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Anyons from nonsolvable finite groups are sufficient for universal quantum computation

Mochon, Carlos (2003) Anyons from nonsolvable finite groups are sufficient for universal quantum computation. Physical Review A, 67 (2). Art. No. 022315. ISSN 1050-2947. doi:10.1103/PhysRevA.67.022315.

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We present a constructive proof that anyonic magnetic charges with fluxes in a nonsolvable finite group can perform universal quantum computations. The gates are built out of the elementary operations of braiding, fusion, and vacuum pair creation, supplemented by a reservoir of ancillas of known flux. Procedures for building the ancilla reservoir and for correcting leakage are also described. Finally, a universal qudit gate set, which is ideally suited for anyons, is presented. The gate set consists of classical computation supplemented by measurements of the X operator.

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Additional Information:©2003 The American Physical Society (Received 1 October 2002; published 28 February 2003) The idea for universal classical computation with simple and perfect groups was initially suggested by Alexei Kitaev, to whom I am highly grateful. The author would also like to thank John Preskill, Jim Harrington, Meg Wessling, and James Chakan. This work was supported in part by the National Science Foundation under Grant No. EIA-0086038 and by the Department of Energy under Grant No. DE-FG03-92-ER40701.
Subject Keywords:quantum computing; quantum theory; anyons
Issue or Number:2
Record Number:CaltechAUTHORS:MOCpra03
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3908
Deposited By: Archive Administrator
Deposited On:18 Jul 2006
Last Modified:08 Nov 2021 20:13

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