Let a simple quantum circuit consist of one qubit and one classical bit. Initially, a qubit has the $|0\rangle$-state and then goes through some sequence of quantum gates, see the circuit below.
The quantum gates affect the qubit by changing its probability of being in one of two states after measuring. Let suppose that the quantum gates of the sequence are unknown. So in order to extract a qubit probability of being in one of two states after measuring it needs to performe such an action several times (the more the more accurate) pushing other qubits of the $|0\rangle$-state into the circuit.
It is interesting is it possible to do it with another way? Is there maybe a quantum algorithm that ables to do such a thing?