Adversary Lower Bounds for the Collision and the Set Equality Problems

28 Jul 2017 · Belovs Aleksandrs, Rosmanis Ansis ·

We prove tight $\Omega(n^{1/3})$ lower bounds on the quantum query complexity of the Collision and the Set Equality problems, provided that the size of the alphabet is large enough. We do this using the negative-weight adversary method. Thus, we reprove the result by Aaronson and Shi, as well as a more recent development by Zhandry.