  We demonstrate numerically that non-Abelian quasihole excitations of the $\nu
= 5/2$ fractional quantum Hall state have some of the key properties necessary
to support quantum computation. We find that as the quasihole spacing is
increased, the unitary transformation which describes winding two quasiholes
around each other converges exponentially to its asymptotic limit and that the
two orthogonal wavefunctions describing a system with four quasiholes become
exponentially degenerate. We calculate the length scales for these two decays
to be $\xi_{U} \approx 2.7 \ell_0$ and $\xi_{E} \approx 2.3 \ell_0$
respectively. Additionally we determine which fusion channel is lower in energy
when two quasiholes are brought close together.
