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.

Noncommutative Quantum Field Theories and UV/IR Mixing

Our present-day understanding of fundamental constituents of matter and their interactions is based on the Standard Model of particle physics, which relies on quantum gauge field theories. On the other hand, the large scale dynamical behaviour of spacetime is understood via the general theory of relativity of Einstein. The merging of these two complementary aspects of nature, quantum and gravity, is one of the greatest goals of modern fundamental physics, the achievement of which would help us understand the short-distance structure of spacetime, thus shedding light on the events in the singular states of general relativity, such as black holes and the Big Bang, where our current models of nature break down. The formulation of quantum field theories in noncommutative spacetime is an attempt to realize the idea of nonlocality at short distances, which our present understanding of these different aspects of Nature suggests, and consequently to find testable hints of the underlying quantum behaviour of spacetime. The formulation of noncommutative theories encounters various unprecedented problems, which derive from their peculiar inherent nonlocality. Arguably the most serious of these is the so-called UV/IR mixing, which makes the derivation of observable predictions especially hard by causing new tedious divergencies, to which our previous well-developed renormalization methods for quantum field theories do not apply. In the thesis I review the basic mathematical concepts of noncommutative spacetime, different formulations of quantum field theories in the context, and the theoretical understanding of UV/IR mixing. In particular, I put forward new results to be published, which show that also the theory of quantum electrodynamics in noncommutative spacetime defined via Seiberg-Witten map suffers from UV/IR mixing. Finally, I review some of the most promising ways to overcome the problem. The final solution remains a challenge for the future.

The Spin-Statistics Relation and Noncommutative Quantum Field Theory

The efforts of combining quantum theory with general relativity have been great and marked by several successes. One field where progress has lately been made is the study of noncommutative quantum field theories that arise as a low energy limit in certain string theories. The idea of noncommutativity comes naturally when combining these two extremes and has profound implications on results widely accepted in traditional, commutative, theories. In this work I review the status of one of the most important connections in physics, the spin-statistics relation. The relation is deeply ingrained in our reality in that it gives us the structure for the periodic table and is of crucial importance for the stability of all matter. The dramatic effects of noncommutativity of space-time coordinates, mainly the loss of Lorentz invariance, call the spin-statistics relation into question. The spin-statistics theorem is first presented in its traditional setting, giving a clarifying proof starting from minimal requirements. Next the notion of noncommutativity is introduced and its implications studied. The discussion is essentially based on twisted Poincaré symmetry, the space-time symmetry of noncommutative quantum field theory. The controversial issue of microcausality in noncommutative quantum field theory is settled by showing for the first time that the light wedge microcausality condition is compatible with the twisted Poincaré symmetry. The spin-statistics relation is considered both from the point of view of braided statistics, and in the traditional Lagrangian formulation of Pauli, with the conclusion that Pauli's age-old theorem stands even this test so dramatic for the whole structure of space-time.

Quantum Chemical Studies of Intermolecular Interactions

This thesis studies the intermolecular interactions in (i) boron-nitrogen based systems for hydrogen splitting and storage, (ii) endohedral complexes, A@C60, and (iii) aurophilic dimers. We first present an introduction of intermolecular interactions. The theoretical background is then described. The research results are summarized in the following sections. In the boron-nitrogen systems, the electrostatic interaction is found to be the leading contribution, as 'Coulomb Pays for Heitler and London' (CHL). For the endohedral complex, the intermolecular interaction is formulated by a one-center expansion of the Coulomb operator 1/rab. For the aurophilic attraction between two C2v monomers, a London-type formula was derived by fully accounting for the anisotropy and point-group symmetry of the monomers.

Studies of new inorganic species using relativistic quantum chemistry

In the present work the methods of relativistic quantum chemistry have been applied to a number of small systems containing heavy elements, for which relativistic effects are important. First, a thorough introduction of the methods used is presented. This includes some of the general methods of computational chemistry and a special section dealing with how to include the effects of relativity in quantum chemical calculations. Second, after this introduction the results obtained are presented. Investigations on high-valent mercury compounds are presented and new ways to synthesise such compounds are proposed. The methods described were applied to certain systems containing short Pt-Tl contacts. It was possible to explain the interesting bonding situation in these compounds. One of the most common actinide compounds, uranium hexafluoride was investigated and a new picture of the bonding was presented. Furthermore the rareness of uranium-cyanide compounds was discussed. In a foray into the chemistry of gold, well known for its strong relativistic effects, investigations on different gold systems were performed. Analogies between Au$^+$ and platinum on one hand and oxygen on the other were found. New systems with multiple bonds to gold were proposed to experimentalists. One of the proposed systems was spectroscopically observed shortly afterwards. A very interesting molecule, which was theoretically predicted a few years ago is WAu$_{12}$. Some of its properties were calculated and the bonding situation was discussed. In a further study on gold compounds it was possible to explain the substitution pattern in bis[phosphane-gold(I)] thiocyanate complexes. This is of some help to experimentalists as the systems could not be crystallised and the structure was therefore unknown. Finally, computations on one of the heaviest elements in the periodic table were performed. Calculation on compounds containing element 110, darmstadtium, showed that it behaves similarly as its lighter homologue platinum. The extreme importance of relativistic effects for these systems was also shown.

