Excess work in counterdiabatic driving
Phys. Rev. A 113, 052608 – Published 12 May, 2026
DOI: https://doi.org/10.1103/h892-xyj1
Abstract
Many years have passed since the conception of the quintessential method of the shortcut to adiabaticity known as counterdiabatic driving (or transitionless quantum driving). However, this method appears to be energetically cost-free and thus continually challenges the task of quantifying the amount of energy it requires to be achieved. This paper proposes that the energy cost of controlling a closed quantum system using the counterdiabatic method can also be assessed using the instantaneous excess work during the process and related quantities, such as the time-averaged excess work. Starting from the Mandelstam-Tamm bound for driven dynamics, we show that the speedup of counterdiabatic driving is linked to the spreading of energy between the eigenstates of the total Hamiltonian, which is necessarily accompanied by transitions between these eigenstates. Nonetheless, although excess work can be used to energetically quantify these transitions, it is well-known that the excess work is zero throughout the entire process under counterdiabatic driving. To recover the excess work as an energetic cost quantifier for counterdiabatic driving, we propose a different interpretation of the parameters of the counterdiabatic Hamiltonian, leading to an excess work different from zero. We illustrate our findings using the Landau-Zener model.
