Trade-Off Between Speed and Cost in Shortcuts to Adiabaticity

Abstract

Achieving effectively adiabatic dynamics is a ubiquitous goal in almost all areas of quantum physics. Here, we study the speed with which a quantum system can be driven when employing transitionless quantum driving. As a main result, we establish a rigorous link between this speed, the quantum speed limit, and the (energetic) cost of implementing such a shortcut to adiabaticity. Interestingly, this link elucidates a trade-off between speed and cost, namely, that instantaneous manipulation is impossible as it requires an infinite cost. These findings are illustrated for two experimentally relevant systems—the parametric oscillator and the Landau-Zener model—which reveal that the spectral gap governs the quantum speed limit as well as the cost for realizing the shortcut.