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 PUmaps (positive linear maps which preserve the unit) is isomorphic to the Kleisli category of a comonad on the category of commutative C*algebras with MIUmaps (linear maps which preserve multiplication, involution and unit). [Furber and Jacobs, 2013] In this paper, we prove a noncommutative variant of this result: the category of C*algebras and PUmaps is isomorphic to the Kleisli category of a comonad on the subcategory of MIUmaps. 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]
 Publication:

arXiv eprints
 Pub Date:
 December 2014
 arXiv:
 arXiv:1501.01020
 Bibcode:
 2015arXiv150101020W
 Keywords:

 Mathematics  Category Theory;
 Mathematics  Operator Algebras
 EPrint:
 In Proceedings QPL 2016, arXiv:1701.00242