Abstract
In this review we present an introduction to topological quantum computation – quantum computing with anyons. This approach is inherently resilient against errors, thus promising to overcome one of the main obstacles for the realisation of quantum computers. We first provide an introduction to anyon models and discuss the general steps how to use them to encode and process quantum information. Then we present a toy microscopic model, Kitaev’s p-wave wire, that supports localised Majorana modes. These are the simplest non-Abelian anyons, which are the subject of intense theoretical and experimental research. We outline how quantum computation could be carried out in this microscopic system in a topologically protected manner, discuss the nature of the topological fault tolerance and review the recent experimental developments in realizing Majorana modes.
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