The Bayesian learner is optimal for noisy binary search (and pretty good for quantum as well)

Michael Ben Or, Avinatan Hassidim

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

67 Scopus citations

Abstract

We use a Bayesian approach to optimally solve problems in noisy binary search. We deal with two variants: Each comparison is erroneous with independent probability 1 - p. At each stage k comparisons can be performed in parallel and a noisy answer is returned. We present a (classical) algorithm which solves both variants optimally (with respect to p and k), up to an additive term of O(loglog n), and prove matching informationtheoretic lower bounds. We use the algorithm to improve the results of Farhi et al. [11], presenting an exact quantum search algorithm in an ordered list of expected complexity less than (log2 n)/3.

Original languageEnglish
Title of host publicationProceedings of the 49th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2008
Pages221-230
Number of pages10
DOIs
StatePublished - 2008
Externally publishedYes
Event49th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2008 - Philadelphia, PA, United States
Duration: 25 Oct 200828 Oct 2008

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
ISSN (Print)0272-5428

Conference

Conference49th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2008
Country/TerritoryUnited States
CityPhiladelphia, PA
Period25/10/0828/10/08

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