Why should anyone care about computing with anyons?

Abstract

In this article we present a pedagogical introduction of the main ideas and recent advances in the area of topological quantum computation. We give an overview of the concept of anyons and their exotic statistics, present various models that exhibit topological behavior, and we establish their relation to quantum computation. Possible directions for the physical realization of topological systems and the detection of anyonic behavior are elaborated.

22 pages, 13 figures. Some changes to existing sections, several references added, and a new section on criteria for TQO and TQC in lattice systems

References in corpus (9)

• Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State
• Bipartite entanglement and entropic boundary law in lattice spin systems
• Realization of a Laughlin quasiparticle interferometer: Observation of fractional statistics
• Topological Computation without Braiding
• Manipulation of Single Neutral Atoms in Optical Lattices
• Qudit surface codes and gauge theory with finite cyclic groups
• An extended Hubbard model with ring exchange: a route to a non-Abelian topological phase
• The Wavefunction of an Anyon
• Aharanov-Bohm interference and fractional statistics in a quantum Hall interferometer

Cited by in corpus (8)

• Non-Abelian Anyons and Topological Quantum Computation
• Anyonic interferometry and protected memories in atomic spin lattices
• Simulations of quantum double models
• Manifestations of topological effects in graphene
• Quantum control of the hyperfine-coupled electron and nuclear spins in alkali atoms
• Constructing Functional Braids for Low-Leakage Topological Quantum Computing
• Non-abelian statistics from an abelian model
• Quantum Control of d-Dimensional Quantum Systems with Application to Alkali Atomic Spins