@article {1510, title = {Super-Polynomial Quantum Speed-ups for Boolean Evaluation Trees with Hidden Structure}, journal = {ITCS {\textquoteright}12 Proceedings of the 3rd Innovations in Theoretical Computer Science Conference}, year = {2012}, month = {2012/01/08}, pages = {249-265}, abstract = { We give a quantum algorithm for evaluating a class of boolean formulas (such as NAND trees and 3-majority trees) on a restricted set of inputs. Due to the structure of the allowed inputs, our algorithm can evaluate a depth $n$ tree using $O(n^{2+\log\omega})$ queries, where $\omega$ is independent of $n$ and depends only on the type of subformulas within the tree. We also prove a classical lower bound of $n^{\Omega(\log\log n)}$ queries, thus showing a (small) super-polynomial speed-up. }, isbn = {978-1-4503-1115-1}, doi = {10.1145/2090236.2090258}, url = {http://arxiv.org/abs/1101.0796v3}, author = {Bohua Zhan and Shelby Kimmel and Avinatan Hassidim} }