Numerical Analysis of Quasiholes of the Moore-Read Wave Function

We demonstrate numerically that non-Abelian quasihole (qh) excitations of the ν=5/2 fractional quantum Hall state have some of the key properties necessary to support quantum computation. We find that as the qh spacing is increased, the unitary transformation which describes winding two qh’s around each other converges exponentially to its asymptotic limit and that the two orthogonal wave functions describing a system with four qh’s become exponentially degenerate. We calculate the length scales for these two decays to be ξ_U≈2.7ℓ₀ and ξ_E≈2.3ℓ₀, respectively. Additionally, we determine which fusion channel is lower in energy when two qh’s are brought close together.