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The physics of a closed quantum mechanical system is governed by itsHamiltonian. However, in most practical situations, this Hamiltonian is notprecisely known, and ultimately all there is are data obtained frommeasurements on the system. In this work, we introduce a highly scalable,data-driven approach to learning families of interacting many-body Hamiltoniansfrom dynamical data, by bringing together techniques from gradient-basedoptimization from machine learning with efficient quantum state representationsin terms of tensor networks. Our approach is highly practical, experimentallyfriendly, and intrinsically scalable to allow for system sizes of above 100spins. In particular, we demonstrate on synthetic data that the algorithm workseven if one is restricted to one simple initial state, a small number ofsingle-qubit observables, and time evolution up to relatively short times. Forthe concrete example of the one-dimensional Heisenberg model our algorithmexhibits an error constant in the system size and scaling as the inverse squareroot of the size of the data set.

Scalably learning quantum many-body Hamiltonians from dynamical data