Super-polynomial quantum speed-ups for boolean evaluation trees with hidden structure

Authors:
Bohua Zhan;Shelby Kimmel;Avinatan Hassidim
Affiliations:
Princeton University;Massachusetts Institute of Technology;Bar Ilan University, Google
Venue:
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Year:
2012

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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(n2+logω) queries, where ω is independent of n and depends only on the type of subformulas within the tree. We also prove a classical lower bound of nΩ(log log n) queries, thus showing a (small) super-polynomial speed-up.