  We consider topological quantum computation (TQC) with a particular class of
anyons that are believed to exist in the Fractional Quantum Hall Effect state
at Landau level filling fraction nu=5/2. Since the braid group representation
describing statistics of these anyons is not computationally universal, one
cannot directly apply the standard TQC technique. We propose to use very noisy
non-topological operations such as direct short-range interaction between
anyons to simulate a universal set of gates. Assuming that all TQC operations
are implemented perfectly, we prove that the threshold error rate for
non-topological operations is above 14%. The total number of non-topological
computational elements that one needs to simulate a quantum circuit with $L$
gates scales as $L(\log L)^3$.
