[quant-ph/0307150] A Lambda Calculus for Quantum Computation
(Submitted on 21 Jul 2003 (v1), last revised 3 Apr 2004 (this version, v5)) Abstract: The classical lambda calculus may be regarded both as a programming language and as a formal algebraic system for reasoning about computation. It provides a computational model equivalent to the Turing machine, and continues to be of enormous benefit in the classical theory of computation. We propose that quantum
qlambdabook.dvi
1 Quantum Lambda Calculus Peter Selinger Dalhousie University, Canada Benoı̂t Valiron INRIA and École Polytechnique, LIX, Palaiseau, France. Abstract We discuss the design of a typed lambda calculus for quantum compu- tation. After a brief discussion of the role of higher-order functions in quantum information theory, we define the quantum lambda calculus and its operational semantics. Safety inv
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https://www.kurims.kyoto-u.ac.jp/~terui/summer1.pdf
https://www.cs.cmu.edu/~fp/courses/linear/handouts/lnd.pdf
https://www.cis.upenn.edu/~jpaykin/papers/pz_linearity_monad_2017.pdf