Quantum Algorithms for Element Distinctness
量子物理
2017-01-10 v2
摘要
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.
引用
@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}
}
备注
15 pages. Supersedes quant-ph/007016v1 and quant-ph/0006136