I am at a loss when it comes to understanding how Grover's Algorithm gives any useful information. Suppose we have a 4-qubit states (|0⟩ to |15⟩), and we are searching for the state |3⟩. The oracle would thus be O=I−2|3⟩⟨3|
And then, at the end, after all the amplitude amplification steps, we would get the state |3⟩ with a high probability, but does this give any new information, since we already used |3⟩ inside the oracle?
I know I am missing out something crucial, but I absolutely cannot put my finger on it.
Please help. Thank you.