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dc.contributor.authorAaronson, Scott
dc.contributor.authorAmbainis, Andris
dc.date.accessioned2015-11-02T19:43:04Z
dc.date.available2015-11-02T19:43:04Z
dc.date.issued2015-06
dc.identifier.isbn9781450335362
dc.identifier.urihttp://hdl.handle.net/1721.1/99662
dc.description.abstractWe achieve essentially the largest possible separation between quantum and classical query complexities. We do so using a property-testing problem called Forrelation, where one needs to decide whether one Boolean function is highly correlated with the Fourier transform of a second function. This problem can be solved using 1 quantum query, yet we show that any randomized algorithm needs Ω(√(N)log(N)) queries (improving an Ω(N[superscript 1/4]) lower bound of Aaronson). Conversely, we show that this 1 versus Ω(√(N)) separation is optimal: indeed, any t-query quantum algorithm whatsoever can be simulated by an O(N[superscript 1-1/2t])-query randomized algorithm. Thus, resolving an open question of Buhrman et al. from 2002, there is no partial Boolean function whose quantum query complexity is constant and whose randomized query complexity is linear. We conjecture that a natural generalization of Forrelation achieves the optimal t versus Ω(N[superscript 1-1/2t]) separation for all t. As a bonus, we show that this generalization is BQP-complete. This yields what's arguably the simplest BQP-complete problem yet known, and gives a second sense in which Forrelation "captures the maximum power of quantum computation."en_US
dc.description.sponsorshipNational Science Foundation (U.S.) (Waterman Award)en_US
dc.description.sponsorshipNational Science Foundation (U.S.) (Grant 1249349)en_US
dc.language.isoen_US
dc.publisherAssociation for Computing Machinery (ACM)en_US
dc.relation.isversionofhttp://dx.doi.org/10.1145/2746539.2746547en_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alikeen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/en_US
dc.sourceMIT web domainen_US
dc.titleForrelation: A Problem That Optimally Separates Quantum from Classical Computingen_US
dc.typeArticleen_US
dc.identifier.citationScott Aaronson and Andris Ambainis. 2015. Forrelation: A Problem that Optimally Separates Quantum from Classical Computing. In Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing (STOC '15). ACM, New York, NY, USA, 307-316.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Scienceen_US
dc.contributor.mitauthorAaronson, Scotten_US
dc.relation.journalProceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing (STOC '15)en_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/ConferencePaperen_US
eprint.statushttp://purl.org/eprint/status/NonPeerRevieweden_US
dspace.orderedauthorsAaronson, Scott; Ambainis, Andrisen_US
dc.identifier.orcidhttps://orcid.org/0000-0003-1333-4045
mit.licenseOPEN_ACCESS_POLICYen_US
mit.metadata.statusComplete


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