Quantum Algorithms for Finding Claws, Collisions and Triangles
Harry Buhrman, Christoph Dürr, Peter Hyer · arXiv (Cornell University) · 2000
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 N^{3/4} log(N) quantum upper bound for the element distinctness problem (contrasting with N\\log(N) classical complexity). We also give an algorithm to finding a triangle in a graph more efficiently than classically.