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Quantum Sub-Gaussian Mean Estimator

Author Yassine Hamoudi

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Author Details

Yassine Hamoudi
  • Université de Paris, IRIF, CNRS, F-75013 Paris, France

Funding

This research was supported in part by the ERA-NET Cofund in Quantum Technologies project QuantAlgo and the French ANR Blanc project RDAM.

Acknowledgements

The authors want to thank the anonymous referees for their valuable comments and suggestions which helped to improve this paper.

Cite AsGet BibTex

Yassine Hamoudi. Quantum Sub-Gaussian Mean Estimator. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 50:1-50:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.ESA.2021.50

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum computation theory
Keywords
  • Quantum algorithm
  • statistical analysis
  • mean estimator
  • sub-Gaussian estimator
  • (ε,δ)-approximation
  • lower bound

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