There is much current interest in the possibility of using "topological qubits", in principle protected from environmental decoherence, for quantum computation. The 5/2 FQHE state is believed to be a non-Abelian quantum Hall state with suitable  "non-Abelian statistics" quasi particles with extra qubit degrees of freedom. Finite-size numerical calculations based on projection into the lowest Landau level have been very valuable for investigating  homogeneous FQHE states, but have not been able to be used for studies of inhomogeneous systems.   I will describe new results on the Hilbert space of  fractional  (Abelian and non-Abelian) statistics FQHE  quasiholes that allow it to be systematically constructed.   Projection into this Hilbert subspace generalizes projection into the lowest Landau level, and makes possible  inhomogeneous finite-size calculations describing quasiholes dragged around by probes, etc., as proposed for topological qubit manipulation.   A remarkably simple "generalized Pauli principle" description of the quasihole Hilbert space emerges.

Last updated on Tuesday, 18 April 2006 by Victor Yakovenko