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Two linearities for quantum computing in the lambda calculus ✩,✩✩

Abstract : We propose a way to unify two approaches of non-cloning in quantum lambda-calculi: logical and algebraic linearities. The first approach is to forbid duplicating variables, while the second is to consider all lambda-terms as algebraic-linear functions. We illustrate this idea by defining a quantum extension of first-order simply-typed lambda-calculus, where the type is linear on superposi-tion, while allows cloning base vectors. In addition, we provide an interpretation of the calculus where superposed types are interpreted as vector spaces and non-superposed types as their basis.
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https://hal.inria.fr/hal-02909128
Contributor : Gilles Dowek <>
Submitted on : Thursday, July 30, 2020 - 9:12:37 AM
Last modification on : Monday, August 3, 2020 - 3:26:19 PM
Long-term archiving on: : Tuesday, December 1, 2020 - 7:43:43 PM

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Alejandro Díaz-Caro, Gilles Dowek, Juan Rinaldi. Two linearities for quantum computing in the lambda calculus ✩,✩✩. BioSystems, Elsevier, 2019. ⟨hal-02909128⟩

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