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. (Extra keywords: quantum programming languages, denotational
semantics, universality.)Comment: 15 pages, LaTe