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arXiv · 1101.0796

Super-Polynomial Quantum Speed-ups for Boolean Evaluation Trees with Hidden Structure

Bohua Zhan·Shelby Kimmel·Avinatan Hassidim
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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 $O(n^{2+\logω})$ 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 $n^{Ω(\log\log n)}$ queries, thus showing a (small) super-polynomial speed-up.

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Bohua Zhan, Shelby Kimmel, Avinatan Hassidim. 2012-07-03. Super-Polynomial Quantum Speed-ups for Boolean Evaluation Trees with Hidden Structure. https://doi.org/10.1145/2090236.2090258

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