Non-Abelian Braiding of Lattice Bosons

Abstract

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