A Calculus of Anyons

Recent developments in theoretical physics have highlighted interestingtopological features of some two-dimensional particles, so-called anyons, thatcan be used to realise robust quantum computation. In this paper we show howan anyon system can be defined as a calculus of quantum functions, i.e. lineartransformations on the space of all possible physical configurations of a set ofanyons. A computation in this calculus represents the braiding of anyons and thefinal term of a computation corresponds to the outcome of a measurement of theanyons final fusion state, i.e. in general a probability distribution on the set ofall possible outcomes. We show that this calculus describes a universal anyonicquantum computer provided that the space of terms satisfies some topologicalproperties