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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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Submitted on : Thursday, July 30, 2020 - 9:12:37 AM
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  • HAL Id : hal-02909128, version 1



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



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