A lambda calculus for quantum computation with classical control

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.

15 pages, submitted to TLCA'05. Note: this is basically the work done during the first author master, his thesis can be found on his webpage. Modifications: almost everything reformulated; recursion removed since the way it was stated didn't satisfy lemma 11; type inference algorithm added; example of an implementation of quantum teleportation added

References in corpus (2)

• A Lambda Calculus for Quantum Computation
• Toward an architecture for quantum programming

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• Overview and Comparison of Gate Level Quantum Software Platforms
• A functional quantum programming language
• Theoretical framework for Higher-Order Quantum Theory
• A logical analysis of entanglement and separability in quantum higher-order functions
• The Quantum Monadology
• The Quantum Effect: A Recipe for QuantumPi