This paper treats the current progress in the research of superconducting quantum bits. It includes background theory in the two distinct fields of superconductivity and quantum bits and how these two research fields relate. Different designs of superconducting quantum bits are presented including the derivation of their respective Hamiltonian. Particular focus is put on the Cooper Pair Box-design and the Transmon-design with their structure more explained in detail and energy levels numerically calculated. The paper concludes by comparing the various designs in terms of sensitivity to outer disturbances. / Denna rapport behandlar forskningsframgångarna inom supraledande kvantbitar. Den innehåller bakgrundsteori i de två distinkta forskningsområdena supraledning och kvantbitar och hur de två relaterar till varandra. Olika varianter av supraledande kvantbitar presenteras inklusive härledningar av deras respektive Hamiltonianer. Särskild fokusläggs på Cooper Pair Box-designen och på Transmon-designen då deras strukturer förklaras mer i detalj och deras energinivåer beräknas numeriskt. Rapporten avslutas meden jämförelse mellan de olika varianternas känslighet mot yttre störningar.

In this thesis crackling systems have been investigated. Applying an external force on these systems they respond with events of all sizes. The size distribution follows a power law of the form S¯ <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Ctau" />. Dierent types appear in nature like avalanches or earthquakes. A magnet exposed to an external magnetic eld will "crackle" as well during its magnetization. Applying the Ising model on the system, a C++ code has been developed to simulate this process. The resulting data has been used to discuss the system with concepts of statistical mechanics like universality or scale invariance. Varying the level of impurity of the magnet, the disorder R, the system exhibits a continuous nonequilibrium phase transition. At its critical point RC the described power law behavior occurs. The critical exponent has been extracted fitting the histogram data with a power law curve. RC has been determined using the behavior of a scaling function for different values of R.

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