| Abstract: | We study the non-abelian statistics characterizing systems where
counter-propagating gapless modes on the edges of fractional quantum
Hall states are gapped by proximity-coupling to superconductors and
ferromagnets. We find that each interface between a region on the
edge coupled to a superconductor and a region coupled to a ferromagnet
corresponds to a non-abelian anyon of quantum dimension $\sqrt{2m}$,
where $1/m$ is the filling fraction of the quantum Hall states. We
calculate the unitary transformations that are associated with
braiding of these anyons, and show that they are able to realize a
richer set of non-abelian representations of the braid group than the
set realized by non-abelian anyons based on Majorana fermions. We
carry out this calculation both explicitly and by applying general
considerations. Finally, we show that topological manipulations with
these anyons cannot realize universal quantum computation.
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