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

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

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