Optimal quantum query bounds for almost all Boolean functions
Quantum Physics
2012-08-07 v1
Abstract
We show that almost all n-bit Boolean functions have bounded-error quantum query complexity at least n/2, up to lower-order terms. This improves over an earlier n/4 lower bound of Ambainis, and shows that van Dam's oracle interrogation is essentially optimal for almost all functions. Our proof uses the fact that the acceptance probability of a T-query algorithm can be written as the sum of squares of degree-T polynomials.
Cite
@article{arxiv.1208.1122,
title = {Optimal quantum query bounds for almost all Boolean functions},
author = {Andris Ambainis and Arturs Backurs and Juris Smotrovs and Ronald de Wolf},
journal= {arXiv preprint arXiv:1208.1122},
year = {2012}
}
Comments
8 pages LaTeX