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DOI: 10.4230/LIPIcs.ESA.2021.50
URN: urn:nbn:de:0030-drops-146318
URL: https://drops.dagstuhl.de/opus/volltexte/2021/14631/
Hamoudi, Yassine
Quantum Sub-Gaussian Mean Estimator
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Abstract
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.
BibTeX - Entry
@InProceedings{hamoudi:LIPIcs.ESA.2021.50,
author = {Hamoudi, Yassine},
title = {{Quantum Sub-Gaussian Mean Estimator}},
booktitle = {29th Annual European Symposium on Algorithms (ESA 2021)},
pages = {50:1--50:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-204-4},
ISSN = {1868-8969},
year = {2021},
volume = {204},
editor = {Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/14631},
URN = {urn:nbn:de:0030-drops-146318},
doi = {10.4230/LIPIcs.ESA.2021.50},
annote = {Keywords: Quantum algorithm, statistical analysis, mean estimator, sub-Gaussian estimator, (\epsilon,\delta)-approximation, lower bound}
}
| Keywords: | Quantum algorithm, statistical analysis, mean estimator, sub-Gaussian estimator, (ε,δ)-approximation, lower bound | |
| Seminar: | 29th Annual European Symposium on Algorithms (ESA 2021) | |
| Issue date: | 2021 | |
| Date of publication: | 31.08.2021 |
