A lambda calculus for quantum computation with classical control. Selinger, P. & Valiron, B. Mathematical Structures in Computer Science, 16(3):527–552, June, 2006. ZSCC: 0000136
A lambda calculus for quantum computation with classical control [link]Paper  doi  abstract   bibtex   
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.
@article{selinger_lambda_2006,
	title = {A lambda calculus for quantum computation with classical control},
	volume = {16},
	issn = {1469-8072, 0960-1295},
	url = {http://www.cambridge.org/core/journals/mathematical-structures-in-computer-science/article/lambda-calculus-for-quantum-computation-with-classical-control/53AB540D33E2E420DF2F28D0073B7F45},
	doi = {10/cb9gnr},
	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.},
	language = {en},
	number = {3},
	urldate = {2019-10-26},
	journal = {Mathematical Structures in Computer Science},
	author = {Selinger, Peter and Valiron, Benoit},
	month = jun,
	year = {2006},
	note = {ZSCC: 0000136},
	pages = {527--552}
}

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