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.

The Catholic Internet discussion on cloning : A study in cognitive rhetoric

This work combines the cognitive theory of folk-theoretical thought with the classical Aristotelian theory of artistic proof in rhetoric. The first half of the work discusses the common ground shared by the elements of artistic proof (logos, pathos, ethos) and the elements of folk-theoretical thought (naïve physics, folk biology, folk psychology, naïve sociology). Combining rhetoric with the cognitive theory of folk-theoretical thought creates a new point of view for argumentation analysis. The logos of an argument can be understood as the inferential relations established between the different parts of an argument. Consequently, within this study the analysis of logos is to be viewed as the analysis of the inferential folk-theoretical elements that make the suggested factual states-of-things appear plausible within given argumentative structures. The pathos of an argumentative structure can be understood as determining the quality of the argumentation in question in the sense that emotive elements play a great part in what can be called a distinction between good and deceptive rhetoric. In the context of this study the analysis of pathos is to be viewed as the analysis of the emotive content of argumentative structures and of whether they aim at facilitating surface- or deep cognitive elaboration of the suggested matters. The ethos of an argumentative structure means both the speaker-presentation and audience-construct that can be discerned within a body of argumentation. In the context of this study, the analysis of ethos is to be understood as the analysis of mutually manifest cognitive environments in the context of argumentation. The theory is used to analyse Catholic Internet discussion concerning cloning. The discussion is divided into six themes: Human Dignity, Sacred Family, Exploitation / Dehumanisation, Playing God, Monsters and Horror Scenarios and Ensoulment. Each theme is analysed for both the rhetorical and the cognitive elements that can be seen creating persuasive force within the argumentative structures presented. It is apparent that the Catholic voices on the Internet extensively oppose cloning. The voices utilise rhetoric that is aggressive and pejorative more often than not. Furthermore, deceptive rhetoric (in the sense presented above) plays a great part in argumentative structures of the Catholic voices. The theory of folk-theoretical thought can be seen as a useful tool for analysing the possible reasons why the Catholic speakers think about cloning and choose to present cloning in their argumentation as they do. The logos utilized in the argumentative structures presented can usually be viewed as based on folk-theoretical inference concerning biology and psychology. The structures of pathos utilized generally appear to aim at generating fear appeal in the assumed audiences, often incorporating counter-intuitive elements. The ethos utilised in the arguments generally revolves around Christian mythology and issues of social responsibility. These structures can also be viewed from the point of view of folk psychology and naïve sociological assumptions.

Characterisation, cloning and production of industrially interesting enzymes: gluconolactone oxidase of Penicillium cyaneo-fulvum and gluconate 5-dehydrogenase of Gluconobacter suboxydans

