Quantum algorithms for element distinctness
Harry Buhrman, Christoph Dürr, Mark Heiligman, Peter Friedrich Hoyer, Frédéric Magniez, Miklós Sántha, Ronald de Wolf · 2002
We present several applications of quantum amplitude amplification to finding claws and collisions in ordered or unordered functions. Our algorithms generalize those of Brassard, Hoyer, and Tapp (1998), and imply an O(N/sup 3/4/ log N) quantum upper bound for the element distinctness problem in the comparison complexity model. This contrasts with /spl Theta/(N log N) classical complexity. We also prove a lower bound of /spl Omega/(/spl radic/N) comparisons for this problem and derive bounds for a number of related problems.