New Generation Computing

, Volume 34, Issue 1, pp 25–68

Semantics for a Quantum Programming Language by Operator Algebras


DOI: 10.1007/s00354-016-0204-3

Cite this article as:
Cho, K. New Gener. Comput. (2016) 34: 25. doi:10.1007/s00354-016-0204-3


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 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. The use of operator algebras allows us to accommodate infinite structures and to handle classical and quantum computations in a unified way.


Quantum Computation Quantum Programming Languages Operator Algebras Denotational Semantics Complete Partial Orders 

Copyright information

© Ohmsha and Springer Japan 2016

Authors and Affiliations

  1. 1.Institute for Computing and Information SciencesRadboud UniversityNijmegenThe Netherlands

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