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

@inproceedings{Zhan2012SuperpolynomialQS,
  title={Super-polynomial quantum speed-ups for boolean evaluation trees with hidden structure},
  author={Bohua Zhan and Shelby Kimmel and Avinatan Hassidim},
  booktitle={ITCS '12},
  year={2012}
}
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 <i>n</i> tree using <i>O</i>(<i>n</i><sup>2+logω</sup>) queries, where ω is independent of <i>n</i> and depends only on the type of subformulas within the tree. We also prove a classical lower bound of <i>n</i><sup>Ω(log log <i>n</i>)</sup> queries, thus showing a (small… 

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