NMR Protocol for Black-Box Ergotropy Estimation via Feedback Algorithm

TL;DR

This paper introduces and experimentally demonstrates a feedback algorithm for estimating quantum ergotropy and preparing passive states using NMR, enabling practical energy extraction at the quantum level.

Contribution

The paper presents a novel feedback-based method for estimating ergotropy and transforming states into passive states, validated through NMR experiments.

Findings

Successfully estimated ergotropy in NMR systems.

Prepared passive states with high accuracy.

Effective even with drive errors.

Abstract

Considering the emerging applications of quantum technologies, studying energy storage and usage at the quantum level is of great interest. In this context, there is a significant contemporary interest in studying ergotropy, the maximum amount of work that can be extracted unitarily from an energy-storing quantum device. Here, we propose and experimentally demonstrate a feedback-based algorithm (FQErgo) for estimating ergotropy. This method also transforms an arbitrary initial state to its passive state, which allows no further unitary work extraction. FQErgo applies drive fields whose strengths are iteratively adjusted via certain expectation values, conveniently read using a single probe qubit. Thus, FQErgo provides a practical way for unitary energy extraction and for preparing passive states. By numerically analyzing FQErgo on random initial states, we confirm the successful preparation of passive states and estimation of ergotropy, even in the presence of drive errors. Finally, we implement FQErgo on two- and three-qubit NMR registers, prepare their passive states, and accurately estimate their ergotropy.