On the completeness of quantum computation models

Authors:
Pablo Arrighi;Gilles Dowek
Affiliations:
École Normale Supérieure de Lyon, LIP, Lyon, France and Université de Grenoble, LIG, Saint Martin d'Hères, France;École polytechnique and INRIA, LIX, École polytechnique, Palaiseau Cedex, France
Venue:
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
Year:
2010

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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.