhecimentos básicos da Mecânica Quântica através de uma linguagem voltada para Teóricos de Computação sem conhecimento prévio na área, de forma a remover a barreira inicial sobre o tema. Em seguida, serão apresentadas inovações na área da Teoria de Computação oriundas da Computação Quântica. Começaremos com os principais Algoritmos Quânticos desenvolvidos até hoje, que foram os primeiros passos para demonstrar a possível superioridade computacional do novo modelo. Dentre estes algoritmos, apresentaremos o famoso Algoritmo de Shor, que fatora números em tempo polinomial. Adicionalmente, neste trabalho foram estudados tópicos mais avançados e atuais em Computabilidade e Complexidade Quânticas. Sobre Autômatos Quânticos, foram estudados aspectos de um modelo que mistura estados clássicos e quânticos, focando na comparação do poder computacional em relação aos Autômatos Finitos Clássicos. Do ponto de vista de Classes de Complexidade, será abordada a questão se em linguagens da classe QMA, o análogo quântico da classe NP, consegue-se atingir probabilidade de erro nulo na aceitação de instâncias positivas
Abstract: Quantum Computing is a relatively new area and it is not well known, mainly among Computer Scientists. It has emerged while physicists tried to simulate Quantum Systems with classical computers efficiently, which has been conjectured impossible. Then, a new computational model that uses the quantum structure of matter to perform computations has been theorized in order to perform these operations. We intend in this work to study the influences of Quantum Computing in Theoretical Computer Science. In order to achieve this goal, we start by presenting the basics of Quantum Computing to Theoretical Computer Science readers with no previous knowledge in this area, removing any initial barriers for a clean understanding of the topic. We will then follow by showing innovations in Theoretical Computer Science introduced by Quantum Computation. We start by showing the main Quantum Algorithms, that exemplify advantages of the new computational model. Among these algorithms, we will present the Shor Algorithm that factors numbers in polynomial time. We follow with more advanced topics in Quantum Computability and Complexity. We study Quantum Finite Automata Models that work with quantum and classical states, focusing on comparing their computational power with Deterministic Finite Automata. In Complexity Theory, we study the question if for languages in QMA, the quantum analogue of NP, zero probability error can be achieved in yes-instances
Mestrado
Ciência da Computação
Mestre em Ciência da Computação
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Prascher, Brian P. "Systematic Approaches to Predictive Computational Chemistry using the Correlation Consistent Basis Sets." Thesis, University of North Texas, 2009. https://digital.library.unt.edu/ark:/67531/metadc9920/.
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The development of the correlation consistent basis sets, cc-pVnZ (where n = D, T, Q, etc.) have allowed for the systematic elucidation of the intrinsic accuracy of ab initio quantum chemical methods. In density functional theory (DFT), where the cc-pVnZ basis sets are not necessarily optimal in their current form, the elucidation of the intrinsic accuracy of DFT methods cannot always be accomplished. This dissertation outlines investigations into the basis set requirements for DFT and how the intrinsic accuracy of DFT methods may be determined with a prescription involving recontraction of the cc-pVnZ basis sets for specific density functionals. Next, the development and benchmarks of a set of cc-pVnZ basis sets designed for the s-block atoms lithium, beryllium, sodium, and magnesium are presented. Computed atomic and molecular properties agree well with reliable experimental data, demonstrating the accuracy of these new s-block basis sets. In addition to the development of cc-pVnZ basis sets, the development of a new, efficient formulism of the correlation consistent Composite Approach (ccCA) using the resolution of the identity (RI) approximation is employed. The new formulism, denoted 'RI-ccCA,' has marked efficiency in terms of computational time and storage, compared with the ccCA formulism, without the introduction of significant error. Finally, this dissertation reports three separate investigations of the properties of FOOF-like, germanium arsenide, and silicon hydride/halide molecules using high accuracy ab initio methods and the cc-pVnZ basis sets.
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Vranckx, Stéphane. "Dynamical study of diatomics : applications to astrochemistry, quantum control and quantum computing." Doctoral thesis, Universite Libre de Bruxelles, 2014. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209261.
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In this work, we theoretically study the properties of diatomic molecular systems, their dynamics, and the control thereof through the use of laser fields. We more specifically study three compounds:1) HeH+, a species of great astrochemical importance which is thought to be the first molecular species to have formed in the universe;
2) CO2+, a metastable dication of particular interest in quantum control experiments due to its long-lived lowest vibrational level;
3) 41K87Rb, a polar molecule that can be formed at very low temperature and trapped, making it a good candidate for quantum computing schemes.
First, we use ab initio methods to compute accurate potential energy curves for the lowest singlet and triplet states of HeH+ as well as the potential energy curves, transition dipole moments and nonadiabatic radial couplings of the ground 3Π state of CO2+ and of its 11 lowest 3Σ- states.
In a second step, we use this ab initio data to compute the photodissociation and radiative association cross sections for the a and b 3Σ+ states of HeH+, as well as the values of the corresponding rate constants for astrophysical environments. The photodissociation cross sections from the lowest vibrational level of CO2+ is also determined.
Going one step further, we optimize laser control fields that drive the photodissociation dynamics of HeH+ and CO2+ towards specific channels. We compare two field optimization methods: a Møller operator-based Local Control approach and Optimal Control Theory. In both cases, we add a constraint that minimizes the area of the optimized fields.
Finally, we focus on one of the potential applications of high-fidelity laser control: the use of small molecular systems as quantum computers. We more specifically study the potential implementation of both intra- and intermolecular logic gates on data encoded in hyperfine states of trapped ultracold polar 41K87Rb molecules, opening interesting perspectives in terms of extensibility.
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Dans cette thèse, nous étudions théoriquement les propriétés de molécules diatomiques, leur dynamique de réaction ainsi que le contrôle de cette dynamique à l'aide de champs laser. Notre travail porte plus spécifiquement sur trois espèces :
1) HeH+, un composé-clé en astrochimie considéré comme la première espèce moléculaire qui s'est formée dans l'univers ;
2) CO2+, un dication métastable qui se prête bien à des expériences de contrôle quantique en raison du relativement long temps de vie de son état vibrationnel le plus bas ;
3) 41K87Rb, une molécule polaire qui présente la particularité de pouvoir être formée à très basse température et piégée, ce qui en fait un bon support physique potentiel pour la réalisation d'un ordinateur quantique moléculaire.
Nous utilisons tout d'abord des méthodes de calcul ab initio afin d'obtenir les courbes d'énergie potentielle des premiers états singulets et triplets de HeH+ avec un haut de degré de précision, ainsi que les courbes d'énergie potentielle, les moments dipolaires de transition et les couplages non-adiabatiques radiaux de l'état fondamental 3Π de CO2+ et de ses 11 premiers états 3Σ-.
Ensuite, nous utilisons ces données ab initio pour calculer les sections efficaces de photodissociation et d'association radiative des états a et b 3Σ+ de HeH+, ainsi que les constantes cinétiques associées à ces processus dans les conditions rencontrées dans des environnements astrophysiques. Les sections efficaces de photodissociation du niveau vibrationnel le plus bas de CO2+ sont également calculées.
Nous allons ensuite un cran plus loin en optimisant des champs laser qui guident la dynamique de photodissociation de HeH+ et CO2+ vers des canaux de dissociation spécifiques. Nous comparons deux méthodes d'optimisation de ces champs: une approche de contrôle local basée sur les opérateurs de Møller et la théorie du contrôle optimal. Dans le deux cas, nous incluons une contrainte qui minimise l'aire des champs.
Enfin, nous nous concentrons sur l'une des applications possibles du contrôle laser à haute fidélité :l'utilisation de petits systèmes moléculaires comme ordinateurs quantiques. Nous étudions plus spécifiquement l'implémentation possible d'opérations logiques intra- et intermoléculaires sur des données encodées dans des états hyperfins de molécules de 41K87Rb piégées, ce qui ouvre des perspectives intéressantes en terme d'extensibilité.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished
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Wright, Christopher James. "Theoretical studies of underscreened Kondo physics in quantum dots." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:62207edb-af3a-4340-a6f2-5264b1374a41.
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We study correlated two-level quantum impurity models coupled to a metallic conduction band in the hope of gaining insight into the physics of nanoscale quantum dot systems. We focus on the possibility of formation of a spin-1 impurity local moment which, on coupling to the band, generates an underscreened (USC) singular Fermi liquid state. By employing physical arguments and the numerical renormalization group (NRG) technique, we analyse such systems in detail examining in particular both the thermodynamic and dynamic properties, including the differential conductance. The quantum phase transitions occurring between the USC phase and a more ordinary Fermi liquid (FL) phase are analysed in detail. They are generically found to be of Kosterlitz-Thouless type; exceptions occur along lines of high symmetry where first-order transitions are found. A `Friedel-Luttinger sum rule' is derived and, together with a generalization of Luttinger's theorem to the USC phase, is used to obtain general results for the $T=0$ zero-bias conductance --- it is expressed solely in terms of the number of electrons present on the impurity and applicable in both the USC and FL phases. Relatedly, dynamical signatures of the quantum phase transition show two broad classes of behaviour corresponding to the collapse of either a resonance or antiresonance in the single-particle density of states. Evidence of both of these behaviours is seen in experimental devices. We study also the effect of a local magnetic field on both single- and two-level quantum impurities. In the former case we attempt to resolve some points of contention that remain in the literature. Specifically we show that the position of the maximum in the spin resolved density of states (and related peaks in the differential conductance) is not linear in the applied field, showing a more complicated form than a simple `Zeeman splitting'. The analytic result for the low-field asymptote is recovered. For two-level impurities we illustrate the manner in which the USC state is destroyed: due to two cancelling effects an abrupt change in the zero-bias conductance does not occur as one might expect. Comparison with experiment is made in both cases and used to interpret experimental findings in a manner contrary to previous suggestions. We find that experiments are very rarely in the limit of strong impurity-host coupling. Further, features in the differential conductance as a function of bias voltage should not be simply interpreted in terms of isolated quantum dot states. The many-body nature of such systems is crucially important to their observed properties.
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Kartsaklis, Dimitrios. "Compositional distributional semantics with compact closed categories and Frobenius algebras." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:1f6647ef-4606-4b85-8f3b-c501818780f2.
