Topological Quantum Computation - An Analysis of an Anyon Model Based on Quantum Double Symmetries

There exists various suggestions for building a functional and a fault-tolerant large-scale quantum computer. Topological quantum computation is a more exotic suggestion, which makes use of the properties of quasiparticles manifest only in certain two-dimensional systems. These so called anyons exhibit topological degrees of freedom, which, in principle, can be used to execute quantum computation with intrinsic fault-tolerance. This feature is the main incentive to study topological quantum computation. The objective of this thesis is to provide an accessible introduction to the theory. In this thesis one has considered the theory of anyons arising in two-dimensional quantum mechanical systems, which are described by gauge theories based on so called quantum double symmetries. The quasiparticles are shown to exhibit interactions and carry quantum numbers, which are both of topological nature. Particularly, it is found that the addition of the quantum numbers is not unique, but that the fusion of the quasiparticles is described by a non-trivial fusion algebra. It is discussed how this property can be used to encode quantum information in a manner which is intrinsically protected from decoherence and how one could, in principle, perform quantum computation by braiding the quasiparticles. As an example of the presented general discussion, the particle spectrum and the fusion algebra of an anyon model based on the gauge group S_3 are explicitly derived. The fusion algebra is found to branch into multiple proper subalgebras and the simplest one of them is chosen as a model for an illustrative demonstration. The different steps of a topological quantum computation are outlined and the computational power of the model is assessed. It turns out that the chosen model is not universal for quantum computation. However, because the objective was a demonstration of the theory with explicit calculations, none of the other more complicated fusion subalgebras were considered. Studying their applicability for quantum computation could be a topic of further research.

Computational Methods for Studies of Quantum Dots and Boson Condensates

This thesis presents ab initio studies of two kinds of physical systems, quantum dots and bosons, using two program packages of which the bosonic one has mainly been developed by the author. The implemented models, \emph{i.e.}, configuration interaction (CI) and coupled cluster (CC) take the correlated motion of the particles into account, and provide a hierarchy of computational schemes, on top of which the exact solution, within the limit of the single-particle basis set, is obtained. The theory underlying the models is presented in some detail, in order to provide insight into the approximations made and the circumstances under which they hold. Some of the computational methods are also highlighted. In the final sections the results are summarized. The CI and CC calculations on multiexciton complexes in self-assembled semiconductor quantum dots are presented and compared, along with radiative and non-radiative transition rates. Full CI calculations on quantum rings and double quantum rings are also presented. In the latter case, experimental and theoretical results from the literature are re-examined and an alternative explanation for the reported photoluminescence spectra is found. The boson program is first applied on a fictitious model system consisting of bosonic electrons in a central Coulomb field for which CI at the singles and doubles level is found to account for almost all of the correlation energy. Finally, the boson program is employed to study Bose-Einstein condensates confined in different anisotropic trap potentials. The effects of the anisotropy on the relative correlation energy is examined, as well as the effect of varying the interaction potential.}

A quantum chemical investigation of the metal centres in cytochrome c oxidase

Quantum effects are often of key importance for the function of biological systems at molecular level. Cellular respiration, where energy is extracted from the reduction of molecular oxygen to water, is no exception. In this work, the end station of the electron transport chain in mitochondria, cytochrome c oxidase, is investigated using quantum chemical methodology. Cytochrome c oxidase contains two haems, haem a and haem a3. Haem a3, with its copper companion, CuB, is involved in the final reduction of oxygen into water. This binuclear centre receives the necessary electrons from haem a. Haem a, in turn, receives its electrons from a copper ion pair in the vicinity, called CuA. Density functional theory (DFT) has been used to clarify the charge and spin distributions of haem a, as well as changes in these during redox activity. Upon reduction, the added electron is shown to be evenly distributed over the entire haem structure, important for the accommodation of the prosthetic group within the protein. At the same time, the spin distribution of the open-shell oxidised state is more localised to the central iron. The exact spin density distribution has been disputed in the literature, however, different experiments indicating different distributions of the unpaired electron. The apparent contradiction is shown to be due to the false assumption of a unit amount of unpaired electron density; in fact, the oxidised state has about 1.3 unpaired electrons. The validity of the DFT results have been corroborated by wave function based coupled cluster calculations. Point charges, for use in classical force field based simulations, have been parameterised for the four metal centres, using a newly developed methodology. In the procedure, the subsystem for which point charges are to be obtained, is surrounded by an outer region, with the purpose of stabilising the inner region, both electronically and structurally. Finally, the possibility of vibrational promotion of the electron transfer step between haem a and a3 has been investigated. Calculating the full vibrational spectra, at DFT level, of a combined model of the two haems, revealed several normal modes that do shift electron density between the haems. The magnitude of the shift was found to be moderate, at most. The proposed mechanism could have an assisting role in the electron transfer, which still seems to be dominated by electron tunnelling.

Theoretical Studies on Coupled Electron and Proton Transfer in Cytochrome c Oxidase

The complexity of life is based on an effective energy transduction machinery, which has evolved during the last 3.5 billion years. In aerobic life, the utilization of the high oxidizing potential of molecular oxygen powers this machinery. Oxygen is safely reduced by a membrane bound enzyme, cytochrome c oxidase (CcO), to produce an electrochemical proton gradient over the mitochondrial or bacterial membrane. This gradient is used for energy-requiring reactions such as synthesis of ATP by F0F1-ATPase and active transport. In this thesis, the molecular mechanism by which CcO couples the oxygen reduction chemistry to proton-pumping has been studied by theoretical computer simulations. By building both classical and quantum mechanical model systems based on the X-ray structure of CcO from Bos taurus, the dynamics and energetics of the system were studied in different intermediate states of the enzyme. As a result of this work, a mechanism was suggested by which CcO can prevent protons from leaking backwards in proton-pumping. The use and activation of two proton conducting channels were also enlightened together with a mechanism by which CcO sorts the chemical protons from pumped protons. The latter problem is referred to as the gating mechanism of CcO, and has remained a challenge in the bioenergetics field for more than three decades. Furthermore, a new method for deriving charge parameters for classical simulations of complex metalloenzymes was developed.

