NonAbelian anyons and topological quantum computation
Abstract
Topological quantum computation has emerged as one of the most exciting approaches to constructing a faulttolerant 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 nonAbelian anyons, meaning that they obey nonAbelian 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 ν=5/2 state, although several other prospective candidates have been proposed in systems as disparate as ultracold atoms in optical lattices and thinfilm superconductors. In this review article, current research in this field is described, focusing on the general theoretical concepts of nonAbelian statistics as it relates to topological quantum computation, on understanding nonAbelian quantum Hall states, on proposed experiments to detect nonAbelian 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 ν=5/2 fractional quantum Hall state as the archetype of a nonAbelian topological state enabling faulttolerant quantum computation.
 Publication:

Reviews of Modern Physics
 Pub Date:
 July 2008
 DOI:
 10.1103/RevModPhys.80.1083
 arXiv:
 arXiv:0707.1889
 Bibcode:
 2008RvMP...80.1083N
 Keywords:

 05.30.Pr;
 03.67.Lx;
 03.67.Pp;
 73.43.f;
 Fractional statistics systems;
 Quantum computation;
 Quantum error correction and other methods for protection against decoherence;
 Quantum Hall effects;
 Condensed Matter  Strongly Correlated Electrons;
 Condensed Matter  Mesoscale and Nanoscale Physics
 EPrint:
 Final Accepted form for RMP