Quantum Algorithms for Element Distinctness
Quantum Physics
2017-01-10 v2
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(N^{3/4} 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(N^{1/2}) comparisons for this problem and derive bounds for a number of related problems.
Cite
@article{arxiv.quant-ph/0007016,
title = {Quantum Algorithms for Element Distinctness},
author = {Harry Buhrman and Christoph Durr and Mark Heiligman and Peter Hoyer and Frederic Magniez and Miklos Santha and Ronald de Wolf},
journal= {arXiv preprint arXiv:quant-ph/0007016},
year = {2017}
}
Comments
15 pages. Supersedes quant-ph/007016v1 and quant-ph/0006136