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.

Capillary electrochromatography: a versatile instrumental technique for nanodomain interaction studies

This doctoral thesis describes the development of a miniaturized capillary electrochromatography (CEC) technique suitable for the study of interactions between various nanodomains of biological importance. The particular focus of the study was low-density lipoprotein (LDL) particles and their interaction with components of the extracellular matrix (ECM). LDL transports cholesterol to the tissues through the blood circulation, but when the LDL level becomes too high the particles begin to permeate and accumulate in the arteries. Through binding sites on apolipoprotein B-100 (apoB-100), LDL interacts with components of the ECM, such as proteoglycans (PGs) and collagen, in what is considered the key mechanism in the retention of lipoproteins and onset of atherosclerosis. Hydrolytic enzymes and oxidizing agents in the ECM may later successively degrade the LDL surface. Metabolic diseases such as diabetes may provoke damage of the ECM structure through the non-enzymatic reaction of glucose with collagen. In this work, fused silica capillaries of 50 micrometer i.d. were successfully coated with LDL and collagen, and steroids and apoB-100 peptide fragments were introduced as model compounds for interaction studies. The LDL coating was modified with copper sulphate or hydrolytic enzymes, and the interactions of steroids with the native and oxidized lipoproteins were studied. Lipids were also removed from the LDL particle coating leaving behind an apoB-100 surface for further studies. The development of collagen and collagen decorin coatings was helpful in the elucidation of the interactions of apoB-100 peptide fragments with the primary ECM component, collagen. Furthermore, the collagen I coating provided a good platform for glycation studies and for clarification of LDL interactions with native and modified collagen. All methods developed are inexpensive, requiring just small amounts of biomaterial. Moreover, the experimental conditions in CEC are easily modified, and the analyses can be carried out in a reasonable time frame. Other techniques were employed to support and complement the CEC studies. Scanning electron microscopy and atomic force microscopy provided crucial visual information about the native and modified coatings. Asymmetrical flow field-flow fractionation enabled size measurements of the modified lipoproteins. Finally, the CEC results were exploited to develop new sensor chips for a continuous flow quartz crystal microbalance technique, which provided complementary information about LDL ECM interactions. This thesis demonstrates the potential of CEC as a valuable and flexible technique for surface interaction studies. Further, CEC can serve as a novel microreactor for the in situ modification of LDL and collagen coatings. The coatings developed in this study provide useful platforms for a diversity of future investigations on biological nanodomains.

Parity violation in molecular magnetic resonance properties

The Standard Model of particle physics consists of the quantum electrodynamics (QED) and the weak and strong nuclear interactions. The QED is the basis for molecular properties, and thus it defines much of the world we see. The weak nuclear interaction is responsible for decays of nuclei, among other things, and in principle, it should also effects at the molecular scale. The strong nuclear interaction is hidden in interactions inside nuclei. From the high-energy and atomic experiments it is known that the weak interaction does not conserve parity. Consequently, the weak interaction and specifically the exchange of the Z^0 boson between a nucleon and an electron induces small energy shifts of different sign for mirror image molecules. This in turn will make the other enantiomer of a molecule energetically favorable than the other and also shifts the spectral lines of the mirror image pair of molecules into different directions creating a split. Parity violation (PV) in molecules, however, has not been observed. The topic of this thesis is how the weak interaction affects certain molecular magnetic properties, namely certain parameters of nuclear magnetic resonance (NMR) and electron spin resonance (ESR) spectroscopies. The thesis consists of numerical estimates of NMR and ESR spectral parameters and investigations of the effects of different aspects of quantum chemical computations to them. PV contributions to the NMR shielding and spin-spin coupling constants are investigated from the computational point of view. All the aspects of quantum chemical electronic structure computations are found to be very important, which makes accurate computations challenging. Effects of molecular geometry are also investigated using a model system of polysilyene chains. PV contribution to the NMR shielding constant is found to saturate after the chain reaches a certain length, but the effects of local geometry can be large. Rigorous vibrational averaging is also performed for a relatively small and rigid molecule. Vibrational corrections to the PV contribution are found to be only a couple of per cents. PV contributions to the ESR g-tensor are also evaluated using a series of molecules. Unfortunately, all the estimates are below the experimental limits, but PV in some of the heavier molecules comes close to the present day experimental resolution.

