The Grover algorithm in real life I wonder about the effectiveness of the Grover algorithm in real life. In particular, if I think of a number in $\{0,...,2^n -1\}$, is it possible to build a "real" machine that guesses my number (with high probability) in $\sim \sqrt{2^n}$ steps ?
By a "machine", I mean some kind of big box or any complicated device (a particle accelerator, if you desire) that could contain, for example, $n$ entangled qbits, combined with a screen and a two-key keyboard ("yes" and "no") such that
1) the screen displays some number in $\{0,...,2^n -1\}$ and the sentence "is this your number?"
2) the machine waits for a human user to press either of the two keys of the keyboard
3) the machine repeats steps 1), 2) for about $\sqrt{2^n}$ times
4) the screen displays some number in $\{0,...,2^n -1\}$ and the sentence "this is your number".
EDIT : I know the Grover algorithm, the problem I have is about the "nature" of the oracle.
 A: This seems to be a common misunderstanding about Grover's algorithm.  It is not about querying a "magic" black box function.  Rather, you have an efficiently computable function $f(x)\in\{0,1\}$ and you want to find some $x_0$ for which $f(x_0)=1$.  Since you know how to realize $f(x)$ (i.e., you have a circuit), you can run $f$ on a quantum computer and use Grover to find such an $x_0$.
The relevance is in the fact that a large number of interesting problems (namely, the class NP) are such that solutions might be hard to find, but they are easy to verify.  Thus, Grover gives a square-root speed-up on any brute-force method to solve such a problem (i.e., any method which does not make use of any special structural property of $f$).
A: No, you can't run Grover's algorithm against a person pressing "no" or "yes" keys when prompted "is this your number?".
Grover's algorithm requires the ability to query under superposition, without decoherence. Humans don't support this kind of operation. We're too large and hot and wet and generally decohering all over the place.
