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

Bohua Zhan, Shelby Kimmel, Avinatan Hassidim

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

11 Scopus citations

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.

Original languageEnglish
Title of host publicationITCS 2012 - Innovations in Theoretical Computer Science Conference
PublisherAssociation for Computing Machinery
Pages249-265
Number of pages17
ISBN (Print)9781450311151
DOIs
StatePublished - 2012
Event3rd Conference on Innovations in Theoretical Computer Science, ITCS 2012 - Cambridge, MA, United States
Duration: 8 Jan 201210 Jan 2012

Publication series

NameITCS 2012 - Innovations in Theoretical Computer Science Conference

Conference

Conference3rd Conference on Innovations in Theoretical Computer Science, ITCS 2012
Country/TerritoryUnited States
CityCambridge, MA
Period8/01/1210/01/12

Bibliographical note

Place of conference:USA

Keywords

  • NAND tree
  • span programs
  • super-polynomial quantum speed-up

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