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 role of productivity in the ecological and evolutionary dynamics of predator-prey interaction

Productivity is predicted to drive the ecological and evolutionary dynamics of predator-prey interaction through changes in resource allocation between different traits. However, resources are seldom constantly available and thus temporal variation in productivity could have considerable effect on the species' potential to evolve. To study this, three long-term microbial laboratory experiments were established where Serratia marcescens prey bacteria was exposed to predation of protist Tetrahymena thermophila in different prey resource environments. The consequences of prey resource availability for the ecological properties of the predator-prey system, such as trophic dynamics, stability, and virulence, were determined. The evolutionary changes in species traits and prey genetic diversity were measured. The prey defence evolved stronger in high productivity environment. Increased allocation to defence incurred cost in terms of reduced prey resource use ability, which probably constrained prey evolution by increasing the effect of resource competition. However, the magnitude of this trade-off diminished when measured in high resource concentrations. Predation selected for white, non-pigmented, highly defensive prey clones that produced predation resistant biofilm. The biofilm defence was also potentially accompanied with cytotoxicity for predators and could have been traded off with high motility. Evidence for the evolution of predators was also found in one experiment suggesting that co-evolutionary dynamics could affect the evolution and ecology of predator-prey interaction. Temporal variation in resource availability increased variation in predator densities leading to temporally fluctuating selection for prey defences and resource use ability. Temporal variation in resource availability was also able to constrain prey evolution when the allocation to defence incurred high cost. However, when the magnitude of prey trade-off was small and the resource turnover was periodically high, temporal variation facilitated the formation of predator resistant biofilm. The evolution of prey defence constrained the transfer of energy from basal to higher trophic levels, decreasing the strength of top-down regulation on prey community. Predation and temporal variation in productivity decreased the stability of populations and prey traits in general. However, predation-induced destabilization was less pronounced in the high productivity environment where the evolution of prey defence was stronger. In addition, evolution of prey defence weakened the environmental variation induced destabilization of predator population dynamics. Moreover, protozoan predation decreased the S. marcescens virulence in the insect host moth (Parasemia plantaginis) suggesting that species interactions outside the context of host-pathogen relationship could be important indirect drivers for the evolution of pathogenesis. This thesis demonstrates that rapid evolution can affect various ecological properties of predator-prey interaction. The effect of evolution on the ecological dynamics depended on the productivity of the environment, being most evident in the constant environments with high productivity.

Outer Membrane Protease/Adhesin PgtE of Salmonella enterica: Role in Salmonella-Host Interaction

Salmonella enterica serovar Typhimurium is a common cause of gastroenteritis in humans and, occasionally, also causes systemic infection. During systemic infection an important characteristic of Salmonella is its ability to survive and replicate within macrophages. The outer membrane protease PgtE of S. enterica is a member of the omptin family of outer membrane aspartate proteases, which are beta-barrel proteins with five surface-exposed loops. The main goals of this study were to characterize biological substrates and pathogenesis-associated functions of PgtE and to determine the conditions where PgtE is fully active. In this study we found that PgtE requires rough lipopolysaccharide (LPS) to be functional but is sterically inhibited by the long O-antigen side chain in smooth LPS. Salmonella isolates normally are smooth with a long oligosaccharide O-antigen, and PgtE remains functionally cryptic in wild-type Salmonella cultivated in vitro. Interestingly, our results showed that due to increased expression of PgtE and to reduced length of the LPS O-antigen chains, the wild-type Salmonella expresses highly functional PgtE when isolated from mouse macrophage-like J774A.1 cells. Salmonella is thought to be continuously released from macrophages to infect new ones, and our results suggest that PgtE is functional during these transient extracellular growth phases. Six novel host protein substrates were identified for PgtE in this work. PgtE was previously known to activate human plasminogen (Plg) to plasmin, a broad-spectrum serine protease, and in this study PgtE was shown to interfere with the Plg system by inactivating the main inhibitor of plasmin, alpha2-antiplasmin. PgtE also interferes with another important proteolytic system of mammals by activating pro-matrix metalloproteinase-9 to an active gelatinase. PgtE also directly degrades gelatin, a component of extracellular matrices. PgtE also increases bacterial resistance against complement-mediated killing in human serum and enhances survival of Salmonella within murine macrophages as well as in the liver and spleen of intraperitoneally infected mice. Taken together, the results in this study suggest that PgtE is a virulence factor of Salmonella that has adapted to interfere with host proteolytic systems and to modify extracellular matrix; these features likely assist the migration of Salmonella during systemic salmonellosis.

