Typing quantum superpositions and measurement
A Díaz-Caro, G Dowek - International Conference on Theory and Practice …, 2017 - Springer
A Díaz-Caro, G Dowek
International Conference on Theory and Practice of Natural Computing, 2017•SpringerWe propose a way to unify two approaches of non-cloning in quantum lambda-calculi. 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 …
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 …
Abstract
We propose a way to unify two approaches of non-cloning in quantum lambda-calculi. 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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