TY - JOUR
T1 - Super-Polynomial Quantum Speed-ups for Boolean Evaluation Trees with Hidden Structure
JF - ITCS '12 Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Y1 - 2012
A1 - Bohua Zhan
A1 - Shelby Kimmel
A1 - Avinatan Hassidim
AB - 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.
U4 - 249-265
SN - 978-1-4503-1115-1
UR - http://arxiv.org/abs/1101.0796v3
J1 - ITCS 2012 Proceedings of the 3rd Innovations in Theoretical Computer Science
U5 - 10.1145/2090236.2090258
ER -