Quantum Programs as Kleisli Maps

Abraham Westerbaan
(Radboud University Nijmegen)

Furber and Jacobs have shown in their study of quantum computation that the category of commutative C*-algebras and PU-maps (positive linear maps which preserve the unit) is isomorphic to the Kleisli category of a comonad on the category of commutative C*-algebras with MIU-maps (linear maps which preserve multiplication, involution and unit). [Furber and Jacobs, 2013]

In this paper, we prove a non-commutative variant of this result: the category of C*-algebras and PU-maps is isomorphic to the Kleisli category of a comonad on the subcategory of MIU-maps.

A variation on this result has been used to construct a model of Selinger and Valiron's quantum lambda calculus using von Neumann algebras. [Cho and Westerbaan, 2016]

In Ross Duncan and Chris Heunen: Proceedings 13th International Conference on Quantum Physics and Logic (QPL 2016), Glasgow, Scotland, 6-10 June 2016, Electronic Proceedings in Theoretical Computer Science 236, pp. 215–228.
Published: 1st January 2017.

ArXived at: http://dx.doi.org/10.4204/EPTCS.236.14 bibtex PDF
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