Fractionalized flux, Majorana fermions and non-Abelian anyons in topological superfluid on optical lattices

Recently, topological excitations obeying non-Abelian statistics attracted intensive attention because of their exotic statistics and possible applications in topological quantum computation. In this paper, based on a topological s-wave superfluid on a Peierls lattice, we find fractionalized flux and non-Abelian anyons, and then give a realistic proposal to realize the universal topological quantum computation, and especially show how to perform the single-qubit gate–phase-shift gate. Finally, we discuss the experimental realization on optical lattices