The following circuit is designed for testing whether |u⟩=|v⟩.
The three-qubit gate in the middle is called the controlled SWAP gate, which swaps the last two qubits if and only if the first qubit is 1
(a) If |u⟩=|v⟩=|+⟩, what is the probability that the measurement outcome is 0?
(b) If |u⟩=|+⟩ and |v⟩=|−⟩, what is the probability that the measurement outcome is 0?