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Universal Quantum Computation with the nu=5/2 Fractional Quantum Hall State

Sergey Bravyi
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Abstract

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 $L(\log L)^3$.

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Sergey Bravyi. 2005-11-17. Universal Quantum Computation with the nu=5/2 Fractional Quantum Hall State. https://doi.org/10.1103/physreva.73.042313

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