The work covered in this thesis is focused on the development of technology for bioconversion of glucose into D-erythorbic acid (D-EA) and 5-ketogluconic acid (5-KGA). The task was to show on proof-of-concept level the functionality of the enzymatic conversion or one-step bioconversion of glucose to these acids. The feasibility of both studies to be further developed for production processes was also evaluated. The glucose - D-EA bioconversion study was based on the use of a cloned gene encoding a D-EA forming soluble flavoprotein, D-gluconolactone oxidase (GLO). GLO was purified from Penicillium cyaneo-fulvum and partially sequenced. The peptide sequences obtained were used to isolate a cDNA clone encoding the enzyme. The cloned gene (GenBank accession no. AY576053) is homologous to the other known eukaryotic lactone oxidases and also to some putative prokaryotic lactone oxidases. Analysis of the deduced protein sequence of GLO indicated the presence of a typical secretion signal sequence at the N-terminus of the enzyme. No other targeting/anchoring signals were found, suggesting that GLO is the first known lactone oxidase that is secreted rather than targeted to the membranes of the endoplasmic reticulum or mitochondria. Experimental evidence supports this analysis, as near complete secretion of GLO was observed in two different yeast expression systems. Highest expression levels of GLO were obtained using Pichia pastoris as an expression host. Recombinant GLO was characterised and the suitability of purified GLO for the production of D-EA was studied. Immobilised GLO was found to be rapidly inactivated during D-EA production. The feasibility of in vivo glucose - D-EA conversion using a P. pastoris strain co-expressing the genes of GLO and glucose oxidase (GOD, E.C. 1.1.3.4) of A. niger was demonstrated. The glucose - 5-KGA bioconversion study followed a similar strategy to that used in the D-EA production research. The rationale was based on the use of a cloned gene encoding a membrane-bound pyrroloquinoline quinone (PQQ)-dependent gluconate 5-dehydrogenase (GA 5-DH). GA 5-DH was purified to homogeneity from the only source of this enzyme known in literature, Gluconobacter suboxydans, and partially sequenced. Using the amino acid sequence information, the GA 5-DH gene was cloned from a genomic library of G. suboxydans. The cloned gene was sequenced (GenBank accession no. AJ577472) and found to be an operon of two adjacent genes encoding two subunits of GA 5-DH. It turned out that GA 5-DH is a rather close homologue of a sorbitol dehydrogenase from another G. suboxydans strain. It was also found that GA 5-DH has significant polyol dehydrogenase activity. The G. suboxydans GA 5-DH gene was poorly expressed in E. coli. Under optimised conditions maximum expression levels of GA 5-DH did not exceed the levels found in wild-type G. suboxydans. Attempts to increase expression levels resulted in repression of growth and extensive cell lysis. However, the expression levels were sufficient to demonstrate the possibility of bioconversion of glucose and gluconate into 5-KGA using recombinant strains of E. coli. An uncharacterised homologue of GA 5-DH was identified in Xanthomonas campestris using in silico screening. This enzyme encoded by chromosomal locus NP_636946 was found by a sequencing project of X. campestris and named as a hypothetical glucose dehydrogenase. The gene encoding this uncharacterised enzyme was cloned, expressed in E. coli and found to encode a gluconate/polyol dehydrogenase without glucose dehydrogenase activity. Moreover, the X. campestris GA 5-DH gene was expressed in E. coli at nearly 30 times higher levels than the G. suboxydans GA 5-DH gene. Good expressability of the X. campestris GA-5DH gene makes it a valuable tool not only for 5-KGA production in the tartaric acid (TA) bioprocess, but possibly also for other bioprocesses (e.g. oxidation of sorbitol into L-sorbose). In addition to glucose - 5-KGA bioconversion, a preliminary study of the feasibility of enzymatic conversion of 5-KGA into TA was carried out. Here, the efficacy of the first step of a prospective two-step conversion route including a transketolase and a dehydrogenase was confirmed. It was found that transketolase convert 5-KGA into TA semialdehyde. A candidate for the second step was suggested to be succinic dehydrogenase, but this was not tested. The analysis of the two subprojects indicated that bioconversion of glucose to TA using X. campestris GA 5-DH should be prioritised first and the process development efforts in future should be focused on development of more efficient GA 5-DH production strains by screening a more suitable production host and by protein engineering.

Positional cloning and pathway analysis of the asthma susceptibility gene, NPSR1

In the present study, we identified a novel asthma susceptibility gene, NPSR1 (neuropeptide S receptor 1) on chromosome 7p14.3 by the positional cloning strategy. An earlier significant linkage mapping result among Finnish Kainuu asthma families was confirmed in two independent cohorts: in asthma families from Quebec, Canada and in allergy families from North Karelia, Finland. The linkage region was narrowed down to a 133-kb segment by a hierarchial genotyping method. The observed 77-kb haplotype block showed 7 haplotypes and a similar risk and nonrisk pattern in all three populations studied. All seven haplotypes occur in all three populations at frequences > 2%. Significant elevated relative risks were detected for elevated total IgE (immunoglobulin E) or asthma. Risk effects of the gene variants varied from 1.4 to 2.5. NPSR1 belongs to the G protein-coupled receptor (GPCR) family with a topology of seven transmembrane domains. NPSR1 has 9 exons, with the two main transcripts, A and B, encoding proteins of 371 and 377 amino acids, respectively. We detected a low but ubiquitous expression level of NPSR1-B in various tissues and endogenous cell lines while NPSR1-A has a more restricted expression pattern. Both isoforms were expressed in the lung epithelium. We observed aberrant expression levels of NPSR1-B in smooth muscle in asthmatic bronchi as compared to healthy. In an experimental mouse model, the induced lung inflammation resulted in elevated Npsr1 levels. Furthermore, we demonstrated that the activation of NPSR1 with its endogenous agonist, neuropeptide S (NPS), resulted in a significant inhibition of the growth of NPSR1-A overexpressing stable cell lines (NPSR1-A cells). To determine which target genes were regulated by the NPS-NPSR1 pathway, NPSR1-A cells were stimulated with NPS, and differentially expressed genes were identified using the Affymetrix HGU133Plus2 GeneChip. A total of 104 genes were found significantly up-regulated and 42 down-regulated 6 h after NPS administration. The up-regulated genes included many neuronal genes and some putative susceptibility genes for respiratory disorders. By Gene Ontology enrichment analysis, the biological process terms, cell proliferation, morphogenesis and immune response were among the most altered. The expression of four up-regulated genes, matrix metallopeptidase 10 (MMP10), INHBA (activin A), interleukin 8 (IL8) and EPH receptor A2 (EPHA2), were verified and confirmed by quantitative reverse-transcriptase-PCR. In conclusion, we identified a novel asthma susceptibility gene, NPSR1, on chromosome 7p14.3. NPS-NPSR1 represents a novel pathway that regulates cell proliferation and immune responses, and thus may have functional relevance in the pathogenesis of asthma.