The CCNOT-gate

What if we wanted to apply a certain gate if and only if two other qubits are in-state $|1\rangle$? If you’ve read this course carefully so far, you may object that AND is not a valid qubit gate. A brief look at the truth table discloses that the AND operator is not reversible. If we get false as its output, we can’t tell what the input was. It could be one of three different states.