%0 Journal Article %J ITCS '12 Proceedings of the 3rd Innovations in Theoretical Computer Science Conference %D 2012 %T Super-Polynomial Quantum Speed-ups for Boolean Evaluation Trees with Hidden Structure %A Bohua Zhan %A Shelby Kimmel %A Avinatan Hassidim %X 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. %B ITCS '12 Proceedings of the 3rd Innovations in Theoretical Computer Science Conference %P 249-265 %8 2012/01/08 %@ 978-1-4503-1115-1 %G eng %U http://arxiv.org/abs/1101.0796v3 %! ITCS 2012 Proceedings of the 3rd Innovations in Theoretical Computer Science %R 10.1145/2090236.2090258