
**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 $\frac{1}{2}\big(|00\rangle + e^{i\pi/4}|01\rangle + e^{i\pi/2}|10\rangle + e^{3i\pi/4}|11\rangle\big) = \frac{1}{2}\begin{bmatrix} 1 \\\ e^{i\pi/4} \\\ e^{i\pi/2} \\\ e^{3i\pi/4} \end{bmatrix}$.

<details>
    <summary><b>Need a hint?</b></summary>
    Represent the target state as a tensor product $\frac{1}{\sqrt2}\big(|0\rangle + e^{i\pi/2}|1\rangle\big) \otimes \frac{1}{\sqrt2}\big(|0\rangle + e^{i\pi/4}|1\rangle\big) = \frac{1}{\sqrt2} \begin{bmatrix} 1 \\\ e^{i\pi/2} \end{bmatrix} \otimes \frac{1}{\sqrt2}\begin{bmatrix} 1 \\\ e^{i\pi/4} \end{bmatrix}$.
</details>
