Structuring quantum effects: superoperators as arrows

Authors:
Juliana Vizzotto;Thorsten Altenkirch;Amr Sabry
Affiliations:
Institute of Informatics, Federal University of Rio Grande do Sul, Porto Alegre, Brazil;School of Computer Science and IT, The University of Nottingham, U.K.;Department of Computer Science, Indiana University, U.S.A.
Venue:
Mathematical Structures in Computer Science
Year:
2006

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Abstract

We show that the model of quantum computation based on density matrices and superoperators can be decomposed into a pure classical (functional) part and an effectful part modelling probabilities and measurement. The effectful part can be modelled using a generalisation of monads called arrows. We express the resulting executable model of quantum computing in the Haskell programming language using its special syntax for arrow computations. However, the embedding in Haskell is not perfect: a faithful model of quantum computing requires type capabilities that are not directly expressible in Haskell.