The physical Church-Turing thesis and the principles of quantum theory

Abstract. Notoriously, quantum computation shatters complexity theory, but is innocuous to computability theory [17]. Yet several works have shown how quantum theory as it stands could breach the physical Church-Turing thesis [26, 25]. We draw a clear line as to when this is the case, in a way that is inspired by Gandy [20]. Gandy formulates postulates about physics, such as homogeneity of space and time, bounded density and velocity of information — and proves that the physical ChurchTuring 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.

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Pablo Arrighi, Gilles Dowek
• Keywords: CORR 2011, Education, Formal Non-trivial Interplay, Quantum, Quantum Computation Shatters