  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 $\nu$, 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 $\nu$ near $1$ and $3/2$, with Berry matrices respectively
consistent with Ising and Fibonacci anyons. Near $\nu=1/2$, the braids commute.
