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Universal quantum computation with the v=5/2 fractional quantum Hall state

Bravyi, Sergey (2006) Universal quantum computation with the v=5/2 fractional quantum Hall state. Physical Review A, 73 (4). Art. No. 042313. ISSN 1050-2947. doi:10.1103/PhysRevA.73.042313.

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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 v =5/2. Since the braid group representation describing the statistics of these anyons is not computationally universal, one cannot directly apply the standard TQC technique. We propose to use very noisy nontopological operations such as direct short-range interactions 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 nontopological operations is above 14%. The total number of nontopological computational elements that one needs to simulate a quantum circuit with L gates scales as L(ln L)to the 3rd.

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Additional Information:©2006 The American Physical Society. Received: 6 January 2006; published: 12 April 2006. Discussions with Alexei Kitaev and Robert Raussendorf are gratefully acknowledged. The author would like to thank David DiVincenzo for a careful reading of this paper and Andrei Soklakov for useful comments concerning the magic-states distillation protocol. This research was carried out when the author was at the Institute for Quantum Information, Caltech, supported by the National Science Foundation under Grant No. EIA-0086038.
Subject Keywords:quantum computing; quantum Hall effect; quantum noise; information theory
Issue or Number:4
Record Number:CaltechAUTHORS:BRApra06
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5784
Deposited By: Lindsay Cleary
Deposited On:02 Nov 2006
Last Modified:08 Nov 2021 20:28

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