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The provision of compositionality in distributional models of meaning, where a word is represented as a vector of co-occurrence counts with every other word in the vocabulary, offers a solution to the fact that no text corpus, regardless of its size, is capable of providing reliable co-occurrence statistics for anything but very short text constituents. The purpose of a compositional distributional model is to provide a function that composes the vectors for the words within a sentence, in order to create a vectorial representation that re ects its meaning. Using the abstract mathematical framework of category theory, Coecke, Sadrzadeh and Clark showed that this function can directly depend on the grammatical structure of the sentence, providing an elegant mathematical counterpart of the formal semantics view. The framework is general and compositional but stays abstract to a large extent. This thesis contributes to ongoing research related to the above categorical model in three ways: Firstly, I propose a concrete instantiation of the abstract framework based on Frobenius algebras (joint work with Sadrzadeh). The theory improves shortcomings of previous proposals, extends the coverage of the language, and is supported by experimental work that improves existing results. The proposed framework describes a new class of compositional models thatfind intuitive interpretations for a number of linguistic phenomena. Secondly, I propose and evaluate in practice a new compositional methodology which explicitly deals with the different levels of lexical ambiguity (joint work with Pulman). A concrete algorithm is presented, based on the separation of vector disambiguation from composition in an explicit prior step. Extensive experimental work shows that the proposed methodology indeed results in more accurate composite representations for the framework of Coecke et al. in particular and every other class of compositional models in general. As a last contribution, I formalize the explicit treatment of lexical ambiguity in the context of the categorical framework by resorting to categorical quantum mechanics (joint work with Coecke). In the proposed extension, the concept of a distributional vector is replaced with that of a density matrix, which compactly represents a probability distribution over the potential different meanings of the specific word. Composition takes the form of quantum measurements, leading to interesting analogies between quantum physics and linguistics.
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Gustafsson, Alexander. "Theoretical modeling of scanning tunneling microscopy." Doctoral thesis, Linnéuniversitetet, Institutionen för fysik och elektroteknik (IFE), 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-69012.
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The main body of this thesis describes how to calculate scanning tunneling microscopy (STM) images from first-principles methods. The theory is based on localized orbital density functional theory (DFT), whose limitations for large-vacuum STM models are resolved by propagating localized-basis wave functions close to the surface into the vacuum region in real space. A finite difference approximation is used to define the vacuum Hamiltonian, from which accurate vacuum wave functions are calculated using equations based on standard single-particle Green’s function techniques, and ultimately used to compute the conductance. By averaging over the lateral reciprocal space, the theory is compared to a series of high-quality experiments in the low- bias limit, concerning copper surfaces with adsorbed carbon monoxide (CO) species and adsorbate atoms, scanned by pure and CO-functionalized copper tips. The theory compares well to the experiments, and allows for further insights into the elastic tunneling regime. A second significant project in this thesis concerns first-principles calculations of a simple chemical reaction of a hydroxyl (oxygen-deuterium) monomer adsorbed on a copper surface. The reaction mechanism is provided by tunneling electrons that, via a finite electron-vibration coupling, trigger the deuterium atom to flip between two nearly identical configurational states along a frustrated rotational motion. The theory suggests that the reaction primarily occurs via nuclear tunneling for the deuterium atom through the estimated reaction barrier, and that over-barrier ladder climbing processes are unlikely.
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Pontes, Renato Borges. "Investigação em eletrônica molecular: um estudo via cálculos de primeiros princípios." Universidade de São Paulo, 2007. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-05052009-185629/.
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O iminente fim da \"era do Silício\" tem motivado a busca de novas tecnologias para utilização na indústria eletrônica. Dentre estas tecnologias, a eletrônica molecular explora o uso moléculas como elementos funcionais em dispositivos eletrônicos. Nesta Tese, realizamos cálculos de primeiros princípios baseados na teoria do funcional da densidade (DFT) para determinar as propriedades eletrônicas, estruturais e de transporte em sistemas com aplicação em eletrônica molecular. Para o benzeno-1,4-ditiol (BDT), considerado um sistema protótipo dentro da eletrônica molecular, correlacionamos a adsorção, em uma superfície de Au, com as propriedades de transporte. Na sequência, analisamos evolução estrutural e o efeito de átomos de Au adsorvidos na superfície de Au na transmitância do BDT entre eletrodos de Au. A importância da correção de auto-interação (SIC), nos cálculos de transporte da junção molecular (Au/BDT/Au), também foi discutida. Em seguida, determinamos as propriedades eletrônicas e estruturais da molécula y[(tpy SH)2]x, onde y representa os metais de transição Co, Fe e Ni e; x está associado aos estados de carga 0, +, 2+ e 3+. Verificamos que os metais de transição ficam em uma configuração de baixo spin e, dependendo do estado de carga do metal de transição uma distorção Jahn-Teller leva a uma redução na simetria local de D2d para C2v. Por fim, devido à possibilidade de aplicação em spintrônica, discutimos o efeito de uma impureza de Cobalto na evolução estrutural e transmitância de um nanofio de Au.The possible end of the road for Silicon has motivated academic researchers and research laboratories to search for new technologies to be applied in the electronic industry. The molecular electronics, which studies the possibility of using molecules as active elements in a new generation of electronic devices, is among these new technologies. In this Thesis, we performed first principles calculations within the density functional theory (DFT) framework to determine the structural, electronic and transport properties of systems with strong application on molecular electronics. We analised the benzene-1,4-dithiol (BDT). For this prototypical system we coupled its adsorption on an Au(111) surface with its transport properties. After this, we investigated its structural evolution between gold leads and the effects of adsorded gold atoms on the Au(111) surface in the trasmitance. The effect of the self-interaction correction (SIC) in the transport calculations of the molecular junction (Au/BDT/Au) was discussed as well. Moreover, we determined the electronic and the structural properties of the molecule y[(tpySH)2]x, where y stands for the transition metals Co, Fe and Ni and; x is associated with the charge states 0, +, 2+ e 3+. We verified that the transition metals are more stable at the low spin configuration. Depending on the charge state a Jahn-Teller distortion leads to a local symmetry reduction: D2d to C2v. Finally, with a spintronic application in mind, we analised the effect of a Cobalt impurity on the structural evolution and transmitance of a gold nanowire.
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Rönnby, Karl. "Quantum Chemical Feasibility Study of Methylamines as Nitrogen Precursors in Chemical Vapor Deposition." Thesis, Linköpings universitet, Kemi, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-132812.
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The possibility of using methylamines instead of ammonia as a nitrogen precursor for the CVD of nitrides is studied using quantum chemical computations of reaction energies: reaction electronic energy (Δ𝑟𝐸𝑒𝑙𝑒𝑐) reaction enthalpy (Δ𝑟𝐻) and reaction free energy (Δ𝑟𝐺). The reaction energies were calculated for three types of reactions: Uni- and bimolecular decomposition to more reactive nitrogen species, adduct forming with trimethylgallium (TMG) and trimethylaluminum (TMA) followed by a release of methane or ethane and surface adsorption to gallium nitride for both the unreacted ammonia or methylamines or the decomposition products. The calculations for the reaction entropy and free energy were made at both STP and CVD conditions (300°C-1300°C and 50 mbar). The ab inito Gaussian 4 (G4) theory were used for the calculations of the decomposition and adduct reactions while the surface adsorptions were calculated using the Density Functional Theory method B3LYP. From the reactions energies it can be concluded that the decomposition was facilitated by the increasing number of methyl groups on the nitrogen. The adducts with mono- and dimethylamine were more favorable than ammonia and trimethylamine. 𝑁𝐻2 was found to be most readily to adsorb to 𝐺𝑎𝑁 while the undecomposed ammonia and methylamines was not willingly to adsorb.
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Crawford, Luke. "Mechanistic insights into enzymatic and homogeneous transition metal catalysis from quantum-chemical calculations." Thesis, University of St Andrews, 2015. http://hdl.handle.net/10023/7818.
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Catalysis is a key area of chemistry. Through catalysis it is possible to achieve better synthetic routes, exploit molecules normally considered to be inactive and also attain novel chemical transformations. The development of new catalysts is crucial to furthering chemistry as a field. Computational chemistry, arising from applying the equations of quantum and classical mechanics to solving chemical problems, offers an essential route to investigating the underlying atomistic detail of catalysis. In this thesis calculations have been applied towards studying a number of different catalytic processes. The processing of renewable chemical sources via homogeneous reactions, specifically cardanol from cashew nuts, is discussed. All routes examined for monoreduction of a diene model by [Ru(H)(iPrOH)(Cl)(C₆H₆)] and [Ru(H)(iPrOH)(C₆H₆)]⁺ are energetically costly and would allow for total reduction of the diene if they were operating. While this accounts for the need of high temperatures, further work is required to elucidate the true mechanism of this small but surprisingly complex system. Gold-mediated protodecarboxylation was examined in tandem with experiment to find the subtle steric and electronic effects that dictate CO₂ extrusion from gold N-heterocyclic carbene activated benzene-derived carboxylic acids. The origin of a switch in the rate limiting step from decarboxylation to protodeauration with less activated substrates was also clearly demonstrated. Studies of gold systems are closed with examinations of 1,2-difluorobenzene C–H activation and CO₂ insertion by [Au(IPr)(OH)]. Calculations highlight that the proposed mechanism for oxazole-derived substrates cannot be extended to 1,2-difluorobenzene and instead a digold complex offers more congruent predicted kinetics. The lens of quantum chemistry was turned upon palladium-mediated methoxycarbonylation reactions. An extensive study was undertaken to attempt to understand the bidentate diphosphine ligand dependency on forming either methylpropanoate (MePro) or copolymers. Mechanisms currently suggested in literature are shown to be incongruous with the formation of MePro by Pd(OAc)₂ and bulky diphosphines. A possible alternative route is proposed in this thesis. Four mechanisms for methoxycarbonylation with Pd(2-PyPPh₂)ₙ are detailed. The most accessible route is found to be congruent with experimental reports of selectivity, acid dependency and slight steric modifications. A modification of 2-PyPPh₂ to 2-(4-NMe₂-6-Me)PyPPh₂ is shown to improve both selectivity and turnover, the latter by four orders of magnitude (highest transition state from 22.9 kcal/mol to 16.7 kcal/mol ∆G), and this new second generation in silico designed ligand is studied for its applicability to wider substrate scope and different solvents. The final chapter of this thesis is a mixed quantum mechanics and molecular mechanics (QM/MM) examination of an enzymatic reaction, discussing the need for certain conditions and the role of particular amino acid residues in an S[sub]N2 hydrolysis reaction.
