Non-Abelian Braiding of Lattice Bosons

We report on a numerical experiment in which we use time-dependent potentials to braid non-Abelian quasiparticles. We consider lattice bosons in a uniform magnetic field within the fractional quantum Hall regime, where v, the ratio of particles to flux quanta, is near 1/2, 1, or 3/2. We introduce time-dependent potentials which move quasiparticle excitations around one another, explicitly simulating a braiding operation which could implement part of a gate in a quantum computation. We find that different braids do not commute for v near 1 and 3/2, with Berry matrices, respectively, consistent with Ising and Fibonacci anyons. Near v = 1/2, the braids commute.