Simulation of Projective Non-Abelian Anyons for Quantum Computation

Fundamental particles in nature can be classified as bosons or fermions, which satisfy their correspondent statistics. However, quasiparticles of condensed matter physics may be neither bosons nor fermions, but can be named as anyons satisfying a generalized statistics. These anyons can be related with topological phases of matter.Interestingly, anyons can be used to encode qubits to perform quantum computations with specific advantages in which the corresponding qubits are naturally fault tolerant due to topological protection.[1,2]This approach is called topological quantum computation. However, its implementation based on natural systems still seems far from realization.