  Taking the view that computation is after all physical, we argue that
physics, particularly quantum physics, could help extend the notion of
computability. Here, we list the important and unique features of quantum
mechanics and then outline a quantum mechanical "algorithm" for one of the
insoluble problems of mathematics, the Hilbert's tenth and equivalently the
Turing halting problem. The key element of this algorithm is the {\em
computability} and {\em measurability} of both the values of physical
observables and of the quantum-mechanical probability distributions for these
values.
