**Input**: three qubits in the state $\ket{\psi} \otimes \ket{00}$, where $\ket{\psi} = \alpha \ket{0} + \beta \ket{1}$ is the state of the first qubit, i.e., `qs[0]`.

**Goal**: prepare a state $\alpha \ket{000} + \beta \ket{111}$ on these qubits.