What will happen if the 'blackbox' function $f$ in Deutsch's algorithm is designed in such a way that it takes millions of years to deliver result if input is $x = 1$ and few seconds if the input is $x = 0$?
How long would it take the oracle $U_f$ to calculate $f$ for all inputs? My understanding is that $U_f$ has such quantum properties, that given a state $|\psi \rangle$ as a superposition of two qubits it will apply $U_f$ (and thus apply internally $f$) to each base state of $|\psi \rangle$ simultaneously.
In the scenario I've described $f$ will, however, take different execution times for different inputs. Will then there be a delay until all base states are evaluated by $ U_f$ (or more precisely by $f$)?