Solution
= Solution
The first register of $|\Phi_3\rangle$ is exactly $|a\rangle$, so the probability of observing the string $a$ is
$$
\boxed{1}.
$$
= Solution
The first register of $|\Phi_3\rangle$ is exactly $|a\rangle$, so the probability of observing the string $a$ is
$$
\boxed{1}.
$$