  Recently a pair of experiments demonstrated a simulation of Abelian anyons in
a spin network of single photons. The experiments were based on an Abelian
discrete gauge theory spin lattice model of Kitaev. Here we describe how to use
linear optics and single photons to simulate non-Abelian anyons. The scheme
makes use of joint qutrit-qubit encoding of the spins and the resources
required are three pairs of parametric down converted photons and 14 beam
splitters.
