TY - GEN

T1 - The Bayesian learner is optimal for noisy binary search (and pretty good for quantum as well)

AU - Or, Michael Ben

AU - Hassidim, Avinatan

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=57949112800&partnerID=8YFLogxK

U2 - 10.1109/FOCS.2008.58

DO - 10.1109/FOCS.2008.58

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AN - SCOPUS:57949112800

SN - 9780769534367

T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

SP - 221

EP - 230

BT - Proceedings of the 49th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2008

T2 - 49th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2008

Y2 - 25 October 2008 through 28 October 2008

ER -