  The physics of a closed quantum mechanical system is governed by its
Hamiltonian. However, in most practical situations, this Hamiltonian is not
precisely known, and ultimately all there is are data obtained from
measurements on the system. In this work, we introduce a highly scalable,
data-driven approach to learning families of interacting many-body Hamiltonians
from dynamical data, by bringing together techniques from gradient-based
optimization from machine learning with efficient quantum state representations
in terms of tensor networks. Our approach is highly practical, experimentally
friendly, and intrinsically scalable to allow for system sizes of above 100
spins. In particular, we demonstrate on synthetic data that the algorithm works
even if one is restricted to one simple initial state, a small number of
single-qubit observables, and time evolution up to relatively short times. For
the concrete example of the one-dimensional Heisenberg model our algorithm
exhibits an error constant in the system size and scaling as the inverse square
root of the size of the data set.
