
**Input:** A two-qubit system in the basis state $|00\rangle = \begin{bmatrix} 1 \\ 0 \\ 0 \\ 0 \end{bmatrix}$.

**Goal:** Transform the system into the state $\frac{1}{2}\big(|00\rangle - |01\rangle + |10\rangle - |11\rangle\big) = \frac{1}{2}\begin{bmatrix} 1 \\ -1 \\ 1 \\ -1 \end{bmatrix}$.

<details>
    <summary><b>Need a hint?</b></summary>
    Represent the target state as a tensor product $\frac{1}{\sqrt2}\big(|0\rangle + |1\rangle\big) \otimes \frac{1}{\sqrt2}\big(|0\rangle - |1\rangle\big) = \frac{1}{\sqrt2} \begin{bmatrix} 1 \\ 1 \end{bmatrix} \otimes \frac{1}{\sqrt2}\begin{bmatrix} 1 \\ -1 \end{bmatrix}$.
</details>
