The fundamental difference between fermions and bosons underlies many physical phenomena. In two-dimensional systems quasi-particles may exist that are neither fermions nor bosons. When these particles are interchanged, their joint quantum mechanical wave function is predicted to pick up any phase in between 0 (as for bosons) and pi (as for fermions), hence the name anyons. Even more intriguing is the class of non-Abelian anyons where interchange of particles completely changes the ground state of the system. This phenomenon lies at the heart of a wealth of theoretical proposals for new types of quantum statistics, quantum teleportation, and topological quantum computation that is robust against decoherence. In my ERC project we aim to experimentally realize a platform to detect and control non-Abelian anyons by combining the particle-hole symmetry of a superconductor with the spin-momentum locking at the surface of a topological insulator.