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 ν, 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 ν near 1 and 3/2, with Berry matrices respectively consistent with Ising and Fibonacci anyons. Near ν=1/2, the braids commute.
@article{arxiv.1109.4561,
title = {Non-Abelian Braiding of Lattice Bosons},
author = {Eliot Kapit and Paul Ginsparg and Erich Mueller},
journal= {arXiv preprint arXiv:1109.4561},
year = {2013}
}