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Topological Quantum Computation—From Basic Concepts to First Experiments

Ady Stern [email protected] and Netanel H. Lindner
Science • 8 Mar 2013 • Vol 339, Issue 6124 • pp. 1179-1184 • DOI: 10.1126/science.1231473
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Abstract

Quantum computation requires controlled engineering of quantum states to perform tasks that go beyond those possible with classical computers. Topological quantum computation aims to achieve this goal by using non-Abelian quantum phases of matter. Such phases allow for quantum information to be stored and manipulated in a nonlocal manner, which protects it from imperfections in the implemented protocols and from interactions with the environment. Recently, substantial progress in this field has been made on both theoretical and experimental fronts. We review the basic concepts of non-Abelian phases and their topologically protected use in quantum information processing tasks. We discuss different possible realizations of these concepts in experimentally available solid-state systems, including systems hosting Majorana fermions, their recently proposed fractional counterparts, and non-Abelian quantum Hall states.
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Science
Volume 339 | Issue 6124
8 March 2013

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Copyright © 2013, American Association for the Advancement of Science.

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Published in print: 8 March 2013

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Acknowledgments

We thank C. Nayak and J. Preskill for helpful discussions, and the Kavli Institute for Theoretical Physics for their hospitality. Supported by the U.S.-Israel Binational Science Foundation, the Minerva foundation, and Microsoft Station Q (A.S.); Defense Advanced Research Projects Agency award N66001-12-1-4034 and the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center, with support of the Gordon and Betty Moore Foundation (N.H.L.); and NSF grant PHY11-25915.

Authors

Affiliations

Ady Stern* [email protected]
Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel.
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Netanel H. Lindner
Institute of Quantum Information and Matter, California Institute of Technology, Pasadena, CA 91125, USA.
Department of Physics, California Institute of Technology, Pasadena, CA 91125, USA.
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Notes

*To whom correspondence should be addressed. E-mail: [email protected]

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