Universal Defect Statistics in Counterdiabatic Quantum Critical Dynamics

Counterdiabatic driving (CD) provides a framework to reduce excitations in nonadiabatic processes. Exact CD protocols require nonlocal control fields, and CD approximations with tailored locality are needed for their implementation. However, the performance of local CD schemes remains poorly understood. We consider the local CD across a quantum phase transition at an arbitrary rate. We establish its efficiency as a function of the degree of locality and demonstrate that the resulting defect statistics exhibit universal behavior. Our results provide an analytical framework for evaluating the effectiveness of local CD protocols in quantum state preparation, control, and optimization.