1. A method for performing quantum computation, the method comprising: providing a lattice comprising a system of real particles, the lattice having an energy operator that consists of only physically-natural terms such that first and second non-Abelian anyons emerge on the lattice as excitations of the system of real particles that form the lattice; moving the first non-Abelian anyon along a first path within the lattice, and moving the second non-Abelian anyon along a second path within the lattice, the first and second paths forming a predetermined braid in the 2D+1-dimensional space-time of the lattice; and determining a computational result from the braid after moving each non-Abelian anyon along its associated path.