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.
A Calculus of Anyons
DI PIERRO, ALESSANDRA;PANAROTTO, Federica
2014-01-01
Abstract
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.
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