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Journal Articles BioSystems Year : 2019

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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Dates and versions

hal-02909128 , version 1 (30-07-2020)

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  • HAL Id : hal-02909128 , version 1

Cite

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

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