Mochon, Carlos (2004) Anyon computers with smaller groups. Physical Review A, 69 (3). Art. No. 032306. ISSN 1050-2947. doi:10.1103/PhysRevA.69.032306. https://resolver.caltech.edu/CaltechAUTHORS:MOCpra04a
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Abstract
Anyons obtained from a finite gauge theory have a computational power that depends on the symmetry group. The relationship between group structure and computational power is discussed in this paper. In particular, it is shown that anyons based on finite groups that are solvable but not nilpotent are capable of universal quantum computation. This extends previously published results to groups that are smaller and therefore more practical. Additionally, a new universal gate set is built out of an operation called a probabilistic projection, and a quasiuniversal leakage correction scheme is discussed.
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| Additional Information: | ©2004 The American Physical Society (Received 10 July 2003; published 11 March 2004) Much of this work is inspired by the construction of Alexei Kitaev, who showed that universal computation was possible with anyons based on the group S3. His construction used the magic state (1/sqrt3)(|0>-|1>-|2>) to build a qubit Toffoli gate. Many of the above ideas were captured by the unpublished notes of John Preskill. I am also indebted to Charlene Ahn and Ben Toner who were kind enough to read and review this paper. This work was supported in part by the National Science Foundation under Grant No. EIA-0086038 and by the U.S. Department of Energy under Grant No. DE-FG03-92-ER40701. | ||||||
| Subject Keywords: | anyons; gauge field theory; group theory; quantum gates; probability | ||||||
| Issue or Number: | 3 | ||||||
| DOI: | 10.1103/PhysRevA.69.032306 | ||||||
| Record Number: | CaltechAUTHORS:MOCpra04a | ||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:MOCpra04a | ||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
| ID Code: | 3906 | ||||||
| Collection: | CaltechAUTHORS | ||||||
| Deposited By: | Archive Administrator | ||||||
| Deposited On: | 18 Jul 2006 | ||||||
| Last Modified: | 08 Nov 2021 20:13 |
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