Provable learning separation for predicting time-evolution of quantum many-body systems

Provable quantum-classical learning separation for predicting quantum many-body time evolution

A new arXiv preprint establishes a rigorous PAC-learning separation between quantum and classical algorithms for predicting the time evolution of quantum many-body systems under an unknown Hamiltonian. The quantum procedure learns the Hamiltonian from short-time samples and uses Hamiltonian simulation with classical shadows for inference, while classical hardness is proven by embedding a BQP-complete computation into Feynman-Kitaev clock Hamiltonian dynamics, ruling out classical polynomial-time solutions unless BQP ⊆ P/poly. The result connects quantum learning theory, quantum simulation, and quantum machine learning, providing one of the first provable learning separations for a physically motivated QML task.