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We consider topological quantum computation (TQC) with a particular class ofanyons that are believed to exist in the Fractional Quantum Hall Effect stateat Landau level filling fraction nu=5/2. Since the braid group representationdescribing statistics of these anyons is not computationally universal, onecannot directly apply the standard TQC technique. We propose to use very noisynon-topological operations such as direct short-range interaction betweenanyons to simulate a universal set of gates. Assuming that all TQC operationsare implemented perfectly, we prove that the threshold error rate fornon-topological operations is above 14%. The total number of non-topologicalcomputational elements that one needs to simulate a quantum circuit with $L$gates scales as $L(\log L)^3$.Comment: 17 pages, 12 eps figure

physical review. a, atomic, molecular, and optical physics/physical review, a, atomic, molecular, and optical physics

Universal quantum computation with the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>ν</mml:mi><mml:mo>=</mml:mo><mml:mn>5</mml:mn><mml:mo>∕</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math>fractional quantum Hall state

Universal quantum computation with theν=5∕2fractional quantum Hall state