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  • Open Access

Operator-aware shadow importance sampling for accurate fidelity estimation

Hyunho Cha1,*, Sangwoo Hong2,†, and Jungwoo Lee1,‡

  • 1NextQuantum and Department of Electrical and Computer Engineering, Seoul National University, Seoul 08826, Republic of Korea
  • 2Department of Computer Science and Engineering, Konkuk University, Seoul 05029, Republic of Korea

  • *Contact author: ovalavo@snu.ac.kr
  • †Contact author: swhong06@konkuk.ac.kr
  • ‡Contact author: junglee@snu.ac.kr
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Phys. Rev. A 113, 042602 – Published 6 April, 2026

DOI: https://doi.org/10.1103/9fr2-dvg7

Abstract

Estimating the fidelity between an unknown quantum state and a fixed target is a fundamental task in quantum information science. Direct fidelity estimation (DFE) enables this without full tomography by sampling observables according to a target-dependent distribution. However, existing approaches face notable trade-offs. Grouping-based DFE achieves strong accuracy for small systems but suffers from exponential scaling, and its applicability is restricted to Pauli measurements. In contrast, classical-shadow-based DFE offers scalability but yields lower accuracy on structured states. In this work, we address these limitations by developing two classes of operator-aware shadow importance sampling algorithms using informationally overcomplete positive operator-valued measures. Instantiated with local Pauli measurements, our algorithm improves over the grouping-based algorithms for Haar-random states. For structured states such as the Greenberger-Horne-Zeilinger (GHZ) and W states, our algorithm also eliminates the exponential memory requirements of previous grouping-based methods. Numerical experiments confirm that our methods achieve state-of-the-art performance across Haar-random, GHZ, and W targets.

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Phys. Rev. A 113, 042602– Published 6 April, 2026
  • Received 23 November 2025
  • Accepted 9 March 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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