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Al-Shimary, Abbas. "Applications of graph theory to quantum computation." Thesis, University of Leeds, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.608359.
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Systems with topologically ordered ground states are considered to be promising candidates for quantum memories. These systems are characterised by a degenerate ground eigenspace separated by an energy gap from the rest of the spectrum. Consequently, topologically ordered systems are resilient to local noise since local errors are suppressed by the gap. Often, knowledge of the gap is not available and a direct approach to the problem is impractical. The first half of this thesis considers the problem of estimating the energy gap of a general class of Hamiltonians in the thermodynamical limit. In particular, we consider a remarkable result from spectral graph theory known as Cheeger inequalities. Cheeger inequalities give an upper and lower bound on the spectral gap of discrete Laplaeians defined on a graph in terms of the geometric characteristics of the graph. We generalise this approach and we employ it to determine if a given discrete Hamiltonian is gapped or not in the thermodynamic limit. A large class of 2D topologically ordered systems, including the Kitaev toric code, were proven to be unstable against thermal fluctuations. There systems can store information for a finite time known as the memory lifetime. The second half of this thesis will be devoted to investigating possible theoretical ways to extend the lifetime of thc 2D toric code. Firstly, we investigate the effect lattice geometry has on the lifetime of the qubit toric code. Importantly, we demonstrate how lattice geometries can be employed to enhance topological systems with intrinsically biased couplings due to physical implementation. Secondly, we improve the error correction properties and lifetime of the generalised 2D toric code by using charge-modifying domain walls. Specifically, we show that we can inhibit the propagation of anyons by introducing domain walls, provided the masses of the anyon types of the model are imbalanced.
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Timpson, Christopher Gordon. "Quantum information theory and the foundations of quantum mechanics." Thesis, University of Oxford, 2004. http://ora.ox.ac.uk/objects/uuid:457a0257-016d-445d-a6b2-f1bdd2648523.
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This thesis is a contribution to the debate on the implications of quantum information theory for the foundational problems of quantum mechanics. In Part I an attempt is made to shed some light on the nature of information and quantum information theory. It is emphasized that the everyday notion of information is to be firmly distinguished from the technical notions arising in information theory; however it is maintained that in both settings ‘information’ functions as an abstract noun, hence does not refer to a particular or substance. The popular claim ‘Information is Physical’ is assessed and it is argued that this proposition faces a destructive dilemma. Accordingly, the slogan may not be understood as an ontological claim, but at best, as a methodological one. A novel argument is provided against Dretske’s (1981) attempt to base a semantic notion of information on ideas from information theory. The function of various measures of information content for quantum systems is explored and the applicability of the Shannon information in the quantum context maintained against the challenge of Brukner and Zeilinger (2001). The phenomenon of quantum teleportation is then explored as a case study serving to emphasize the value of recognising the logical status of ‘information’ as an abstract noun: it is argued that the conceptual puzzles often associated with this phenomenon result from the familiar error of hypostatizing an abstract noun. The approach of Deutsch and Hayden (2000) to the questions of locality and information flow in entangled quantum systems is assessed. It is suggested that the approach suffers from an equivocation between a conservative and an ontological reading; and the differing implications of each is examined. Some results are presented on the characterization of entanglement in the Deutsch-Hayden formalism. Part I closes with a discussion of some philosophical aspects of quantum computation. In particular, it is argued against Deutsch that the Church-Turing hypothesis is not underwritten by a physical principle, the Turing Principle. Some general morals are drawn concerning the nature of quantum information theory. In Part II, attention turns to the question of the implications of quantum information theory for our understanding of the meaning of the quantum formalism. Following some preliminary remarks, two particular information-theoretic approaches to the foundations of quantum mechanics are assessed in detail. It is argued that Zeilinger’s (1999) Foundational Principle is unsuccessful as a foundational principle for quantum mechanics. The information-theoretic characterization theorem of Clifton, Bub and Halvorson (2003) is assessed more favourably, but the generality of the approach is questioned and it is argued that the implications of the theorem for the traditional foundational problems in quantum mechanics remains obscure.
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Tempel, David Gabriel. "Time-Dependent Density Functional Theory for Open Quantum Systems and Quantum Computation." Thesis, Harvard University, 2012. http://dissertations.umi.com/gsas.harvard:10208.
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First-principles electronic structure theory explains properties of atoms, molecules and solids from underlying physical principles without input from empirical parameters. Time-dependent density functional theory (TDDFT) has emerged as arguably the most widely used first-principles method for describing the time-dependent quantum mechanics of many-electron systems. In this thesis, we will show how the fundamental principles of TDDFT can be extended and applied in two novel directions: The theory of open quantum systems (OQS) and quantum computation (QC). In the first part of this thesis, we prove theorems that establish the foundations of TDDFT for open quantum systems (OQS-TDDFT). OQS-TDDFT allows for a first principles description of non-equilibrium systems, in which the electronic degrees of freedom undergo relaxation and decoherence due to coupling with a thermal environment, such as a vibrational or photon bath. We then discuss properties of functionals in OQS-TDDFT and investigate how these differ from functionals in conventional TDDFT using an exactly solvable model system. Next, we formulate OQS-TDDFT in the linear-response regime, which gives access to environmentally broadened excitation spectra. Lastly, we present a hybrid approach in which TDDFT can be used to construct master equations from first-principles for describing energy transfer in condensed phase systems. In the second part of this thesis, we prove that the theorems of TDDFT can be extended to a class of qubit Hamiltonians that are universal for quantum computation. TDDFT applied to universal Hamiltonians implies that single-qubit expectation values can be used as the basic variables in quantum computation and information theory, rather than wavefunctions. This offers the possibility of simplifying computations by using the principles of TDDFT similar to how it is applied in electronic structure theory. Lastly, we discuss a related result; the computational complexity of TDDFT.Physics
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Babbush, Ryan Joseph. "Towards Viable Quantum Computation for Chemistry." Thesis, Harvard University, 2015. http://nrs.harvard.edu/urn-3:HUL.InstRepos:17467325.
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Since its introduction one decade ago, the quantum algorithm for chemistry has been among the most anticipated applications of quantum computers. However, as the age of industrial quantum technology dawns, so has the realization that even “polynomial” resource overheads are often prohibitive. There remains a large gap between the capabilities of existing hardware and the resources required to quantum compute classically intractable problems in chemistry. The primary contribution of this dissertation is to take meaningful steps towards reducing the costs of three approaches to quantum computing chemistry. First, we discuss how chemistry problems can be embedded in Hamiltonians suitable for commercially manufactured quantum annealing machines. We introduce schemes for more efficiently compiling problems to annealing Hamiltonians and apply the techniques to problems in protein folding, gene expression, and cheminformatics. Second, we introduce the first adiabatic quantum algorithm for fermionic simulation. Towards this end, we develop tools which embed arbitrary universal Hamiltonians in constrained hardware at a reduced cost. Finally, we turn our attention to the digital quantum algorithm for chemistry. By exploiting the locality of physical interactions, we quadratically reduce the number of terms which must be simulated. By analyzing the scaling of time discretization errors in terms of chemical properties, we obtain significantly tighter bounds on the minimum number of time steps which must be simulated. Also included in this dissertation is a protocol for preparing configuration interaction states that is asymptotically superior to all prior results and the details of the most accurate experimental quantum simulation of chemistry ever performed.Chemical Physics
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Roland, Jérémie. "Adiabatic quantum computation." Doctoral thesis, Universite Libre de Bruxelles, 2004. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/211148.
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Le développement de la Théorie du Calcul Quantique provient de l'idée qu'un ordinateur est avant tout un système physique, de sorte que ce sont les lois de la Nature elles-mêmes qui constituent une limite ultime sur ce qui peut être calculé ou non. L'intérêt pour cette discipline fut stimulé par la découverte par Peter Shor d'un algorithme quantique rapide pour factoriser un nombre, alors qu'actuellement un tel algorithme n'est pas connu en Théorie du Calcul Classique. Un autre résultat important fut la construction par Lov Grover d'un algorithme capable de retrouver un élément dans une base de donnée non-structurée avec un gain de complexité quadratique par rapport à tout algorithme classique. Alors que ces algorithmes quantiques sont exprimés dans le modèle ``standard' du Calcul Quantique, où le registre évolue de manière discrète dans le temps sous l'application successive de portes quantiques, un nouveau type d'algorithme a été récemment introduit, où le registre évolue continûment dans le temps sous l'action d'un Hamiltonien. Ainsi, l'idée à la base du Calcul Quantique Adiabatique, proposée par Edward Farhi et ses collaborateurs, est d'utiliser un outil traditionnel de la Mécanique Quantique, à savoir le Théorème Adiabatique, pour concevoir des algorithmes quantiques où le registre évolue sous l'influence d'un Hamiltonien variant très lentement, assurant une évolution adiabatique du système. Dans cette thèse, nous montrons tout d'abord comment reproduire le gain quadratique de l'algorithme de Grover au moyen d'un algorithme quantique adiabatique. Ensuite, nous montrons qu'il est possible de traduire ce nouvel algorithme adiabatique, ainsi qu'un autre algorithme de recherche à évolution Hamiltonienne, dans le formalisme des circuits quantiques, de sorte que l'on obtient ainsi trois algorithmes quantiques de recherche très proches dans leur principe. Par la suite, nous utilisons ces résultats pour construire un algorithme adiabatique pour résoudre des problèmes avec structure, utilisant une technique, dite de ``nesting', développée auparavant dans le cadre d'algorithmes quantiques de type circuit. Enfin, nous analysons la résistance au bruit de ces algorithmes adiabatiques, en introduisant un modèle de bruit utilisant la théorie des matrices aléatoires et en étudiant son effet par la théorie des perturbations.Doctorat en sciences appliquées
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Welch, Jonathan M. "On the Synthesis of Quantum Circuits for Diagonal Operators in Quantum Computation." Thesis, Harvard University, 2015. http://nrs.harvard.edu/urn-3:HUL.InstRepos:23845468.
