Operator-aware shadow importance sampling for accurate fidelity estimation

• URL: http://arxiv.org/abs/2511.01608v1
• Date: Mon, 03 Nov 2025 14:09:31 GMT
• Title: Operator-aware shadow importance sampling for accurate fidelity estimation
• Authors: Hyunho Cha, Sangwoo Hong, Jungwoo Lee,
• Abstract summary: Grouping-based DFE achieves strong accuracy for small systems but suffers from exponential scaling.<n>Our algorithm improves upon the grouping-based algorithms for Haar-random states.<n>For structured states such as the GHZ and W states, our algorithm also eliminates the exponential memory requirements of previous grouping-based methods.
• Score: 8.212934913387384
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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 upon the grouping-based algorithms for Haar-random states. For structured states such as the 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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