Cost of counterdiabatic driving and work output

TL;DR

This paper investigates the effectiveness and costs of counterdiabatic quantum driving in finite-time work extraction, introducing a measure called exigency to quantify the need for external driving without detailed knowledge of the driving Hamiltonian.

Contribution

It demonstrates that counterdiabatic driving is not always beneficial for work extraction, proposes a method to reduce its cost based on measurement outcomes, and introduces the exigency measure for quantifying adiabaticity needs.

Findings

Counterdiabatic driving effectiveness depends on process timescale and physical realization.

Cost of counterdiabatic driving can be reduced by outcome-dependent Hamiltonian selection.

Exigency measure quantifies the need for external driving without explicit Hamiltonian knowledge.

Abstract

Unitary processes allow for the transfer of work to and from Hamiltonian systems. However, to achieve nonzero power for the practical extraction of work, these processes must be performed within a finite time, which inevitably induces excitations in the system. We show that depending on the time scale of the process and the physical realization of the external driving employed, the use of counterdiabatic quantum driving to extract more work is not always effective. We also show that by virtue of the two-time energy measurement definition of quantum work, the cost of counterdiabatic driving can be significantly reduced by selecting a restricted form of the driving Hamiltonian that depends on the outcome of the first energy measurement. Lastly, we introduce a measure, the exigency, that quantifies the need for an external driving to preserve quantum adiabaticity which does not require knowledge of the explicit form of the counterdiabatic drivings, and can thus always be computed. We apply our analysis to systems ranging from a two-level Landau-Zener problem to many-body problems, namely, the quantum Ising and Lipkin-Meshkov-Glick models.