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Diagonal unitary operators are commonly found in many quantum algorithms. They find application as analytical potential operators for quantum simulation, as well as for complex oracles used in quantum searches. However, in order to implement a quantum algorithm on a given quantum device, each operator must be decomposed into a sequence of fault-tolerant, device-level instructions. In general, to implement an $n$-qubit diagonal unitary {\em exactly} on a quantum computer generally requires $2^{n+1}-3$ one- and two-qubit gates. However, for most practical implementations of diagonal unitaries, some degree of approximation will be necessary if the circuit is to be efficient. In this thesis we develop two complementary methods for the approximate synthesis of quantum circuits for diagonal unitaries. We show how to apply these techniques to real-space quantum simulation and show how efficient high fidelity quantum simulations can be implemented with low-depth quantum circuits.Engineering and Applied Sciences - Applied Physics
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Gheorghiu, Alexandru. "Robust verification of quantum computation." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/31542.
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Quantum computers promise to offer a considerable speed-up in solving certain problems, compared to the best classical algorithms. In many instances, the gap between quantum and classical running times is conjectured to be exponential. While this is great news for those applications where quantum computers would provide such an advantage, it also raises a significant challenge: how can classical computers verify the correctness of quantum computations? In attempting to answer this question, a number of protocols have been developed in which a classical client (referred to as verifier) can interact with one or more quantum servers (referred to as provers) in order to certify the correctness of a quantum computation performed by the server(s). These protocols are of one of two types: either there are multiple non-communicating provers, sharing entanglement, and the verifier is completely classical; or, there is a single prover and the classical verifier has a device for preparing or measuring quantum states. The latter type of protocols are, arguably, more relevant to near term quantum computers, since having multiple quantum computers that share a large amount of entanglement is, from a technological standpoint, extremely challenging. Before the realisation of practical single-prover protocols, a number of challenges need to be addressed: how robust are these protocols to noise on the verifier's device? Can the protocols be made fault-tolerant without significantly increasing the requirements of the verifier? How do we know that the verifier's device is operating correctly? Could this device be eliminated completely, thus having a protocol with a fully classical verifier and a single quantum prover? Our work attempts to provide answers to these questions. First, we consider a single-prover verification protocol developed by Fitzsimons and Kashefi and show that this protocol is indeed robust with respect to deviations on the quantum state prepared by the verifier. We show that this is true even if those deviations are the result of a correlation with the prover's system. We then use this result to give a verification protocol which is device- independent. The protocol consists of a verifier with a measurement device and a single prover. Device-independence means that the verifier need not trust the measurement device (nor the prover) which can be assumed to be fully malicious (though not communicating with the prover). A key element in realising this protocol is a robust technique of Reichardt, Unger and Vazirani for testing, using non-local correlations, that two untrusted devices share a large number of entangled states. This technique is referred to as rigidity of non-local correlations. Our second result is to prove a rigidity result for a type of quantum correlations known as steering correlations. To do this, we first show that steering correlations can be used in order to certify maximally entangled states, in a setting in which each test is independent of the previous one. We also show that the fidelity with which we characterise the state, in this specific test, is optimal. We then improve the previous result by removing the independence assumption. This then leads to our desired rigidity result. We make use of it, in a similar fashion to the device-independent case, in order to give a verification protocol that is one-sided device-independent. The importance of this application is to show how different trust assumptions affect the efficiency of the protocol. Next, we describe a protocol for fault-tolerantly verifying quantum computations, with minimal "quantum requirements" for the verifier. Specifically, the verifier only requires a device for measuring single-qubit states. Both this device, and the prover's operations are assumed to be prone to errors. We show that under standard assumptions about the error model, it is possible to achieve verification of quantum computation using fault-tolerant principles. As a proof of principle, and to better illustrate the inner workings of the protocol, we describe a toy implementation of the protocol in a quantum simulator, and present the results we obtained, when running it for a small computation. Finally, we explore the possibility of having a verification protocol, with a classical verifier and a single prover, such that the prover is blind with respect to the verifier's computation. We give evidence that this is not possible. In fact, our result is only concerned with blind quantum computation with a classical client, and uses complexity theoretic results to argue why it is improbable for such a protocol to exist. We then use these complexity theoretic techniques to show that a client, with the ability to prepare and send quantum states to a quantum server, would not be able to delegate arbitrary NP problems to that server. In other words, even a client with quantum capabilities cannot exploit those capabilities to delegate the computation of NP problems, while keeping the input, to that computation, private. This is again true, provided certain complexity theoretic conjectures are true.
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Henriksson, Johan. "Molecular Quadratic Response Properties with Inclusion of Relativity." Doctoral thesis, Linköping : Department of Physics, Chemistry and Biology, Linköping University, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-11035.
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Marsden, Daniel. "Logical aspects of quantum computation." Thesis, University of Oxford, 2015. http://ora.ox.ac.uk/objects/uuid:e99331a3-9d93-4381-8075-ad843fb9b77c.
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A fundamental component of theoretical computer science is the application of logic. Logic provides the formalisms by which we can model and reason about computational questions, and novel computational features provide new directions for the development of logic. From this perspective, the unusual features of quantum computation present both challenges and opportunities for computer science. Our existing logical techniques must be extended and adapted to appropriately model quantum phenomena, stimulating many new theoretical developments. At the same time, tools developed with quantum applications in mind often prove effective in other areas of logic and computer science. In this thesis we explore logical aspects of this fruitful source of ideas, with category theory as our unifying framework. Inspired by the success of diagrammatic techniques in quantum foundations, we begin by demonstrating the effectiveness of string diagrams for practical calculations in category theory. We proceed by example, developing graphical formulations of the definitions and proofs of many topics in elementary category theory, such as adjunctions, monads, distributive laws, representable functors and limits and colimits. We contend that these tools are particularly suitable for calculations in the field of coalgebra, and continue to demonstrate the use of string diagrams in the remainder of the thesis. Our coalgebraic studies commence in chapter 3, in which we present an elementary formulation of a representation result for the unitary transformations, following work developed in a fibrational setting in [Abramsky, 2010]. That paper raises the question of what a suitable "fibred coalgebraic logic" would be. This question is the starting point for our work in chapter 5, in which we introduce a parameterized, duality based frame- work for coalgebraic logic. We show sufficient conditions under which dual adjunctions and equivalences can be lifted to fibrations of (co)algebras. We also prove that the semantics of these logics satisfy certain "institution conditions" providing harmony between syntactic and semantic transformations. We conclude by studying the impact of parameterization on another logical aspect of coalgebras, in which certain fibrations of predicates can be seen as generalized invariants. Our focus is on the lifting of coalgebra structure along a fibration from the base category to an associated total category of predicates. We show that given a suitable parameterized generalization of the usual liftings of signature functors, this induces a "fibration of fibrations" capturing the relationship between the two different axes of variation.
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Lee, Ciaran M. "Bounds on computation from physical principles." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:39451e29-3719-4cf4-a030-57c07e603380.
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The advent of quantum computing has challenged classical conceptions of which problems are efficiently solvable in our physical world. This raises the general question of what broad relationships exist between physical principles and computation. The current thesis explores this question within the operationally-defined framework of generalised probabilistic theories. In particular, we investigate the limits on computational power imposed by simple physical principles. At present, the best known upper bound on the power of quantum computers is that BQP is contained in AWPP, where AWPP is a classical complexity class contained in PP. We define a circuit-based model of computation in the above mentioned operational framework and show that in theories where local measurements suffice for tomography, efficient computations are also contained in AWPP. Moreover, we explicitly construct a theory in which the class of efficiently solvable problems exactly equals AWPP, showing this containment to be tight. We also investigate how simple physical principles bound the power of computational paradigms which combine computation and communication in a non-trivial fashion, such as interactive proof systems. Additionally, we show how some of the essential components of computational algorithms arise from certain natural physical principles. We use these results to investigate the relationship between interference behaviour and computational power, demonstrating that non-trivial interference behaviour is a general resource for post-classical computation. We then investigate whether post-quantum interference is a resource for post-quantum computation. Sorkin has defined a hierarchy of possible post-quantum interference behaviours where, informally, the order in the hierarchy corresponds to the number of paths that have an irreducible interaction in a multi-slit experiment. In quantum theory, at most pairs of paths can ever interact in a fundamental way. We consider how Grover's speed-up depends on the order of interference in a theory, and show that, surprisingly, the quadratic lower bound holds regardless of the order of interference.
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Pégny, Maël. "Sur les limites empiriques du calcul : calculabilité, complexité et physique." Thesis, Paris 1, 2013. http://www.theses.fr/2013PA010673/document.
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Durant ces dernières décennies, la communauté informatique a montré un intérêt grandissant pour les modèles de calcul non-standard, inspirés par des phénomènes physiques, biologiques ou chimiques. Les propriétés exactes de ces modèles ont parfois été l'objet de controverses: que calculent-ils? Et à quelle vitesse? Les enjeux de ces questions sont renforcés par la possibilité que certains de ces modèles pourraient transgresser les limites acceptées du calcul, en violant soit la thèse de Church-Turing soit la thèse de Church-Turing étendue. La possibilité de réaliser physiquement ces modèles a notamment été au coeur des débats. Ainsi, des considérations empiriques semblent introduites dans les fondements même de la calculabilité et de la complexité computationnelle, deux théories qui auraient été précédemment considérées comme des parties purement a priori de la logique et de l'informatique. Par conséquent, ce travail est consacré à la question suivante : les limites du calcul reposent-elles sur des fondements empiriques? Et si oui, quels sont-ils? Pour ce faire, nous examinons tout d'abord la signification précise des limites du calcul, et articulons une conception épistémique du calcul, permettant la comparaison des modèles les plus variés. Nous répondrons à la première question par l'affirmative, grâce à un examen détaillé des débats entourant la faisabilité des modèles non-standard. Enfin, nous montrerons les incertitudes entourant la deuxième question dans l'état actuel de la recherche, en montrant les difficultés de la traduction des concepts computationnels en limites physiquesRecent years have seen a surge in the interest for non-standard computational models, inspired by physical, biological or chemical phenomena. The exact properties of some of these models have been a topic of somewhat heated discussion: what do they compute? And how fast do they compute? The stakes of these questions were heightened by the claim that these models would violate the accepted limits of computation, by violating the Church-Turing Thesis or the Extended Church-Turing Thesis. To answer these questions, the physical realizability of some of those models - or lack thereof - has often been put at the center of the argument. It thus seems that empirical considerations have been introduced into the very foundations of computability and computational complexity theory, both subjects that would have been previously considered purely a priori parts of logic and computer science. Consequently, this dissertation is dedicated to the following question: do computability and computational complexity theory rest on empirical foundations? If yes, what are these foundations? We will first examine the precise meaning of those limits of computation, and articulate a philosophical conception of computation able to make sense of this variety of models. We then answer the first question by the affirmative, through a careful examination of current debates around non-standard models. We show the various difficulties surrounding the second question, and study how they stem from the complex translation of computational concepts into physical limitations
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Martos, Prieto Ruben. "The Baum-Connes conjecture for Quantum Groups : stability properties and K-theory computations." Thesis, Sorbonne Paris Cité, 2018. http://www.theses.fr/2018USPCC198/document.
