High-accuracy Hamiltonian learning via delocalized quantum state evolutions

In this paper, we propose a method to learn the unknown Hamiltonian governing the dynamics of a quantum many-body system, using measurements on a single time-dependent state. We investigate the error scaling of our reconstruction with respect to the experiment duration, measuring an exponential decrease during the equilibration time. We prove that the accuracy of the learning process is maximised for states that are delocalized in the Hamiltonian eigenstates, capable of exploring a large sample of the Hilbert space. This behavior is exploited to select optimal initial states for the learning algorithm. We provide two examples of our learning algorithm on simulated quantum systems