1. A method for performing quantum computation, the method comprising: identifying a first quantum state of a lattice, the lattice comprising a system of real particles; moving within a 2D+1-dimensional space-time of the lattice non-Abelian excitations of least energy states of the system of real particles; identifying a second quantum state of the lattice after the excitations have been moved; and determining a computational result based on the first and second quantum states of the lattice.