Superconductors and superfluids have ever since their discovery been of great academic interest in physics. This is reflected by the fact that twenty people have been awarded Nobel prizes for studying such systems during the last century. The 2016 Nobel Prize in physics was given for the first works on topological phase transitions in superfluids and topological states of matter. Such phase transitions are driven by proliferation of topological defects or vortices -- a feature shared by many of the systems investigated in this project. More recently it was realized that superconductors are the best topological materials that can be used to build qubits for quantum computation. This started the pursuit to use these states for implementation of qubits for quantum computers and quantum emulators, which forms a growing part part of this project. Another aspect of our research direction is the physics of multicomponent systems. In recent years there was a number of experimental breakthroughs in condensed-matter systems which exhibit multi-component many-body degrees of freedom, making it a rich emergent field of research. As a consequence of having several types of carriers responsive for superconductivity, these materials behave fundamentally differently from traditional superconductors. These superconducting states require theoretical understanding from the fundamental viewpoint, and also in order to use such materials in practical applications which we plan to address in the project.