Quantum walk algorithm for element distinctness
Quantum Physics
2014-05-01 v9 Data Structures and Algorithms
Abstract
We use quantum walks to construct a new quantum algorithm for element distinctness and its generalization. For element distinctness (the problem of finding two equal items among N given items), we get an O(N^{2/3}) query quantum algorithm. This improves the previous O(N^{3/4}) query quantum algorithm of Buhrman et.al. (quant-ph/0007016) and matches the lower bound by Shi (quant-ph/0112086). The algorithm also solves the generalization of element distinctness in which we have to find k equal items among N items. For this problem, we get an O(N^{k/(k+1)}) query quantum algorithm.
Cite
@article{arxiv.quant-ph/0311001,
title = {Quantum walk algorithm for element distinctness},
author = {Andris Ambainis},
journal= {arXiv preprint arXiv:quant-ph/0311001},
year = {2014}
}
Comments
33 pages, 1 figure, v9 typos with signs corrected on pages 11-12