ABSTRACT
This review presents an entry-level 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 introduce the concept of anyon models and review the literature on condensed matter systems where anyons can emerge. Then we discuss the general steps how to use anyons to encode and process quantum information, as well as discuss various ways topological protection might fail. Finally, these abstract concepts are demonstrated in the concrete system of Kitaev's topological nanowire. This model supports localised Majorana zero modes -- the simplest and experimentally most tractable types of non-Abelian anyons -- and it describes the low-energy physics of several experimentally relevant settings.
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