Topological superconductors are known to harbor Majorana bound states at their boundaries and inside vortex cores. Their non local properties and non-Abelian exchange statistics make Majorana bound states potential candidates in fault tolerant quantum computational schemes. Recently it has been pointed out that interacting topological superconductors support even more exotic non-Abelian excitations, that may allow to perform universal quantum computation in a manner that is inherently protected against common sources of decoherence. However, the setups that have been proposed to reveal these interacting topological phases are hard to realize experimentally. The theoretical research outlined in this proposal is expected to identify new experimental realizations of interacting topological superconductors, to establish the unique properties of their emergent end states and the way in which they manifest in experiments, in order to facilitate their detection. The novel approach that lies at the foundation of this proposal is the study of an open interacting system by coupling it to external leads, and the use of scattering theory of the open system to establish its topological classification. If successful, this research may single out the most promising experimental setup that supports fractional non-Abelian end states, thus constituting an important leap forward in the strive to implement topologically protected quantum computation.
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