The Physical Church-Turing Thesis and the Principles of Quantum Theory

Abstract : As was emphasized by Deutsch, quantum computation shatters complexity theory, but is innocuous to computability theory. Yet Nielsen and others have shown how quantum theory as it stands could breach the physical Church-Turing thesis. We draw a clear line as to when this is the case, in a way that is inspired by Gandy. Gandy formulates postulates about physics, such as homogeneity of space and time, bounded density and velocity of information -- and proves that the physical Church-Turing thesis is a consequence of these postulates. We provide a quantum version of the theorem. Thus this approach exhibits a formal non-trivial interplay between theoretical physics symmetries and computability assumptions.
Document type :
Journal articles
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-00944482
Contributor : Nicolas Peltier <>
Submitted on : Monday, February 10, 2014 - 4:35:05 PM
Last modification on : Thursday, October 11, 2018 - 8:48:04 AM

Identifiers

Citation

Pablo Arrighi, Gilles Dowek. The Physical Church-Turing Thesis and the Principles of Quantum Theory. International Journal of Foundations of Computer Science, World Scientific Publishing, 2012, 23 (5), pp.1131-1146. ⟨10.1142/S0129054112500153⟩. ⟨hal-00944482⟩

Share

Metrics

Record views

279