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  • Open Access

Efficient sampling for Pauli-measurement-based shadow tomography in direct fidelity estimation

Hyunho Cha* and Jungwoo Lee†

  • *Contact author: aiden132435@cml.snu.ac.kr
  • †Contact author: junglee@snu.ac.kr
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Phys. Rev. A 112, 032427 – Published 15 September, 2025

DOI: https://doi.org/10.1103/4pzk-lznf

Abstract

A constant number of random Clifford measurements allows the classical shadow protocol to perform direct fidelity estimation (DFE) with high precision. However, estimating properties of an unknown quantum state is expected to be more feasible with random Pauli measurements than with random Clifford measurements in the near future. Inspired by the importance sampling technique applied to sampling Pauli measurements for DFE, we show that similar strategies can be derived from classical shadows. Specifically, we describe efficient methods using only local Pauli measurements to perform DFE with Greenberger-Horne-Zeilinger (GHZ), W, and Dicke states, establishing tighter bounds (by factors of 14.22 and 16 for GHZ and W/Dicke, respectively) on the number of measurements required for desired precision. These protocols are derived by adjusting the distribution of observables. Notably, they require no preprocessing steps other than the sampling algorithms.

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Phys. Rev. A 112, 032427– Published 15 September, 2025
  • Received 11 February 2025
  • Accepted 13 August 2025
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