Trade-off between speed and cost in shortcuts to adiabaticity

TL;DR

This paper explores the fundamental trade-off between the speed and energetic cost of implementing shortcuts to adiabaticity in quantum systems, establishing a rigorous link with the quantum speed limit and illustrating it with relevant models.

Contribution

It introduces a theoretical framework connecting the speed, cost, and quantum speed limit in shortcuts to adiabaticity, highlighting the impossibility of instantaneous control due to infinite cost.

Findings

Spectral gap determines quantum speed limit and cost

Instantaneous manipulation requires infinite energetic cost

Trade-off between speed and cost is fundamental in quantum control

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.