On the completeness of quantum computation models
Pablo Arrighi, Gilles Dowek
TL;DR
This paper establishes a stable notion of computability for infinite-dimensional quantum systems with finite tensorial dimension, providing a rigorous foundation for quantum computation models and their universality.
Contribution
It introduces a formal framework for the completeness of quantum computation models based on finite tensorial dimension, clarifying the quantum Church-Turing thesis.
Findings
Computability is stable over certain infinite-dimensional vector spaces.
A formal notion of completeness for quantum models is defined.
The framework supports a precise interpretation of quantum universality.
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. (Extra keywords: quantum programming languages, denotational semantics, universality.)
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