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Geometric quantum speed limits quantify the trade-off between the rate withwhich quantum states can change and the resources that are expended during theevolution. Counterdiabatic driving is a unique tool from shortcuts toadiabaticity to speed up quantum dynamics while completely suppressingnonequilibrium excitations. We show that the quantum speed limit forcounterdiabatically driven systems undergoing quantum phase transitions fullyencodes the Kibble-Zurek mechanism by correctly predicting the transition fromadiabatic to impulse regimes. Our findings are demonstrated for threescenarios, namely the transverse field Ising, the Landau-Zener, and theLipkin-Meshkov-Glick models.

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