2026-07-21T03:11:31Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:14631 2024-03-06T10:54:29Z ddc:004 open_access

Quantum Sub-Gaussian Mean Estimator Hamoudi, Yassine Quantum algorithm statistical analysis mean estimator sub-Gaussian estimator (ε,δ)-approximation lower bound We present a new quantum algorithm for estimating the mean of a real-valued random variable obtained as the output of a quantum computation. Our estimator achieves a nearly-optimal quadratic speedup over the number of classical i.i.d. samples needed to estimate the mean of a heavy-tailed distribution with a sub-Gaussian error rate. This result subsumes (up to logarithmic factors) earlier works on the mean estimation problem that were not optimal for heavy-tailed distributions [Brassard et al., 2002; Brassard et al., 2011], or that require prior information on the variance [Heinrich, 2002; Montanaro, 2015; Hamoudi and Magniez, 2019]. As an application, we obtain new quantum algorithms for the (ε,δ)-approximation problem with an optimal dependence on the coefficient of variation of the input random variable. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Yassine Hamoudi 2021 Is Part Of LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ESA.2021.50 urn:nbn:de:0030-drops-146318 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.50 eng https://creativecommons.org/licenses/by/4.0/legalcode