  Quantum computation provides a unique opportunity to explore new regimes of
physical systems through the creation of non-trivial quantum states far outside
of the classical limit. However, such computation is remarkably sensitive to
noise and undergoes rapid dephasing in most cases. One potential solution to
these prosaic concerns is to encode and process the information using
topological manipulations of so-called anyons, particles in two dimensions with
non-Abelian statistics. Unfortunately, practical implementation of such a
topological system remains far from complete, both in terms of physical methods
but also in terms of connecting the underlying topological field theory with a
specific physical model, including the imperfections expected in any realistic
device. Here we develop a complete picture of such topological quantum
computation using a variation of the Kitaev honeycomb Hamiltonian as the basis
for our approach. We show the robustness of this system against noise, confirm
the non-Abelian statistics of the quasi-particles to be Ising anyons, and
develop new techniques for turning topological information into measurable spin
quantities.
