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Structuring quantum effects: superoperators as arrows

Published online by Cambridge University Press:  04 July 2006

JULIANA VIZZOTTO ,
THORSTEN ALTENKIRCH  and
AMR SABRY
JULIANA VIZZOTTO
Affiliation:
Institute of Informatics, Federal University of Rio Grande do Sul, Porto Alegre, Brazil
THORSTEN ALTENKIRCH
Affiliation:
School of Computer Science and IT, The University of Nottingham, U.K.
AMR SABRY
Affiliation:
Department of Computer Science, Indiana University, U.S.A.
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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.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 16 , Issue 3 , June 2006 , pp. 453 - 468
Copyright
2006 Cambridge University Press

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