Magnetically induced currents and magnetic response properties of molecules

The magnetically induced currents in organic monoring and multiring molecules, in Möbius shaped molecules and in inorganic all-metal molecules have been investigated by means of the Gauge-including magnetically induced currents (GIMIC) method. With the GIMIC method, the ring-current strengths and the ring-current density distributions can be calculated. For open-shell molecules, also the spin current can be obtained. The ring-current pathways and ring-current strengths can be used to understand the magnetic resonance properties of the molecules, to indirectly identify the effect of non-bonded interactions on NMR chemical shifts, to design new molecules with tailored properties and to discuss molecular aromaticity. In the thesis, the magnetic criterion for aromaticity has been adopted. According to this, a molecule which has a net diatropic ring current might be aromatic. Similarly, a molecule which has a net paratropic current might be antiaromatic. If the net current is zero, the molecule is nonaromatic. The electronic structure of the investigated molecules has been resolved by quantum chemical methods. The magnetically induced currents have been calculated with the GIMIC method at the density-functional theory (DFT) level, as well as at the self-consistent field Hartree-Fock (SCF-HF), at the Møller-Plesset perturbation theory of the second order (MP2) and at the coupled-cluster singles and doubles (CCSD) levels of theory. For closed-shell molecules, accurate ring-current strengths can be obtained with a reasonable computational cost at the DFT level and with rather small basis sets. For open-shell molecules, it is shown that correlated methods such as MP2 and CCSD might be needed to obtain reliable charge and spin currents. The basis set convergence has to be checked for open-shell molecules by performing calculations with large enough basis sets. The results discussed in the thesis have been published in eight papers. In addition, some previously unpublished results on the ring currents in the endohedral fullerene Sc3C2@C80 and in coronene are presented. It is shown that dynamical effects should be taken into account when modelling magnetic resonance parameters of endohedral metallofullerenes such as Sc3C2@C80. The ring-current strengths in a series of nano-sized hydrocarbon rings are related to static polarizabilities and to H-1 nuclear magnetic resonance (NMR) shieldings. In a case study on the possible aromaticity of a Möbius-shaped [16]annulene we found that, according to the magnetic criterion, the molecule is nonaromatic. The applicability of the GIMIC method to assign the aromatic character of molecules was confirmed in a study on the ring currents in simple monocylic aromatic, homoaromatic, antiaromatic, and nonaromatic hydrocarbons. Case studies on nanorings, hexaphyrins and [n]cycloparaphenylenes show that explicit calculations are needed to unravel the ring-current delocalization pathways in complex multiring molecules. The open-shell implementation of GIMIC was applied in studies on the charge currents and the spin currents in single-ring and bi-ring molecules with open shells. The aromaticity predictions that are made based on the GIMIC results are compared to other aromaticity criteria such as H-1 NMR shieldings and shifts, electric polarizabilities, bond-length alternation, as well as to predictions provided by the traditional Hückel (4n+2) rule and its more recent extensions that account for Möbius twisted molecules and for molecules with open shells.

Double-Edged Imitation : Theories and Practices of Pastiche in Literature

This study concentrates on the contested concept of pastiche in literary studies. It offers the first detailed examination of the history of the concept from its origins in the seventeenth century to the present, showing how pastiche emerged as a critical concept in interaction with the emerging conception of authorial originality and the copyright laws protecting it. One of the key results of this investigation is the contextualisation of the postmodern debate on pastiche. Even though postmodern critics often emphasise the radical novelty of pastiche, they in fact resuscitate older positions and arguments without necessarily reflecting on their historical conditions. This historical background is then used to analyse the distinction between the primarily French conception of pastiche as the imitation of style and the postmodern notion of it as the compilation of different elements. The latter s vagueness and inclusiveness detracts from its value as a critical concept. The study thus concentrates on the notion of stylistic pastiche, challenging the widespread prejudice that it is merely an indication of lack of talent. Because it is multiply based on repetition, pastiche is in fact a highly ambiguous or double-edged practice that calls into question the distinction between repetition and original, thereby undermining the received notion of individual unique authorship as a fundamental aesthetic value. Pastiche does not, however, constitute a radical upheaval of the basic assumptions on which the present institution of literature relies, since, in order to mark its difference, pastiche always refers to a source outside itself against which its difference is measured. Finally, the theoretical analysis of pastiche is applied to literary works. The pastiches written by Marcel Proust demonstrate how it can become an integral part of a writer s poetics: imitation of style is shown to provide Proust with a way of exploring the role of style as a connecting point between inner vision and reality. The pastiches of the Sherlock Holmes stories by Michael Dibdin, Nicholas Meyer and the duo Adrian Conan Doyle and John Dickson Carr illustrate the functions of pastiche within a genre detective fiction that is itself fundamentally repetitive. A.S. Byatt s Possession and D.M. Thomas s Charlotte use Victorian pastiches to investigate the conditions of literary creation in the age of postmodern suspicion of creativity and individuality. The study thus argues that the concept of pastiche has valuable insights to offer to literary criticism and theory, and that literary pastiches, though often dismissed in reviews and criticism, are a particularly interesting object of study precisely because of their characteristic ambiguity.