 In a brilliant undercover operation, Agent 13 has managed to secure two crucial bits of information concerning the whereabouts of the arch-villain Siegfried: the phone number of the secret hideout from which he intends to begin carrying out KAOS’s plans for world domination, and the fact that the number is a listed one (apparently an oversight on Siegfried’s part). Unfortunately you and your colleagues at CONTROL have no other information besides this. Can you find Siegfried’s hideout using only this number and a phone directory? In theoretical computer science this task is known as an unstructured search. In the worst case, if there are \(n\) entries in the directory, the computational resources required to find the entry will be linear in \(n\). Grover (1996) showed how this task could be done with a quantum algorithm using computational resources on the order of only \(\sqrt{n}\). Agreed, this “speed-up” is more modest than Shor’s since unstructured search belongs to the class \(\mathbf{P}\), but contrary to Shor’s case, where the classical complexity of factoring is still unknown, here the superiority of the quantum algorithm, however modest, is definitely provable. That this quadratic “speed-up” is also the optimal quantum “speed-up” possible for this problem was proved by Bennett, Bernstein, Brassard, &amp; Vazirani (1997).