28 Mar 2008 | Chetan Nayak1,2, Steven H. Simon3, Ady Stern4, Michael Freedman1, Sankar Das Sarma5,
This review article explores the emerging field of topological quantum computation, which leverages the unique properties of non-Abelian anyons to construct fault-tolerant quantum computers. Non-Abelian anyons are particles that exhibit non-Abelian braiding statistics, meaning that the order in which they are braided matters and results in non-trivial rotations within the degenerate multi-quasiparticle Hilbert space. The article covers the theoretical concepts of non-Abelian statistics, the emergence of non-Abelian anyons in various physical systems, and the experimental detection of these particles. It also discusses the potential for using non-Abelian anyons in quantum computing, including the realization of qubits and gates in gated GaAs devices and the universal topological quantum computation enabled by non-Abelian anyons. The review highlights the importance of the $\nu = 5/2$ fractional quantum Hall state as a prototype for non-Abelian topological states and addresses the challenges and future directions in this field.This review article explores the emerging field of topological quantum computation, which leverages the unique properties of non-Abelian anyons to construct fault-tolerant quantum computers. Non-Abelian anyons are particles that exhibit non-Abelian braiding statistics, meaning that the order in which they are braided matters and results in non-trivial rotations within the degenerate multi-quasiparticle Hilbert space. The article covers the theoretical concepts of non-Abelian statistics, the emergence of non-Abelian anyons in various physical systems, and the experimental detection of these particles. It also discusses the potential for using non-Abelian anyons in quantum computing, including the realization of qubits and gates in gated GaAs devices and the universal topological quantum computation enabled by non-Abelian anyons. The review highlights the importance of the $\nu = 5/2$ fractional quantum Hall state as a prototype for non-Abelian topological states and addresses the challenges and future directions in this field.