Semantics for a Quantum Programming Language by Operator Algebras

Kenta Cho
(Radboud University Nijmegen)

This paper presents a novel semantics for a quantum programming language by operator algebras, which are known to give a formulation for quantum theory that is alternative to the one by Hilbert spaces. We show that the opposite category of the category of W*-algebras and normal completely positive subunital maps is an elementary quantum flow chart category in the sense of Selinger. As a consequence, it gives a denotational semantics for Selinger's first-order functional quantum programming language QPL. The use of operator algebras allows us to accommodate infinite structures and to handle classical and quantum computations in a unified way.

In Bob Coecke, Ichiro Hasuo and Prakash Panangaden: Proceedings of the 11th workshop on Quantum Physics and Logic (QPL 2014), Kyoto, Japan, 4-6th June 2014, Electronic Proceedings in Theoretical Computer Science 172, pp. 165–190.
Published: 28th December 2014.

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