Geometric Construction of Minimal-Dissipation Counterdiabatic Protocols for Open Quantum Systems

Thermodynamic geometry bestows a Riemannian metric structure on the space of a system's thermodynamic states, relating optimal minimum-dissipation protocols that drive between different states to geodesics of the thermodynamic metric in a linear response regime. Recent research has demonstrated an equivalence between thermodynamic geometry and optimal transport for overdamped Langevin dynamics, which has consequently allowed for the construction of optimal protocols beyond the linear response regime as a sum of a geodesic term and a counterdiabatic term readily calculable with the Fisher information metric. We extend these results to open quantum systems governed by Lindbladian dynamics, showing that minimal-dissipation counterdiabatic protocols that are valid for arbitrary driving strengths and speeds may be constructed using the thermodynamic and Fisher information metrics defined on the space of Gibbs states alone. We assess the performance of these geodesic-counterdiabatic protocols on simple toy models, including an analytic single-qubit system interacting with a heat bath.