Non-Abelian braiding of Majorana time crystals

ABSTRACT

Time crystals are a new phase matter exhibiting spontaneouslybrokentime translational symmetry. In time periodic systems, the so called discrete time crystals are marked by the existence of a physical observable showing a rigid periodicity in time at period integer times larger than that of the Hamiltonian. While such discrete time crystals have been extensively studied and even successfully observed in two recent experiments, their potential applications have remained unexplored up to this date. In this paper, we fill in this gap by proposing a scheme which allows the manipulation of a particular type of discrete time crystals, termed `Majorana time crystals', in a single superconducting wire. Such a scheme is shown to be robust against disorders and imperfections in the system parameters. Remarkably, due to the emergence of time lattice in the system, it may lead to non-Abelian braiding of two Majoranas which are separated in time. We find that the same scheme also allows the generation of a magic state, which constitutes the missing building block for universal quantum computation. Our results thus show a fascinating means to harness the extra time dimension offered by discrete time crystals with potential applications in topological quantum computation.