Operator-aware shadow importance sampling for accurate fidelity estimation

TL;DR

This paper introduces operator-aware shadow importance sampling algorithms that enhance fidelity estimation accuracy and scalability for various quantum states, overcoming limitations of previous methods.

Contribution

It develops two classes of algorithms using informationally overcomplete POVMs, improving accuracy and reducing memory requirements for structured quantum states.

Findings

Outperforms existing grouping-based DFE on Haar-random states.

Eliminates exponential memory needs for structured states like GHZ and W.

Achieves state-of-the-art fidelity estimation across multiple quantum state types.

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.