Compressed Sensing for Efficient Fidelity Estimation of GHZ States

TL;DR

This paper introduces a compressed sensing method to efficiently estimate the fidelity of GHZ states, reducing measurement effort while maintaining accuracy, and demonstrates its effectiveness on simulators and quantum hardware.

Contribution

It presents a novel compressed sensing protocol tailored for GHZ state fidelity estimation, leveraging state sparsity for efficiency and robustness in noisy quantum experiments.

Findings

Significant reduction in measurement overhead for fidelity estimation.

High accuracy maintained despite noise in experimental environments.

Successful implementation on both simulators and trapped-ion hardware.

Abstract

Accurately characterizing multipartite entangled states is a critical challenge in quantum information processing. In this work, we focus on applying compressed sensing techniques to efficiently estimate the fidelity of Greenberger-Horne-Zeilinger (GHZ) states. By exploiting the inherent sparsity of these states, our compressed sensing protocol drastically reduces the measurement overhead traditionally required for state verification while maintaining high accuracy. To evaluate the practical performance of this approach, we test the protocol on GHZ states using both quantum simulators and Quantinuum's trapped-ion hardware. Furthermore, we implement error detection techniques during our hardware evaluations, demonstrating the robustness and viability of compressed sensing for fidelity estimation in noisy experimental environments.