This is the crypto stack exchange. And if there is one thing I learned in crypto, you always have to specify everything, especially the power of the participants.
Therefore, because you did not specify the knowledge of the children, I assume all children have graduated in computer science and quantum mechanics. Thus, they will easily understand the following:
- Initialize the system to the uniform superposition over all states:
$$
|\psi_0\rangle = \frac{1}{\sqrt{N}} \sum_{i=0}^{N-1} |i\rangle,
$$
Obviously $N$ is the search space.
- Oracle for state $|\psi_0\rangle$ to invert $|w\rangle$:
\begin{equation}
|\psi_1\rangle = U_w |\psi_0\rangle = \frac{1}{\sqrt{N}} \sum_{i=0}^{N-1} (-1)^{f(i)} |i\rangle,
\end{equation}
where $f(i) = 1$ if $i=w$ or $f(i) = 0$
Amplify $|w\rangle$ with:
\begin{equation}
|\psi_2\rangle = S D |\psi_1\rangle = S \left(2 |\psi_1\rangle \langle \psi_1| - \mathbb{I} \right) |\psi_1\rangle,
\end{equation}
with:
\begin{equation}
S|i\rangle = (-1)^{i=w}|i\rangle.
\end{equation}
and:
\begin{equation}
D = 2|\psi_0\rangle\langle\psi_0| - I,
\end{equation}
Iterate over 2. and 3. $O(\sqrt{N})$ times to increase probability. Trivial.
Measure quantum state. Everyone knows how that works.
"Yes, it really is that simple"
Edit: I forgot the relation to crypto. Just assume a cryptographic scheme as the black box function to which the Grovers algorithm is applied and brute force the key.
/s
Maybe this answers your question.
