High-accuracy Hamiltonian learning via delocalized quantum state evolutions

Learning the unknown Hamiltonian gov-erning the dynamics of a quantum many -body system is a challenging task. In this manuscript, we propose a possible strat-egy based on repeated measurements on a single time-dependent state. We prove that the accuracy of the learning process is maximized for states that are delocal-ized in the Hamiltonian eigenbasis. This implies that delocalization is a quantum re-source for Hamiltonian learning, that can be exploited to select optimal initial states for learning algorithms. We investigate the error scaling of our reconstruction with re-spect to the number of measurements, and we provide examples of our learning algo-rithm on simulated quantum systems.