Two linearities for quantum computing in the lambda calculus

  title={Two linearities for quantum computing in the lambda calculus},
  author={Alejandro D{\'i}az-Caro and G. Dowek and J. Rinaldi},
  journal={Bio Systems},
  • Alejandro Díaz-Caro, G. Dowek, J. Rinaldi
  • Published 2019
  • Computer Science, Mathematics, Medicine
  • Bio Systems
  • 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… CONTINUE READING
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