Díaz-Caro A, Dowek G, Rinaldi JP. Two linearities for quantum computing in the lambda calculus.
Biosystems 2019;
186:104012. [PMID:
31757589 DOI:
10.1016/j.biosystems.2019.104012]
[Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2018] [Revised: 07/29/2019] [Accepted: 07/30/2019] [Indexed: 10/25/2022]
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 superposition, 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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