Full textAbstract:
Cette thèse porte sur la conjecture de Baum-Connes pour les groupes quantiques. Le but principal de ce travail est l'étude de la stabilité de la conjecture de Baum-Connes par certaines constructions de groupes quantiques discrets.Dans un premier temps, nous réalisons une étude détaillé et approfondie de la reformulation catégorielle de la conjecture de Baum-Connes d'après les travaux de R. Meyer et R. Nest. Ensuite, nous appliquons ces techniques au cas concret des groupes quantiques discrets sans torsion.Nous réalisons une étude exhaustive des produits croisés afin de pouvoir les manipuler aisément en connexion avec la conjecture de Baum-Connes. Notamment nous donnons une preuve de la propriété universelle d'un produit croisé réduit par un groupe quantique discret. Nous analysons également quelques propriétés d'importance pour le contexte de cette thèse. Mentionnons particulièrement la propriété d'associativité du produit croisé par rapport à un produit semi-direct.En s'inspirant des travaux pionniers de J. Chabert nous menons une généralisation pour les groupes quantiques discrets de la stabilité de la conjecture de Baum-Connes par rapport à un produit semi-direct. Deux propriétés d'invariance d'intérêt indépendant sont également étudiées, à savoir le phénomène de torsion et la K-moyennabilité. Nous observons que l'hypothèse sans torsion force un biproduit crosié compact à être un produit semi-direct quantique sans torsion. Ainsi, la conjecture de Baum-Connes correspondante ne fournit pas d'information remarquable dans ce cas. La stratégie générale pour mener à bien une telle généralisation consiste à définir un foncteur de “décomposition” entre les catégories de Kasparov suivant l'opération de produit semi-direct. Nous observons que cette stratégie peut être extrapolée à d'autres constructions de groupes quantiques. Notamment un produit direct de groupe quantiques. Dans ce cas, nous établissons une connexion avec la formule de Künneth de manière analogue à ce qui a été démontré par J. Chabert, S. Echterhoff et H. Oyono-Oyono pour les groupes localement compacts classiques. Les propriétés de torsion et de K-moyennabilité ont également été étudiées.Nous savons, grâce à R. Vergnioux and C. Voigt, que la conjecture de Baum-Connes forte est préservée par le passage aux sous-groupes quantiques discrets divisibles. Le même résultat est vrai pour la propriété de torsion forte, grâce à Y. Arano et K. De Commer. Dans ce travail nous montrons qu'aussi bien la conjecture de Baum-Connes usuelle que la propriété de torsion usuelle sont préservées par le passage aux sous-groupes quantiques discrets divisibles. La propriété de K-moyennabilité a également été étudiée.Une notable propriété de permanence inclue dans cette thèse est la stabilité de la conjecture de Baum-Connes forte par produit en couronne libre. Pour cela, nous réalisons une complète classification des actions de torsion pour un produit libre quantique, ce qui permet de donner une formulation adéquate de la conjecture de Baum-Connes forte pour un produit en couronne libre inspirés par le travail pionnier de C. Voigt. Une application majeure est un calcul explicite de K-théorie, dans trois situations pertinentes, pour le groupe quantique compact de Lemeux-Tarrago qui est monoïdallement équivalent à un produit en couronne libre. Cette propriété de stabilité pour un produit en couronne libre ainsi que les calculs de K-théorie s'intègrent dans un travail en collaboration avec A. Freslon. Pour conclure, nous nous questionnons sur les résultats obtenus afin de proposer une liste de questions, problems et objectifs que l'auteur a rencontré durant l'intégralité de la période de recherche de cette thèse et qui rassemblent quelques unes des lignes de travail pour ses projets futures de rechercheThe present dissertation is focused on the Baum-Connes conjecture for quantum groups. The main purpose of this work is the study of the Baum-Connes conjecture stability under some constructions of discrete quantum groups. In a first phase, we carry out a detailed and extensive study about the categorical reformulation of the Baum-Connes conjecture according to the results of R. Meyer and R. Nest. Next, we apply these techniques to the specific case of torsion-free discrete quantum groups. We carry out an exhaustive study of crossed products in order to handle them comfortably in connexion with the Baum-Connes conjecture. Notably, we give a proof of the universal property satisfied by a reduced crossed product by a discrete quantum group. We analyze as well some important properties for this dissertation. Let us mention in particular the associativity property of the crossed product with respect to a semi-direct product. Being inspired by the pionneer work of J. Chabert, we perform a generalization for discrete quantum groups of the invariance property of the Baum-Connes conjecture under the semi-direct product construction. Two permanence properties of own interest are studied as well. Namely, the torsion-freeness and the K-amenability. We observe that the torsion-freeness assumption forces a compact bicrossed product to be a torsion-free quantum semi-direct product, so that the corresponding Baum-Connes conjecture does not give any relevant information in this case. The general strategy used to accomplish such a generalization consists in defining a “decomposition” functor between the corresponding Kasparov categories in accordance with the semi-direct product operation. Thus, we observe that this strategy can be extrapolate to other (quantum) group constructions. Namely, to a quantum direct product. In this case, we state a connexion with the Künneth formula as pointed out by J. Chabert, S. Echterhoff and H. Oyono-Oyono for classical locally compact groups. The properties of torsion-frenness and K-amenability are also analyzed. It is known, thanks to R. Vergnioux and C. Voigt, that the strong Baum-Connes conjecture is preserved by divisible discrete quantum subgroups. The same is true for the strong torsion-freeness property, thanks to Y. Arano and K. De Commer. Here we show that both the usual Baum-Connes conjecture and the usual torsion-freeness property are preserved by divisible discrete quantum subgroups. The K-amenability property is analyzed too. A notably permanence property included in this dissertation is the invariance of the strong Baum-Connes conjecture under the free wreath product construction. For this, we carry out a complete classification of torsion actions of a quantum free product, which allows to give an appropriated formulation of the strong Baum-Connes conjecture for a free wreath product inspired by the pioneer work of C. Voigt. A major application is an explicit K-theory computation, in three relevant situations, for the Lemeux-Tarrago's compact quantum group which is monoidally equivalent to a free wreath product. Both this stability property for a free wreath product and the K-theory computations are part of a collaboration work with A. Freslon. To conclude, we question ourselves about the results obtained in order to suggest a list of questions, problems and goals that the author has encountered during the whole research period of the present dissertation and that are part of his future research projects
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Sheppeard, Marni Dee. "Gluon Phenomenology and a Linear Topos." Thesis, University of Canterbury. Physics and Astronomy, 2007. http://hdl.handle.net/10092/1436.
Full textAbstract:
In thinking about quantum causality one would like to approach rigorous QFT from outside the perspective of QFT, which one expects to recover only in a specific physical domain of quantum gravity. This thesis considers issues in causality using Category Theory, and their application to field theoretic observables. It appears that an abstract categorical Machian principle of duality for a ribbon graph calculus has the potential to incorporate the recent calculation of particle rest masses by Brannen, as well as the Bilson-Thompson characterisation of the particles of the Standard Model. This thesis shows how Veneziano n point functions may be recovered in such a framework, using cohomological techniques inspired by twistor theory and recent MHV techniques. This distinct approach fits into a rich framework of higher operads, leaving room for a generalisation to other physical amplitudes. The utility of operads raises the question of a categorical description for the underlying physical logic. We need to consider quantum analogues of a topos. Grothendieck's concept of a topos is a genuine extension of the notion of a space that incorporates a logic internal to itself. Conventional quantum logic has yet to be put into a form of equal utility, although its logic has been formulated in category theoretic terms. Axioms for a quantum topos are given in this thesis, in terms of braided monoidal categories. The associated logic is analysed and, in particular, elements of linear vector space logic are shown to be recovered. The usefulness of doing so for ordinary quantum computation was made apparent recently by Coecke et al. Vector spaces underly every notion of algebra, and a new perspective on it is therefore useful. The concept of state vector is also readdressed in the language of tricategories.
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Gunhan, Ali Can. "Environmental Effects On Quantum Geometric Phase And Quantum Entanglement." Phd thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/3/12609450/index.pdf.
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We investigate the geometric phase (GP) acquired by the states of a spin-1/2 nucleus which is subject to a static magnetic field. This nucleus as the carrier system of GP,
is taken as coupled to a dissipative environment, so that it evolves non-unitarily. We study the effects of different characteristics of different environments on GP as nucleus
evolves in time. We showed that magnetic field strength is the primary physical parameter that determines the stability of GPits stability decreases as the magnetic field strength increases. (By decrease in stability what we mean is the increase in the time rate of change of GP.) We showed that this decrease can be very rapid, and so it could be impossible to make use of it as a quantum logic gate in quantum information theory (QIT). To see if these behaviors differ in different environments, we analyze the same system for a fixed temperature environment which is under the influence of an electromagnetic field in a squeezed state. We find that the general dependence of GP on magnetic field does not change, but this time the effects are smoother. Namely, increase in magnetic field decreases the stability of GP also for in this environment
but this decrease is slower in comparison with the former case, and furthermore it occurs gradually. As a second problem we examine the entanglement of two atoms, which can be used as a two-qubit system in QIT. The entanglement is induced by an external quantum system. Both two-level atoms are coupled to a third two-level system by dipole-dipole interaction. The two atoms are assumed to be in ordinary vacuum and the third system is taken as influenced by a certain environment. We examined different types of environments. We show that the steady-state bipartite entanglement can be achieved in case the environment is a strongly fluctuating, that is a squeezed-vacuum, while it is not possible for a thermalized environment.
