Typing Quantum Superpositions and Measurement
Conference paper
First Online:
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.
Keywords
Quantum computing Lambda-calculus Algebraic linearity Linear logic MeasurementNotes
Acknowledgements
We would like to thank Eduardo Bonelli, Luca Paolini, Simona Ronchi della Rocca and Luca Roversi for interesting comments and suggestions.
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