Communication Dans Un Congrès Année : 2021

Quantum Sub-Gaussian Mean Estimator

Résumé

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 [BHMT02,BDGT11], or that require prior information on the variance [Hein02,Mon15,HM19]. As an application, we obtain new quantum algorithms for the $(\epsilon,\delta)$-approximation problem with an optimal dependence on the coefficient of variation of the input random variable.

Dates et versions

hal-03454632 , version 1 (29-11-2021)

Identifiants

Citer

Yassine Hamoudi. Quantum Sub-Gaussian Mean Estimator. 29th Annual European Symposium on Algorithms, Sep 2021, Lisbon, Portugal. ⟨10.4230/LIPIcs.ESA.2021.50⟩. ⟨hal-03454632⟩
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