Journal article
Non-Abelian anyons and topological quantum computation
Reviews of Modern Physics, Vol.80(3), pp.1083-1159
Jul/2008
Abstract
Topological quantum computation has emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as non-Abelian anyons, meaning that they obey non-Abelian braiding statistics. Quantum information is stored in states with multiple quasiparticles, which have a topological degeneracy. The unitary gate operations that are necessary for quantum computation are carried out by braiding quasiparticles and then measuring the multiquasiparticle states. The fault tolerance of a topological quantum computer arises from the nonlocal encoding of the quasiparticle states, which makes them immune to errors caused by local perturbations. To date, the only such topological states thought to have been found in nature are fractional quantum Hall states, most prominently the nu=5/2 state, although several other prospective candidates have been proposed in systems as disparate as ultracold atoms in optical lattices and thin-film superconductors. In this review article, current research in this field is described, focusing on the general theoretical concepts of non-Abelian statistics as it relates to topological quantum computation, on understanding non-Abelian quantum Hall states, on proposed experiments to detect non-Abelian anyons, and on proposed architectures for a topological quantum computer. Both the mathematical underpinnings of topological quantum computation and the physics of the subject are addressed, using the nu=5/2 fractional quantum Hall state as the archetype of a non-Abelian topological state enabling fault-tolerant quantum computation.
Details
- Title
- Non-Abelian anyons and topological quantum computation
- Creators
- Chetan Nayak (null)Steven H. Simon (null)Ady Stern (null)Michael Freedman (null)Sarma, Sankar Das Sarma (null)
- Resource Type
- Journal article; Review
- Publication Details
- Reviews of Modern Physics, Vol.80(3), pp.1083-1159; Jul/2008
- Number of pages
- 77
- Language
- English
- DOI
- https://doi.org/10.1103/RevModPhys.80.1083
- Grant note
- The authors are grateful for support from Microsoft Station Q, the National Science Foundation under Grant No. DMR-0411800, the Army Research Office under Grant No. W911NF-04-1-0236, LPS-NSA-CMTC, the Minerva Foundation, the Israel Science Foundation, the U.S.-Israel Binational Science Foundation, and Alcatel-Lucent Bell Labs.
- Record Identifier
- 993265258703596
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