A lambda calculus for quantum computation with classical control

Authors:
Peter Selinger;Benoit Valiron
Affiliations:
Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada;Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario, Canada
Venue:
Mathematical Structures in Computer Science
Year:
2006

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Abstract

In this paper we develop a functional programming language for quantum computers by extending the simply-typed lambda calculus with quantum types and operations. The design of this language adheres to the ‘quantum data, classical control’ paradigm, following the first author's work on quantum flow-charts. We define a call-by-value operational semantics, and 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.