**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 basis state $|11\rangle = \begin{bmatrix} 0 \\\ 0 \\\ 0 \\\ 1 \end{bmatrix}$.
