Algorithm 3: Grover [59]

Perform a Walsh-Hadamard transform on the initial state ${\left|0\right.〉}^{\otimes n}\left|1\right.〉$, and then repeat the following steps $\sqrt{2^n}$ times. Apply the oracle Perform a Walsh-Hadamard transform of the query register Apply $(I-2\left|0\rangle \langle 0\right|)$ to the query register. This is an n-controlled-Z with all controls inverted (including the target Z). Perform a Walsh-Hadamard transform of the query register   Then measure the query register, which will give you the satisfying assignment with highprobability (see further [30]). One repetition of the steps 1–4 is known as the Grover operator.