Publication Type
Journal Article
Version
publishedVersion
Publication Date
10-2025
Abstract
The classical shadows protocol, introduced by Huang et al (2020 Nat. Phys. 16 1050), makes use of the median-of-means (MoM) estimator to efficiently estimate the expectation values of M observables with failure probability δ using only O ( log ( M / δ ) ) measurements. In their analysis, Huang et al used loose constants in their asymptotic performance bounds for simplicity. However, the specific values of these constants can significantly affect the number of shots used in practical implementations. To address this, we studied a modified MoM estimator proposed by Minsker (2023 Proc. 36th Conf. on Learning Theory (PMLR) 195 5925) that uses optimal constants and involves a U-statistic over the data set. For efficient estimation, we implemented two types of incomplete U-statistics estimators, the first based on random sampling and the second based on cyclically permuted sampling. We compared the performance of the original and modified estimators when used with the classical shadows protocol with single-qubit Clifford unitaries (Pauli measurements) for an Ising spin chain, and global Clifford unitaries (Clifford measurements) for the Greenberger-Horne-Zeilinger state. While the original estimator outperformed the modified estimators for Pauli measurements, the modified estimators showed improved performance over the original estimator for Clifford measurements. Our findings highlight the importance of tailoring estimators to specific measurement settings to optimize the performance of the classical shadows protocol in practical applications.
Keywords
Classical, estimation, quantum, shadows, tomography
Discipline
Theory and Algorithms
Publication
Quantum Science and Technology
Volume
10
Issue
3
First Page
1
Last Page
21
ISSN
2058-9565
Identifier
10.1088/2058-9565/addffd
Publisher
IOP Publishing
Citation
FU, Winston; KOH, Dax Enshan; GOH, Siong Thye; and KONG, Jian Feng.
Classical shadows with improved median-of-means estimation. (2025). Quantum Science and Technology. 10, (3), 1-21.
Available at: https://ink.library.smu.edu.sg/sis_research/10383
Copyright Owner and License
Authors CC-BY
Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.
Additional URL
https://doi.org/10.1088/2058-9565/addffd