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Sharkey, Keeper Layne. "Very Accurate Quantum Mechanical Non-Relativistic Spectra Calculations of Small Atoms & Molecules Employing All-Particle Explicitly Correlated Gaussian Basis Functions." Diss., The University of Arizona, 2015. http://hdl.handle.net/10150/560835.
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Due to the fast increasing capabilities of modern computers it is now feasible to calculate spectra of small atom and molecules with the greater level of accuracy than high-resolution measurements. The mathematical algorithms developed and implemented on high performance supercomputers for the quantum mechanical calculations are directly derived from the first principles of quantum mechanics. The codes developed are primarily used to verify, refine, and predict the energies associated within a given system and given angular momentum state of interest. The Hamiltonian operator used to determine the total energy in the approach presented is called the internal Hamiltonian and is obtained by rigorously separating out the center-of-mass motion (or the elimination of translational motion) from the laboratory-frame Hamiltonian. The methods utilized in the articles presented in this dissertation do not include relativistic corrections and quantum electrodynamic effects, nor do these articles assume the Born-Oppenheimer (BO) approximation with the exception of one publication. There is one major review article included herein which describes the major differences between the non-BO method and the BO approximation using explicitly correlated Gaussian (ECG) basis functions. The physical systems studied in this dissertation are the atomic elements with Z < 7 (although the discussion is not limited to these) and diatomic molecules such as H₂⁺ and H₂ including nuclear isotopic substitution studies with deuterium and tritium, as well as electronic substitutions with the muon particle. Preliminary testing for triatomic molecular functionals using a model potential is also included in this dissertation. It has been concluded that using all-particle ECGs with including the addition of nonzero angular momentum functions to describe nonzero angular momentum states is sufficient in determining the energies of these states for both the atomic and molecular case.
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Engdahl, Erik. "Computation of resonance energies and spectral densities in the complex energy plane : application of complex scaling techniques for atoms, molecules and surfaces /." Uppsala : Uppsala Universitet, 1988. http://bibpurl.oclc.org/web/32938.
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Hu, Fan. "Computation of exciton transfer in the one- and two-dimensional close-packed quantum dot arrays." Virtual Press, 2005. http://liblink.bsu.edu/uhtbin/catkey/1319543.
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Forster theory of energy transfer is applied in diluted systems, and yet it remains unknown if it can be applied to the dense media. We have studied the exciton transfer in one-dimensional (1-D) close-packed pure and mixed quantum dot (QD) array under different models and two-dimensional (2-D) perfect lattice. Our approach is based on the master equation created by treating the exciton relaxation as a stochastic process. The random parameter has been used to describe dot-to-dot distance variations. The master equation has been investigated analytically for 1-D and 2-D perfect lattices and numerically for 1-D disordered systems. The suitability of Forster decay law on the excitation decay of close-packed solid has been discussed. The necessity to consider the effect of the further nearest interdot interactions has been checked.Department of Physics and Astronomy
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Gul, Yusuf. "Entanglement Transformations And Quantum Error Correction." Phd thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/2/12610773/index.pdf.
Full textAbstract:
The main subject of this thesis is the investigation of the transformations of pure
multipartite entangled states having Schmidt rank 2 by using only local operations
assisted with classical communications (LOCC). A new parameterization is used for
describing the entangled state of p particles distributed to p distant, spatially separated
persons. Product, bipartite and truly multipartite states are identified in this new
parametrization. Moreover, alternative parameterizations of local operations carried
out by each party are provided. For the case of a deterministic transformation to
a truly multipartite final state, one can find an analytic expression that determines
whether such a transformation is possible. In this case, a chain of measurements by
each party for carrying out the transformation is found. It can also be seen that,
under deterministic LOCC transformations, there are some quantities that remain
invariant. For the purpose of applying the results of this thesis in the context of the
quantum information and computation, brief reviews of the entanglement purification,
measurement based quantum computation and quantum codes are given.
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Dong, Wenzheng. "Quantum Information Processing with Color Center Qubits: Theory of Initialization and Robust Control." Diss., Virginia Tech, 2021. http://hdl.handle.net/10919/103438.
Full textAbstract:
Quantum information technologies include secure quantum communications and ultra precise quantum sensing that are significantly more efficient than their classical counterparts. To enable such technologies, we need a scalable quantum platform in which qubits are con trollable. Color centers provide controllable optically-active spin qubits within the coherence time limit. Moreover, the nearby nuclear spins have long coherence times suitable for quantum memories. In this thesis, I present a theoretical understanding of and control protocols for various color centers. Using group theory, I explore the wave functions and laser pumping-induced dynamics of VSi color centers in silicon carbide. I also provide dynamical decoupling-based high-fidelity control of nuclear spins around the color center. I also present a control technique that combines holonomic control and dynamically corrected control to tolerate simultaneous errors from various sources. The work described here includes a theoretical understanding and control techniques of color center spin qubits and nuclear spin quantum memories, as well as a new platform-independent control formalism towards robust qubit control.Doctor of Philosophy
Quantum information technologies promise to offer efficient computations of certain algorithms and secure communications beyond the reach of their classical counterparts. To achieve such technologies, we must find a suitable quantum platform to manipulate the quantum information units (qubits). Color centers host spin qubits that can enable such technologies. However, it is challenging due to our incomplete understanding of their physical properties and, more importantly, the controllability and scalability of such spin qubits. In this thesis, I present a theoretical understanding of and control protocols for various color centers. By using group theory that describes the symmetry of color centers, I give a phenomenological model of spin qubit dynamics under optical control of VSi color centers in silicon carbide. I also provide an improved technique for controlling nuclear spin qubits with higher precision. Moreover, I propose a new qubit control technique that combines two methods - holonomic control and dynamical corrected control - to provide further robust qubit control in the presence of multiple noise sources. The works in this thesis provide knowledge of color center spin qubits and concrete control methods towards quantum information technologies with color center spin qubits.
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Mirsakiyeva, Amina. "Electronic and optical properties of conducting polymers from quantum mechanical computations." Doctoral thesis, KTH, Materialfysik, MF, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-214979.
Full textAbstract:
Conductive polymers are also known as "organic metals" due to their semiconducting properties. They are found in a wide range of applications in the field of organic electronics. However, the growing number of experimental works is not widely supported with theoretical calculations. Hence, the field of conductive polymers is experiencing lack of understanding of mechanisms occurring in the polymers. In this PhD thesis, the aim is to increase understanding of conductive polymers by performing theoretical calculations. The polymers poly(3,4-ethylenedioxythiophene) (PEDOT) together with its selenium (PEDOS) and tellurium (PEDOTe) derivatives, poly(p-phenylene) (PPP) and naphthobischalcogenadiazoles (NXz) were studied. Several computational methods were applied for analysis of mentioned structures, including density functional theory (DFT), tight-binding modelling (TB), and Car-Parrinello molecular dynamics (CPMD) calculations. The combination of CPMD and DFT calculations was applied to investigate the PEDOT, PEDOS and PEDOTe. The polymers were studied using four different functionals in order to investigate the full picture of structural changes, electronic and optical properties. Temperature effects were studied using molecular dynamics simulations. Wide statistics for structural and molecular orbitals analysis were collected. The TB method was employed for PPP. The formation and motion of the excitations, polarons and bipolarons, along the polymer backbone was investigated in presence of electric and magnetic fields. The influence of non-magnetic and magnetic impurities was determined. The extended π-conjugated structures of NXz were computed using B3LYP and ωB97XD functionals in combination with the 6-31+G(d) basis set. Here, the structural changes caused by polaron formation were analyzed. The combined analysis of densities of states and absorption spectra was used for understanding of the charge transition.QC 20170928
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O'Hara, Michael James. "Adiabatic quantum computation noise in the adiabatic theorem and using the Jordan-Wigner transform to find effective Hamiltonians /." College Park, Md.: University of Maryland, 2008. http://hdl.handle.net/1903/8113.
Full textAbstract:
Thesis (Ph. D.) -- University of Maryland, College Park, 2008.Thesis research directed by: Applied Mathematics and Scientific Computation Program. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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Polad, Serkan. "Quantum Mechanical Treatment Of Fullerene-based Systems Doped With Various Metal And Non-metal Elements As Prospective Spin-qubits." Master's thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612173/index.pdf.
Full textAbstract:
In this thesis, We have calculated the optimized geometries, electronic structures and spin distributions of metal and non-metal elements Li, Na, N and P doped C60 fullerene dimers and trimers with different spin multiplicities using hybrid density functional theory (DFT) at the B3LYP/6-31G level of theory. Natural population analysis and Mulliken population analysis show that non-metal elements (N, P) inside the C60 fullerene dimers and trimers are well isolated and preserve their electronic structures while charge transfer processes occur between metal elements(Li, Na) and C60 structures. Energy calculations showed that both doped and undoped linear C60 structures are energetically lower than triangular C60 structures. Calculated spin density distributions make non-metal doped C60 structures advantageous over metal doped C60 cages as spin cluster qubits.
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Lamoureux, Louis-Philippe. "Theoretical and experimental aspects of quantum cryptographic protocols." Doctoral thesis, Universite Libre de Bruxelles, 2006. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210776.
Full textAbstract:
La mécanique quantique est sans aucun doute la théorie la mieux vérifiée qui n’a jamais existée. En se retournant vers le passé, nous constatons qu’un siècle de théorie quantique a non seulement changé la perception que nous avons de l’univers dans lequel nous vivons mais aussi est responsable de plusieurs concepts technologiques qui ont le potentiel de révolutionner notre monde.
