Figure 3. Exemplary state evolutions of two CX gates between (a) two bare qubits and (b) a bare qubit and an encoded qubit. (a) The control qubit $q_0$ is in state $\ket{1}$, hence the state of the target qubit $q_1$ is flipped. (b) The encoded qubit $q_0$ inside the ququart controls the CX gate targeting the bare qubit $q$. The ququart state $\ket{3}$ corresponds to the two-qubit state $\ket{q_0 q_1} = \ket{11}$, so the state of $q$ is flipped.