Kibble-Zurek scaling in quantum speed limits for shortcuts to adiabaticity

TL;DR

This paper demonstrates that geometric quantum speed limits for counterdiabatic driving inherently encode the Kibble-Zurek mechanism, accurately predicting the transition from adiabatic to impulse regimes in quantum phase transitions across multiple models.

Contribution

It reveals that quantum speed limits for counterdiabatic driving naturally incorporate the Kibble-Zurek mechanism, linking quantum speed limits with phase transition dynamics.

Findings

Quantum speed limits predict adiabatic to impulse transition.

Kibble-Zurek mechanism is encoded in quantum speed limits.

Validated across Ising, Landau-Zener, and Lipkin-Meshkov-Glick models.

Abstract

Geometric quantum speed limits quantify the trade-off between the rate with which quantum states can change and the resources that are expended during the evolution. Counterdiabatic driving is a unique tool from shortcuts to adiabaticity to speed up quantum dynamics while completely suppressing nonequilibrium excitations. We show that the quantum speed limit for counterdiabatically driven systems undergoing quantum phase transitions fully encodes the Kibble-Zurek mechanism by correctly predicting the transition from adiabatic to impulse regimes. Our findings are demonstrated for three scenarios, namely the transverse field Ising, the Landau-Zener, and the Lipkin-Meshkov-Glick models.