A lambda calculus for quantum computation with classical control

Authors:
Peter Selinger;Benoît Valiron
Affiliations:
Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario, Canada;Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario, Canada
Venue:
TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
Year:
2005

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Abstract

The objective of this paper is to develop a functional programming language for quantum computers. We develop a lambda calculus for the classical control model, following the first author's work on quantum flow-charts. We define a call-by-value operational semantics, and we give a type system using affine intuitionistic linear logic. The main results of this paper are the safety properties of the language and the development of a type inference algorithm.