Variational Quantum Algorithm for Estimating the Quantum Fisher Information

TL;DR

This paper introduces a variational quantum algorithm called VQFIE that efficiently estimates bounds on the Quantum Fisher Information of mixed states, aiding quantum sensing without requiring explicit sensor dynamics.

Contribution

The paper presents VQFIE, a novel variational algorithm that estimates bounds on QFI for mixed states without needing explicit sensor dynamics, improving accuracy over existing methods.

Findings

VQFIE provides tighter bounds on QFI as state purity increases.

Simulation results demonstrate VQFIE's effectiveness in a magnetometry setup.

Bounds compare favorably to existing literature bounds.

Abstract

The Quantum Fisher information (QFI) quantifies the ultimate precision of estimating a parameter from a quantum state, and can be regarded as a reliability measure of a quantum system as a quantum sensor. However, estimation of the QFI for a mixed state is in general a computationally demanding task. In this work we present a variational quantum algorithm called Variational Quantum Fisher Information Estimation (VQFIE) to address this task. By estimating lower and upper bounds on the QFI, based on bounding the fidelity, VQFIE outputs a range in which the actual QFI lies. This result can then be used to variationally prepare the state that maximizes the QFI, for the application of quantum sensing. In contrast to previous approaches, VQFIE does not require knowledge of the explicit form of the sensor dynamics. We simulate the algorithm for a magnetometry setup and demonstrate the tightening of our bounds as the state purity increases. For this example, we compare our bounds to literature bounds and show that our bounds are tighter.