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A lambda calculus for quantum computation with classical control

Peter Selinger·Benoit Valiron
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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.

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Peter Selinger, Benoit Valiron. 2004-11-12. A lambda calculus for quantum computation with classical control. https://doi.org/10.1007/11417170_26

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