Abstract
Recent developments in theoretical physics have highlighted interesting topological features of some two-dimensional particles, so-called anyons, that can be used to realise robust quantum computation. In this paper we show how an anyon system can be defined as a calculus of quantum functions, i.e. linear transformations on the space of all possible physical configurations of a set of anyons. A computation in this calculus represents the braiding of anyons and the final term of a computation corresponds to the outcome of a measurement of the anyons final fusion state, i.e. in general a probability distribution on the set of all possible outcomes. We show that this calculus describes a universal anyonic quantum computer provided that the space of terms satisfies some topological properties.
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Di Pierro, A., Panarotto, F. (2014). A Calculus of Anyons. In: Kohlenbach, U., Barceló, P., de Queiroz, R. (eds) Logic, Language, Information, and Computation. WoLLIC 2014. Lecture Notes in Computer Science, vol 8652. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44145-9_11
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DOI: https://doi.org/10.1007/978-3-662-44145-9_11
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