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NMR protocol for black-box ergotropy estimation via feedback algorithm

Jitendra Joshi* and T. S. Mahesh†

  • *Contact author: jitendra.joshi@students.iiserpune.ac.in
  • †Contact author: mahesh.ts@iiserpune.ac.in
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Phys. Rev. A 113, 032407 – Published 4 March, 2026

DOI: https://doi.org/10.1103/7pjs-146q

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 a feedback-based quantum algorithm for ergotropy estimation using Lyapunov control techniques. By iteratively adjusting the strengths of applied drive fields, our algorithm achieves both unitary energy extraction and passive state preparation efficiently. Unlike previous approaches, this algorithm does not require any classical optimization, is resilient to cumulative errors, and eliminates the need for any time-consuming quantum state tomography. We validate these advantages via numerical simulations demonstrating robustness even under noisy conditions. Additionally, we experimentally implement the algorithm on up to three-qubit NMR registers, establishing its practical viability.

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Phys. Rev. A 113, 032407– Published 4 March, 2026
  • Received 11 October 2024
  • Accepted 9 February 2026
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