Provably Efficient Adiabatic Learning for Quantum-Classical Dynamics

Quantum-classical hybrid dynamics is crucial for accurately simulating complex systems where both quantum and classical behaviors need to be considered. However, coupling between classical and quantum degrees of freedom and the exponential growth of the Hilbert space present significant challenges. Current machine learning approaches for predicting such dynamics, while promising, remain unknown in their error bounds, sample complexity, and generalizability. In this work, we establish a generic theoretical framework for analyzing quantum-classical adiabatic dynamics with learning algorithms. Based on quantum information theory, we develop a provably efficient adiabatic learning (PEAL) algorithm with logarithmic system size sampling complexity and favorable time scaling properties. We benchmark PEAL on the Holstein model, and demonstrate its accuracy in predicting single-path dynamics and ensemble dynamics observables as well as transfer learning over a family of Hamiltonians. Our framework and algorithm open up new avenues for reliable and efficient learning of quantum-classical dynamics.