**Input:** A qubit in an arbitrary state $|\psi\rangle = \alpha|0\rangle + \beta|1\rangle$.

**Goal:** Use several Pauli gates to change the qubit state to $- \alpha|0\rangle + \beta|1\rangle$, i.e., apply the transformation represented by the following matrix:

$$\begin{bmatrix} -1 & 0 \\\ 0 & 1 \end{bmatrix}$$
