1. A system for performing quantum computation, the system comprising: a processor; and a storage device having instructions stored therein, the instructions, when executed by the processor, cause the processor to perform acts comprising: modeling a lattice having a system of non-Abelian anyons disposed thereon, the lattice comprising a system of particles, the non-Abelian anyons being excitations of least energy states of the system of particles that form the lattice, wherein each of the non-Abelian anyons is associated with a respective initial position in the lattice, wherein the lattice is modeled as a Kagome lattice comprising a plurality of hexagons, and wherein each hexagon contains exactly one particle, wherein each particle is a real, nonquasi-particle; identifying a first quantum state of the lattice; modeling movement of the non-Abelian anyons within a 2D+1 space-time of the lattice; identifying a second quantum state of the lattice after movement of the non-Abelian anyons has been modeled; and determining a computational result based on the first and second quantum states of the lattice model.