Quantum Programs as Kleisli Maps
Abstract
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]
Keywords
Cite
@article{arxiv.1501.01020,
title = {Quantum Programs as Kleisli Maps},
author = {Abraham Westerbaan},
journal= {arXiv preprint arXiv:1501.01020},
year = {2017}
}
Comments
In Proceedings QPL 2016, arXiv:1701.00242