**Input:** A qubit in an arbitrary state $\ket{\psi} = \alpha\ket{0} + \beta\ket{1}$.

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

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