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.

Comprehensive Two-Dimensional Gas Chromatography: Instrumental and Methodological Development

Comprehensive two-dimensional gas chromatography (GC×GC) offers enhanced separation efficiency, reliability in qualitative and quantitative analysis, capability to detect low quantities, and information on the whole sample and its components. These features are essential in the analysis of complex samples, in which the number of compounds may be large or the analytes of interest are present at trace level. This study involved the development of instrumentation, data analysis programs and methodologies for GC×GC and their application in studies on qualitative and quantitative aspects of GC×GC analysis. Environmental samples were used as model samples. Instrumental development comprised the construction of three versions of a semi-rotating cryogenic modulator in which modulation was based on two-step cryogenic trapping with continuously flowing carbon dioxide as coolant. Two-step trapping was achieved by rotating the nozzle spraying the carbon dioxide with a motor. The fastest rotation and highest modulation frequency were achieved with a permanent magnetic motor, and modulation was most accurate when the motor was controlled with a microcontroller containing a quartz crystal. Heated wire resistors were unnecessary for the desorption step when liquid carbon dioxide was used as coolant. With use of the modulators developed in this study, the narrowest peaks were 75 ms at base. Three data analysis programs were developed allowing basic, comparison and identification operations. Basic operations enabled the visualisation of two-dimensional plots and the determination of retention times, peak heights and volumes. The overlaying feature in the comparison program allowed easy comparison of 2D plots. An automated identification procedure based on mass spectra and retention parameters allowed the qualitative analysis of data obtained by GC×GC and time-of-flight mass spectrometry. In the methodological development, sample preparation (extraction and clean-up) and GC×GC methods were developed for the analysis of atmospheric aerosol and sediment samples. Dynamic sonication assisted extraction was well suited for atmospheric aerosols collected on a filter. A clean-up procedure utilising normal phase liquid chromatography with ultra violet detection worked well in the removal of aliphatic hydrocarbons from a sediment extract. GC×GC with flame ionisation detection or quadrupole mass spectrometry provided good reliability in the qualitative analysis of target analytes. However, GC×GC with time-of-flight mass spectrometry was needed in the analysis of unknowns. The automated identification procedure that was developed was efficient in the analysis of large data files, but manual search and analyst knowledge are invaluable as well. Quantitative analysis was examined in terms of calibration procedures and the effect of matrix compounds on GC×GC separation. In addition to calibration in GC×GC with summed peak areas or peak volumes, simplified area calibration based on normal GC signal can be used to quantify compounds in samples analysed by GC×GC so long as certain qualitative and quantitative prerequisites are met. In a study of the effect of matrix compounds on GC×GC separation, it was shown that quality of the separation of PAHs is not significantly disturbed by the amount of matrix and quantitativeness suffers only slightly in the presence of matrix and when the amount of target compounds is low. The benefits of GC×GC in the analysis of complex samples easily overcome some minor drawbacks of the technique. The developed instrumentation and methodologies performed well for environmental samples, but they could also be applied for other complex samples.

Stock Option Compensation in Finland: An Analysis of Economic Determinants, Contracting Frequency, and Design

This paper addresses several questions in the compensation literature by examining stock option compensation practices of Finnish firms. First, the results indicate that principal-agent theory succeeds quite well in predicting the use of stock options. Proxies for monitoring costs, growth opportunities, ownership structure, and risk are found to determine the use of incentives consistent with theory. Furthermore, the paper examines whether determinants of stock options targeted to top management differ from determinants of broad-based stock option plans. Some evidence is found that factors driving these two types of incentives differ. Second, the results reveal that systematic risk significantly increases the likelihood that firms adopt stock option plans, whereas total firm risk and unsystematic risk do not seem to affect this decision. Third, the results show that growth opportunities are related to time-dimensional contracting frequency, consistent with the argument that incentive levels deviate more rapidly from optimum in firms with high growth opportunities. Finally, the results suggest that vesting schedules are decreasing in financial leverage, and that contract maturity is decreasing in firm focus. In addition, both vesting schedules and contract maturity tend to be longer in firms involving state ownership.