**Input:** $n \ge 2$ qubits in the $\ket{0 \dots 0}$ state.

**Goal:**  Change the state of the qubits to a periodic state with alternating $1, 1, -1, -1$ amplitudes of basis states:

$$\frac1{\sqrt{2^n}} \big(\ket{0} + \ket{1} - \ket{2} - \ket{3} + ... - \ket{2^n-2} - \ket{2^n-1} \big)$$

> For example, for $n = 2$ the goal state is $\frac12 \big(\ket{0} + \ket{1} - \ket{2} - \ket{3}\big)$.
