Taking it on trust: Reason and observability in quantum computing

If quantum computing is located somewhere between physics and theoretical computing, a basic question concerns which characteristic features are derived from the latter. From a logical point of view, the concept of computation provides a definition of the natural process of calculare. It rests on trust that a procedure of reason can be reproduced mechanically. Turing argues for the adequacy of the concept by introducing a requirement of “observability,” which is expressed through finiteness and locality conditions. However, according to the uncertainty principle, no computational path can be observed. How does quantum computing contend with Turing’s constraints? What observables are relevant to the computation? This is an attempt to sharpen such questions.