La présente dissertation a pour but de mettre en avance ces potentiels, tant dans le domaine théorique qu’expérimental. Plus précisément, dans un premier temps, nous étudierons des protocoles de communication quantique et démontrerons que ces protocoles offrent des avantages de sécurité qui n’ont pas d’égaux en communication classique. Dans un deuxième temps nous étudierons trois problèmes spécifiques en clonage quantique ou chaque solution
apportée pourrait, à sa façon, être exploitée dans un problème de communication quantique.
Nous débuterons par décrire de façon théorique le premier protocole de communication quantique qui a pour but la distribution d’une clé secrète entre deux parties éloignées. Ce chapitre nous permettra d’introduire plusieurs concepts et outils théoriques qui seront nécessaires dans les chapitres successifs. Le chapitre suivant servira aussi d’introduction, mais cette fois-ci penché plutôt vers le côté expériemental. Nous présenterons une élégante technique qui nous permettra d’implémenter des protocoles de communication quantique de façon simple. Nous décrirons ensuite des expériences originales de communication quantique basées sur cette technique. Plus précisément, nous introduirons le concept de filtration d’erreur et utiliserons cette technique afin d’implémenter une distribution de clé quantique bruyante qui ne pourrait pas être sécurisé sans cette technique. Nous démontrerons ensuite des expériences implémentant le tirage au sort quantique et d’identification quantique.
Dans un deuxième temps nous étudierons des problèmes de clonage quantique basé sur le formalisme introduit dans le chapitre d’introduction. Puisqu’il ne sera pas toujours possible de prouver l’optimalité de nos solutions, nous introduirons une technique numérique qui nous
permettra de mettre en valeur nos résultats.
Doctorat en sciences, Spécialisation physique
info:eu-repo/semantics/nonPublished
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Vittorini, Grahame D. "Stability of ion chains in a cryogenic surface-electrode ion trap." Diss., Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/50239.
Full textAbstract:
Cold, trapped atomic ions have enabled the investigation of fundamental physics and generated a rich field of applications. Foremost among these is quantum computation which has recently driven the development of the sophisticated, scalable surface-electrode trap. Despite the many advantages of surface-electrode traps, the typically smaller ion-electrode distance, d, in these traps results in an increased ion heating rate that is proportional to d^(-4) and a decreased trap well-depth that is proportional to d^(-2). These shortcomings can be simultaneously addressed by installing the trap into a cryogenic environment. With this in mind, a closed-cycle, cryogenic ion trapping apparatus that maintains excellent vacuum, is highly modular, has increased optical access, and uses a simple vibration isolation system has been developed.
Single ions are trapped and used to characterize system properties such as the motion of the vibration isolation stage. In order to compare this system to a similar room temperature apparatus, the ion trapping lifetime and heating rate are determined. A single ion also serves as a sensitive electric field probe that is used to measure and compensate stray electric fields across the trap.
Due to the long dark ion lifetimes in this system, it is well-suited to probing the stability of small, linear ion crystals. Linear ion crystals of arbitrary length are built in an automated fashion using transport waveforms and the scaling of dark lifetime with ion number for N <= 6 is investigated. These data are then used to consider the relevance of various loss channels.
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Cosme, Carlos Magno Martins. "Quantum Algorithm for the Non Abelian Hidden Subgroup Problem." Laboratório Nacional de Computação Científica, 2008. http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=149.
Full textAbstract:
We present an efficient quantum algorithm for the Hidden Subgroup Problem (HSP) on the semidirect product of the cyclic groups and , where is any odd prime number, and are positives integers and the homomorphism which defines the group is given by the root such that . As a consequence we can solve efficiently de HSP on the semidirect product of the groups by , where has a special prime factorization.Neste trabalho apresentamos um algoritmo quântico eficiente para o Problema do Subgrupos Oculto (PSO) no produto semidireto dos grupos cíclicos e , onde é qualquer número primo ímpar, e são inteiros positivos e o homomorfismo que define o grupo é dado por uma raiz para a qual . Como conseqüência, podemos resolver eficientemente o PSO também no produto semidireto dos grupos por , onde o inteiro possui uma especial fatoração prima.
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Cervati, Neto Alaor. "Teoria de controle ótimo em sistemas abertos." Universidade Estadual Paulista (UNESP), 2018. http://hdl.handle.net/11449/152661.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
A teoria de informação e computação quântica é uma área de pesquisa que vem crescendo de maneira acentuada nos últimos anos devido aos inúmeros avanços tecnológicos que a acompanham. Neste mestrado começamos nossos estudos nesta área de pesquisa onde nos introduzimos e aprofundamos em seus aspectos intrigantes e peculiares. Dada nossa formação inicial na área de ciências da computação, inicialmente nos dedicamos a entender os aspectos fundamentais da mecânica quântica, assim como da teoria de informação e computação quântica. Focamos principalmente nos sistemas quânticos abertos, visto que o maior obstáculo a ser superado para o desenvolvimento destes computadores é o efeito deletério do meio ambiente. A princípio, concentramos nossos estudos nos ditos processos não-Markovianos, que apresentam efeitos de memória. Aprendemos sobre as novas medidas de não-Markovianidade, principalmente as medidas baseadas na dinâmica do emaranhamento e na dinâmica da informação mútua. Conseguimos publicar nosso primeiro resultado, onde provamos a inequivalência destas duas medidas de não-Markovianidade. De fato, mostramos que tais medidas, em geral, podem discordar sobre o tipo de processo dissipativo, sendo que uma pode reconhecê-lo como Markoviano enquanto outra pode reconhecê-lo como não-Markoviano. Como mostramos, esta inequivalência está diretamente relacionada com o refluxo de informação do meio ambiente para o sistema, e como mensuramos tal informação nestas duas medidas distintas de não-Markovianidade. Finalmente, na fase final de nossos estudos, tivemos como objetivo encontrar um meio de otimizar o controle das operações lógicas. Especificamente, trabalhamos com um método numérico utilizado em sistemas fechados para otimizar sistemas abertos Markovianos. Observamos que a eficácia deste método depende do tipo e intensidade da interferência do ambiente e das condições iniciais do sistema, obtendo melhores resultados em casos específicos.
Quantum information theory and computation is a field of research that has been growing acutely in the past few years due to the many technological improvements it follows. In this masters’ course, we began our studies in this area of research where we were introduced and immersed in its intriguing and peculiar aspects. Given our initial formation in computer science, we initially dedicated ourselves to understanding the fundamentals of quantum mechanics, as well as of information theory and quantum computation. Our main focus were open quantum systems, since the greatest obstacle to the development of these computers is the harmful effect of the environment. At first, we concentrated our studies in the so called non-Markovian processes, that show memory effects. We learned about the new non-Markovianity measurements, mainly those based on the dynamics of entanglement and mutual information. We managed to publish our first result, where we proved the inequivalence of these two measurements of non-Markovianity. Indeed, we showed that such measurements, in general, can disagree about the dissipative process, so that one can regard it as Markovian and the other as non-Markovian. As we demonstrated, this inequivalence is directly related to the information back-flow from the environment to the system, and how this information is measured by each of the two distinct measurements. Finally, in the last stage of our studies, our goal was to find a way to optimize the control of the logical operations. Specifically, we worked with a numeric method used in closed systems to optimize Markovian open systems. We have observed that the effectiveness of this method depends on the type and intensity of the interference of the environment and of its initial conditions, attaining better results for specific cases.
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Lumia, Luca. "Digital quantum simulations of Yang-Mills lattice gauge theories." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/22355/.
Full textAbstract:
I metodi di calcolo tradizionali per le teorie di gauge su reticolo risultano problematici in regioni di diagrammi di fase a grandi valori del potenziale chimico o quando sono utilizzate per riprodurre la dinamica in tempo reale di un modello. Tali problemi possono essere evitati da simulazioni quantistiche delle teorie di gauge su reticolo, le quali stanno diventando sempre più riproducibili sperimentalmente, grazie ai recenti progressi tecnologici. In questa tesi formuliamo una versione delle teorie di Yang-Mills su reticolo appropriata per risolvere il problema della dimensione infinita dello spazio di Hilbert associato ai bosoni di gauge. Questa formulazione è adatta per essere riprodotta in un simulatore quantistico e ne implementiamo una completa simulazione su un computer quantistico digitale, sfruttando il framework Qiskit. In questa simulazione misuriamo le energie del ground state e i valori di aspettazione di alcuni Wilson loop al variare dell'accoppiamento della teoria, per studiarne le fasi e valutare la prestazione dei metodi usati.
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Brito, Frederico Borges de. "Um estudo sobre processos de descoerência em qubits de estado sólido." [s.n.], 2006. http://repositorio.unicamp.br/jspui/handle/REPOSIP/277286.
