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Presheaf Models of Quantum Computation: An Outline

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Computation, Logic, Games, and Quantum Foundations. The Many Facets of Samson Abramsky

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7860))

Abstract

This paper outlines the construction of categorical models of higher-order quantum computation. We construct a concrete denotational semantics of Selinger and Valiron’s quantum lambda calculus, which was previously an open problem. We do this by considering presheaves over appropriate base categories arising from first-order quantum computation. The main technical ingredients are Day’s convolution theory and Kelly and Freyd’s notion of continuity of functors. We first give an abstract description of the properties required of the base categories for the model construction to work. We then exhibit a specific example of base categories satisfying these properties.

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Author information

Authors and Affiliations

  1. IMERL-FING, Universidad de la República, Montevideo, Uruguay

    Octavio Malherbe

  2. Dept. of Mathematics and Statistics, University of Ottawa, Canada

    Philip Scott

  3. Dept. of Mathematics and Statistics, Dalhousie University, Halifax, Canada

    Peter Selinger

Authors
  1. Octavio Malherbe
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  2. Philip Scott
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  3. Peter Selinger
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Oxford, Parks Road, Wolfson Building, OX1 3QD, Oxford, UK

    Bob Coecke  & Luke Ong  & 

  2. Department of Computer Science, McGill University, 3480 Rue University, H3A 0E9, Montréal, QC, Canada

    Prakash Panangaden

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Malherbe, O., Scott, P., Selinger, P. (2013). Presheaf Models of Quantum Computation: An Outline. In: Coecke, B., Ong, L., Panangaden, P. (eds) Computation, Logic, Games, and Quantum Foundations. The Many Facets of Samson Abramsky. Lecture Notes in Computer Science, vol 7860. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38164-5_13

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  • DOI: https://doi.org/10.1007/978-3-642-38164-5_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38163-8

  • Online ISBN: 978-3-642-38164-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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