Topological properties of superconducting nanostructures

One of the pillars of the scientific method is the fact that... Oh wait, it’s a different one. One of the pillars of the technological development is the fact that if the existing design does not achieve the goal or cannot be applied in new conditions, one could propose a totally different design that may achieve the goal. The only constraints in this way being the laws of physics. This is the main message of the lecture by Richard Feynman on tiny machines. The role of different designs can also be noted on a purely theoretical level. There, changing the well-known model can have far reaching consequences on its properties and possible applications.
One of the main goals in the focus of modern quantum technology is realization of a quantum computer. The appeal of this device is in the difference from the classical analogous computer, being reasonable proposals for error correction. Another aspect is that one may use topological quantum states that are robust by themselves against certain noises. There is a lot of effort in trying different approaches and designs to experimentally realize and detect these states. Two main approaches are to either realize topological compounds or combine topologically trivial compounds to effectively realize non-trivial topological properties. There have been advances in both topological and non-topological quantum computation. One of the most famous examples being the achieved quantum supremacy (or, after censorship, quantum advantage). Despite that, the technology is still far away from being used at home. Also, during the process of development of technology other things may come about on the way. Anyhow, regardless of the outcome, the way itself is always more important than the resulting point. In this thesis we discuss certain theoretical findings discovered on the way.