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