Characterization of inhibition of platelet function by paracetamol and its interaction with diclofenac and parecoxib

Aim: To characterize the inhibition of platelet function by paracetamol in vivo and in vitro, and to evaluate the possible interaction of paracetamol and diclofenac or valdecoxib in vivo. To assess the analgesic effect of the drugs in an experimental pain model. Methods: Healthy volunteers received increasing doses of intravenous paracetamol (15, 22.5 and 30 mg/kg), or the combination of paracetamol 1 g and diclofenac 1.1 mg/kg or valdecoxib 40 mg (as the pro-drug parecoxib). Inhibition of platelet function was assessed with photometric aggregometry, the platelet function analyzer (PFA-100), and release of thromboxane B2. Analgesia was assessed with the cold pressor test. The inhibition coefficient of platelet aggregation by paracetamol was determined as well as the nature of interaction between paracetamol and diclofenac by an isobolographic analysis in vitro. Results: Paracetamol inhibited platelet aggregation and TxB2-release dose-dependently in volunteers and concentration-dependently in vitro. The inhibition coefficient was 15.2 mg/L (95% CI 11.8 - 18.6). Paracetamol augmented the platelet inhibition by diclofenac in vivo, and the isobole showed that this interaction is synergistic. Paracetamol showed no interaction with valdecoxib. PFA-100 appeared insensitive in detecting platelet dysfunction by paracetamol, and the cold-pressor test showed no analgesia. Conclusions: Paracetamol inhibits platelet function in vivo and shows synergism when combined with diclofenac. This effect may increase the risk of bleeding in surgical patients with an impaired haemostatic system. The combination of paracetamol and valdecoxib may be useful in patients with low risk for thromboembolism. The PFA-100 seems unsuitable for detection of platelet dysfunction and the cold-pressor test seems unsuitable for detection of analgesia by paracetamol.

Interaction of alcohol and smoking in the pathogenesis of upper digestive tract cancers - possible chemoprevention with cysteine

Background: Alcohol consumption and smoking are the main causes of upper digestive tract cancers. These risk factors account for over 75% of all cases in developed countries. Epidemiological studies have shown that alcohol and tobacco interact in a multiplicative way to the cancer risk, but the pathogenetic mechanism behind this is poorly understood. Strong experimental and human genetic linkage data suggest that acetaldehyde is one of the major factors behind the carcinogenic effect. In the digestive tract, acetaldehyde is mainly formed by microbial metabolism of ethanol. Acetaldehyde is also a major constituent of tobacco smoke. Thus, acetaldehyde from both of these sources may have an interacting carcinogenic effect in the human upper digestive tract. Aims: The first aim of this thesis was to investigate acetaldehyde production and exposure in the human mouth resulting from alcohol ingestion and tobacco smoking in vivo. Secondly, specific L-cysteine products were prepared to examine their efficacy in the binding of salivary acetaldehyde in order to reduce the exposure of the upper digestive tract to acetaldehyde. Methods: Acetaldehyde levels in saliva were measured from human volunteers during alcohol metabolism, during tobacco smoking and during the combined use of alcohol and tobacco. The ability of L-cysteine to eliminate acetaldehyde during alcohol metabolism and tobacco smoking was also investigated with specifically developed tablets. Also the acetaldehyde production of Escherichia coli - an important member of the human microbiota - was measured in different conditions prevailing in the digestive tract. Results and conclusions: These studies established that smokers have significantly increased acetaldehyde exposure during ethanol consumption even when not actively smoking. Acetaldehyde exposure was dramatically further increased during active tobacco smoking. Thus, the elevated aerodigestive tract cancer risk observed in smokers and drinkers may be the result of the increased acetaldehyde exposure. Acetaldehyde produced in the oral cavity during ethanol challenge was significantly decreased by a buccal L-cysteine -releasing tablet. Also smoking-derived acetaldehyde could be totally removed by using a tablet containing L-cysteine. In conclusion, this thesis confirms the essential role of acetaldehyde in the pathogenesis of alcohol- and smoking-induced cancers. This thesis presents a novel experimental approach to decrease the local acetaldehyde exposure of the upper digestive tract with L-cysteine, with the eventual goal of reducting the prevalence of upper digestive tract cancers.