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On the Completeness of Quantum Computation Models

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Programs, Proofs, Processes (CiE 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6158))

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Abstract

The notion of computability is stable (i.e. independent of the choice of an indexing) over infinite-dimensional vector spaces provided they have a finite “tensorial dimension”. Such vector spaces with a finite tensorial dimension permit to define an absolute notion of completeness for quantum computation models and give a precise meaning to the Church-Turing thesis in the framework of quantum theory.

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Author information

Authors and Affiliations

  1. École normale supérieure de Lyon, LIP, 46 allée d’Italie, 69008, Lyon, France

    Pablo Arrighi

  2. Université de Grenoble, LIG, 220 rue de la chimie, 38400, Saint Martin d’Hères, France

    Pablo Arrighi

  3. École polytechnique and INRIA, LIX, École polytechnique, 91128, Palaiseau Cedex, France

    Gilles Dowek

Authors
  1. Pablo Arrighi
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  2. Gilles Dowek
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Editor information

Editors and Affiliations

  1. Departamento de Matemática, Universidade de Lisboa, Campo Grande, Edifício C6, 1749-016, Lisboa, Portugal

    Fernando Ferreira

  2. Institute for Logic, Language and Computation (ILLC), Universiteit van Amsterdam, P.O. Box 94242, 1090, Amsterdam, GE, The Netherlands

    Benedikt Löwe

  3. Departamento de Informática e Ingeniería de Sistemas, Universidad de Zaragoza, María de Luna 1, 50018, Zaragoza, Spain

    Elvira Mayordomo

  4. Universidade dos Açores, Campus de Ponta Delgada, Apartado 1422, 9501-801, Ponta Delgada, Açores, Portugal

    Luís Mendes Gomes

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Arrighi, P., Dowek, G. (2010). On the Completeness of Quantum Computation Models. In: Ferreira, F., Löwe, B., Mayordomo, E., Mendes Gomes, L. (eds) Programs, Proofs, Processes. CiE 2010. Lecture Notes in Computer Science, vol 6158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13962-8_3

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  • DOI: https://doi.org/10.1007/978-3-642-13962-8_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13961-1

  • Online ISBN: 978-3-642-13962-8

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