Robust estimation of the Quantum Fisher Information on a quantum processor

TL;DR

This paper demonstrates an experimental method to accurately estimate the quantum Fisher information on a quantum processor, enabling certification of entanglement and analysis of quantum states under noise.

Contribution

It introduces a robust measurement protocol for QFI estimation that mitigates errors, and applies it to complex quantum states including GHZ and Ising model ground states.

Findings

Successfully measured QFI for GHZ states, confirming multipartite entanglement.

Estimated QFI for Ising model ground state at criticality, analyzing noise effects.

Developed a noise-resilient randomized measurement technique.

Abstract

We present the experimental measurement, on a quantum processor, of a series of polynomial lower bounds that converge to the quantum Fisher information (QFI), a fundamental quantity for certifying multipartite entanglement that is useful for metrological applications. We combine advanced methods of the randomized measurement toolbox to obtain estimators that are robust against drifting errors caused uniquely during the randomized measurement protocol. We estimate the QFI for Greenberg-Horne-Zeilinger states, observing genuine multipartite entanglement. Then, we prepare the ground state of the transverse field Ising model at the critical point using a variational circuit. We estimate its QFI and investigate the interplay between state optimization and noise induced by increasing the circuit depth.