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Semantics for a Quantum Programming Language by Operator Algebras

Abstract

This paper presents a novel semantics for a quantum programming language by operator algebras, which are known to give a formulation for quantum theory that is alternative to the one by Hilbert spaces. We show that the opposite of the category of W*-algebras and normal completely positive subunital maps is an elementary quantum flow chart category in the sense of Selinger. As a consequence, it gives a denotational semantics for Selinger’s first-order functional quantum programming language. The use of operator algebras allows us to accommodate infinite structures and to handle classical and quantum computations in a unified way.

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Correspondence to Kenta Cho.

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Cho, K. Semantics for a Quantum Programming Language by Operator Algebras. New Gener. Comput. 34, 25–68 (2016). https://doi.org/10.1007/s00354-016-0204-3

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Keywords

  • Quantum Computation
  • Quantum Programming Languages
  • Operator Algebras
  • Denotational Semantics
  • Complete Partial Orders