Full textAbstract:
Orientador: Amir Ordacgi CaldeiraTese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin
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Resumo: Esta tese teve como objetivo estudar processos de perda de coerência quântica, chamados de descoerência, em sistemas de matéria condensada eleitos pela literatura como possíveis implementações do bit quântico (qubit). Esta perda de coerência quântica ocorre devido ao inevitável acoplamento do sistema de interesse com o seu ambiente. Como os estados de superposição quântica são a chave para a realização de operações baseadas na lógica quântica, tem-se que tais processos limitam ou até mesmo impedem o uso de determinados sistemas na esperada realização física do computador quântico. Os sistemas de matéria condensada padecem de uma dificuldade maior para se isolar o qubit do seu ambiente, o que acarreta, em geral, na observação de tempos de coerência piores do que os encontrados em seus concorrentes. Por outro lado, a possibilidade de construção de vários qubits acoplados e de manipulação de cada um de modo individual, usando-se técnicas convencionais de engenharia, têm impulsionado esforços nestes tipos de dispositivos. Os sistemas abordados na tese foram: qubits supercondutores contendo junções Josephson; e qubits de pontos quânticos. Para a investigação completa do primeiro tipo tivemos que desenvolver o modelo Caldeira-Leggett para o caso de várias fontes de dissipação acopladas ao qubit. Com a prescrição apresentada aqui, pudemos determinar o número de banhos de osciladores necessários para a correta descrição das fontes, e verificar que as taxas totais de relaxação e de descoerência não são necessariamente as somas das taxas devido a cada fonte individualmente. Além disso, pudemos aplicar o formalismo desenvolvido no estudo de um qubit de uxo em investigação. Para o sistema de pontos quânticos seguimos a linha de determinação do banho efetivo visto pelo grau de liberdade de spin do elétron aprisionado no ponto quântico. Determinada a função espectral efetiva, pudemos encontrar soluções analíticas para a dinâmica do valor esperado para cada uma das componentes de spin s x,y,z. o que permitiu uma análise completa dos efeitos de cada parâmetro físico do sistema. Em ambos os casos, fomos capazes de indicar os melhores regimes de operação de cada qubit, e dar estimativas dos tempos de relaxação e de descoerência
Abstract: The purpose of this thesis was to study the process of loss of quantum coherence, named decoherence, in condensed matter systems cited in the literature as possible candidates for the implementation of a quantum bit (qubit). Decoherence occurs due to the inevitable coupling of the system of interest to its environment. Once the quantum superposition states are the key to perform operations based on quantum logic, these processes limit, or even hinder, the utilization of some of those systems in the physical realization of the quantum computer. Relatively to its competitors, condensed matter systems usually present a higher degree of difficulty as one tries to minimize the coupling between the qubit and its environment, which, generally, worsens its coherence time observations. On the other hand, these devices present advantages which stimulates its study, such as: the possibility of construction of several coupled qubits and the possibility of manipulating each one individually, using conventional engineering techniques. The systems studied in this thesis were: superconducting qubits with Josephson junctions; and electronic spins quantum dots. Aiming at a complete investigation of the first system, we developed the Caldeira-Leggett model for the case of several dissipation sources coupled to the qubit. With the prescription presented here, we determine the number of oscillator baths needed to the correct description of the noise sources, and verify that the total relaxation and decoherence rates are not necessarily the sum of the individual rates relative to each source. Moreover, we applied this formalism to the study of a ux qubit currently under investigation. For the quantum dot qubits, we employed the effective bath approach to treat the dynamics of the spin of the electron localized in the quantum dot. As a result, we found analytical solutions for the dynamics of the average value of each one of the spin components s x,y,z . In both cases, we indicated the best operational regime of each qubit and gave estimates of the relaxation and decoherence times
Doutorado
Física da Matéria Condensada
Doutor em Ciências
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Agudelo, Juan Carlos Agudelo. "Computação paraconsistente : uma abordagem logica a computação quantica." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/280061.
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Orientador: Walter Alexandre CarnielliTese (doutorado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciencias Humanas
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Resumo: Neste trabalho levantamos, e investigamos do ponto de vista conceitual, evidências de que a complexidade algorítmica pode ser vista como relativa à lógica. Propomos, para tanto, novos modelos de computação fundados sobre lógicas não-clássicas, estudando suas características quanto à expressabilidade computacional e eficiência. A partir desta visão, sugerimos um novo caminho para estudar a eficiência dos modelos de computação quântica, enfatizando a análise de uma lógica subjacente a tais modelos. O conteúdo da tese está estruturado da seguinte maneira: no primeiro capítulo apresentamos uma análise conceitual da noção de 'computação', indicando como este conceito tem mudado desde os trabalhos fundacionais da década de 1930, e discutindo se o conceito deve ser considerado como puramente físico, puramente lógicomatemático ou uma combinação de ambos. O Capítulo 2 introduz duas versões de 'máquinas de Turing paraconsistentes', usando sistemas lógicos diferentes e obtendo modelos com diferentes poderes computacionais (quanto à eficiência); tal resultado constitui uma primeira evidência a favor da relatividade lógica da computação que queremos defender. Outra evidência na mesma direção é apresentada no Capitulo 3, através da generalização dos circuitos booleanos para lógicas não-clássicas, em particular para a lógica paraconsistente mbC e para a lógica modal S5, e da análise do poder computacional de tais generalizações. O Capítulo 4 consiste numa introdução à computação quântica, para logo (no Capítulo 5) estabelecer algumas relações entre modelos de computação quântica e modelos de computação paraconsistente, de maneira a propor uma interpretação lógica dos modelos quânticos. No capítulo final (Capítulo 6) descrevemos várias relações entre mecânica quântica e lógica paraix consistente, relações estas que sugerem potencialidades com alto grau de relevância a respeito da abordagem paraconsistente dos fenômenos computacionais quânticos e que incitam a continuar explorando esta alternativa.
Abstract: This work provides evidences to view computational complexity as logic-relative, by introducing new models of computation through non-classical logics and by studying their features with respect to computational expressivity and efficiency. From this point of view, we suggest a new way to study the efficiency of quantum computational models consisting in the analysis of an underlying logic. The contents of the thesis is structured in the following way: the first chapter presents a conceptual analysis of the notion of 'computation', showing how this concept evolved since the decade of 1930 and discussing whether it can be considered a pure physical or a pure logic-mathematical concept, or a combination of both paradigms. Chapter 2 introduces two versions of 'paraconsistent Turing machines', by considering different logic systems and obtaining models with different computational capabilities (with respect to efficiency); such a result constitute a first evidence in favor of the logical relativity of computation that we are defending here. Another evidence in the same direction is presented in Chapter 3 through a generalization of boolean circuits to non-classical logics, particularly for the paraconsistent logic mbC and for the modal logic S5, and by analyzing the computational power of such generalizations. Chapter 4 consists in an introduction to quantum computation. This is used in Chapter 5 to establish some relationships between quantum and paraconsistent models of computation, in order to propose a logic interpretation of quantum models. The final chapter (Chapter 6) describes several connections between quantum mechanics and paraconsistent logic; such relationship suggests highly relevant potentialities in favor of the paraconsistent approach to quantum computation phenomena encouraging to continue exploring this alternative.
Doutorado
Logica
Doutor em Filosofia
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Garolera, Huguet Blai. "Probing gauge theories: Exact results and holographic computations." Doctoral thesis, Universitat de Barcelona, 2015. http://hdl.handle.net/10803/289346.
Full textAbstract:
The holographic duality between gauge theories and string theories has opened a new door to access the strongly coupled regime of quantum field theories and offers, at the same time, a completely new way to understand the elusive nature of quantum gravity and the non-perturbative regime of string theory. After almost two decades of research, the current status of the correspondence is that of a solid conjecture that has passed a great number of nontrivial tests, to the point that it is generally believed to be true.
The present thesis includes a collection of four papers published in peer-reviewed scientific journals, all of them in the context of the AdS/CFT correspondence and with a particular focus on studying gauge theories by inserting heavy external probes, following prescribed trajectories and transforming under various representations of the gauge group.
Each of these works reports a little step forward in the development of new strategies for capturing correc- tions beyond the leading order as well as in using exact results available in quantum field theory in order to derive exact expressions for other relevant observables and new non-trivial string theory predictions.
In chapters 2 and 3 we use the AdS/CFT correspondence in order to compute several observables of N = 4 SU (N ) super Yang-Mills theory related with the presence of an infinitely heavy particle transforming in the k-symmetric or the k-antisymmetric representations of the gauge group and following particular trajectories. This is achieved by means of adding certain D-brane probes with electric fluxes turned on and reaching the boundary of AdS on the very trajectories followed by the dual particles. For the antisymmetric case we consider D5-branes reaching the boundary at arbitrary time-like trajectories, while for the symmetric case, we consider a D3-brane fully embedded in AdS5 that reaches the boundary at either a straight line or a hyperbola. This generalizes previous computations that used fundamental strings, which are claimed to be dual to infinitely heavy point particles transforming in the fundamental. Besides the intrinsic interest of these generalizations, our main motivation in studying them is that, as it happens in the computation of certain Wilson loops, the results obtained with D3-branes give an all- orders series of corrections in 1/N to the leading order result for the fundamental representation obtained by means of fundamental strings.
It is important to remark, one more time, that we can not really extrapolate up to k = 1, since this is beyond the regime of validity of the supergravity approximation. Therefore, it is not justified a priori to set k = 1 in our results. Nevertheless, when compared with the exact results available, we find that the D3-brane computation reproduces the correct result in the large N , λ limit and with k = 1.
This better than expected performance suggests the exciting possibility that certain D3-branes with electric fluxes might capture correctly all the 1/N corrections, but it is fair to say that we still lack of a precise string-theoretic argument to prove this.Durant les darreres dues dècades ha aparegut un nou paradigma que permet reformular completament certes teories quàntiques de camps i ens aporta una nova eina que ens permet realitzar càlculs analítics en règims fins ara inaccessibles. Aquest nou paradigma sorgeix del descobriment d’una correspondència o dualitat exacta entre dues teories aparentment molt diferents. Per una banda de la dualitat tenim certes teories quàntiques de camps, com per exemple les denominades teories de Yang-Mills, similars a les teories del Model Estàndard. Aquestes descriuen partícules interactuant en un espai pla d-dimensional sense gravetat. A l’altra banda de la dualitat trobem teories que inclouen la gravetat, com ara la Teoria de la Relativitat General d’Einstein o les seves generalitzacions en el marc de la Teoria de Cordes. Aquestes teories de gravetat estan definides sobre espais de dimensió més alta que d, i és per això que aquesta correspondència rep sovint l’adjectiu de “hologràfica”. Depenent del context, aquesta rep el nom de dualitat gauge/gravetat, dualitat gauge/corda o AdS/CFT (acrònim anglès per la correspondència particular entre teoria de cordes a espais d’Anti-de Sitter i teories de camps conformes). Fins ara, una de les correspondències més ben estudiades i que comprenem millor (i sobre la qual es centra la present tesi) és la dualitat entre la teoria quatre-dimensional N = 4 super Yang-Mills amb grup de gauge SU (N ) i teoria de cordes tipus IIB en un espai deu-dimensional AdS5 × S5 . Aquesta tesi presenta una recopilació de quatre articles publicats en revistes científiques d’alt impacte, tots ells en el camp de la correspondència AdS/CFT i centrats en l’estudi de teories gauge supersimètriques mitjançant la inserció de partícules de prova infinitament massives, seguint trajectòries determinades i transformant sota diverses representacions del grup de gauge. Cadascun d’aquests treballs aporta un pas endavant en el desenvolupament de noves estratègies per calcular correccions més enllà del primer ordre així com en l’ús de resultats exactes accessibles a la Teoria Quàntica de Camps per tal de derivar expressions exactes d’altres observables rellevants de la teoria i realitzar prediccions de Teoria de Cordes.