Quantum Algorithms for Element Distinctness
Harry Buhrman, Christoph Durr, Mark Heiligman, Peter Hoyer, Frederic Magniez, Miklos Santha, Ronald de Wolf
Abstract
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, and imply an O(N3/4 log N) quantum upper bound for the element distinctness problem in the comparison complexity model (contrasting with Theta(N log N) classical complexity). We also prove a lower bound of Omega(N1/2) comparisons for this problem and derive bounds for a number of related problems.
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