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I consider quantum computation with non-Abelian anyons in the simplest
realistic model corresponding to the fractional quantum Hall state at
the filling fraction 5/2. It is known that topological operations
(braiding and fusion of anyons) are not computationally universal in
this model. I demonstrate that universal set of gates can be reliably
simulated with additional very noisy non-topological operations (such
s direct short-range interaction between anyons) if the noise level
is below threshold value about 15%.
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