Quantum Complexity of Testing Group Commutativity
Abstract
We consider the problem of testing the commutativity of a black-box group specified by its k generators. The complexity (in terms of k) of this problem was first considered by Pak, who gave a randomized algorithm involving O(k) group operations. We construct a quite optimal quantum algorithm for this problem whose complexity is in O (k^{2/3}). The algorithm uses and highlights the power of the quantization method of Szegedy. For the lower bound of Omega(k^{2/3}), we give a reduction from a special case of Element Distinctness to our problem. Along the way, we prove the optimality of the algorithm of Pak for the randomized model.
Keywords
Cite
@article{arxiv.quant-ph/0506265,
title = {Quantum Complexity of Testing Group Commutativity},
author = {Frederic Magniez and Ashwin Nayak},
journal= {arXiv preprint arXiv:quant-ph/0506265},
year = {2018}
}
Comments
10 pages, requires fullpage,amsthm,amsfonts,amsmath; To appear in Algorithmica; earlier version appeared in ICALP 2005; corrects minor typos, results are unchanged