Quantifying protocol efficiency: a thermodynamic figure of merit for classical and quantum state-transfer protocols

TL;DR

This paper introduces a thermodynamic figure of merit called protocol grading to evaluate classical and quantum state-transfer protocols, demonstrating quantum protocols outperform classical ones in speed and accuracy.

Contribution

The paper develops a new protocol grading metric based on fundamental physical quantities, enabling comparison of classical and quantum transfer protocols.

Findings

Quantum protocols are faster and more accurate than classical ones.

Quantum protocols achieve higher protocol grading scores.

The protocol grading accounts for quantum speed limit, fidelity, and thermodynamics.

Abstract

Manipulating quantum systems undergoing non-Gaussian dynamics in a fast and accurate manner is becoming fundamental to many quantum applications. Here, we focus on classical and quantum protocols transferring a state across a double-well potential. The classical protocols are achieved by deforming the potential, while the quantum ones are assisted by a counter-diabatic driving. We show that quantum protocols perform more quickly and accurately. Finally, we design a figure of merit for the performance of the transfer protocols -- namely, the protocol grading -- that depends only on fundamental physical quantities, and which accounts for the quantum speed limit, the fidelity and the thermodynamic of the process. We test the protocol grading with classical and quantum protocols, and show that quantum protocols have higher protocol grading than the classical ones.