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%.