How Low Can Approximate Degree and Quantum Query Complexity be for Total Boolean Functions?
Quantum Physics
2013-03-26 v2
Abstract
It has long been known that any Boolean function that depends on n input variables has both degree and exact quantum query complexity of Omega(log n), and that this bound is achieved for some functions. In this paper we study the case of approximate degree and bounded-error quantum query complexity. We show that for these measures the correct lower bound is Omega(log n / loglog n), and we exhibit quantum algorithms for two functions where this bound is achieved.
Keywords
Cite
@article{arxiv.1206.0717,
title = {How Low Can Approximate Degree and Quantum Query Complexity be for Total Boolean Functions?},
author = {Andris Ambainis and Ronald de Wolf},
journal= {arXiv preprint arXiv:1206.0717},
year = {2013}
}
Comments
10 pages LaTeX. Version 2: added some clarification and an appendix with a proof of Lemma 2