  Identifying an accurate model for the dynamics of a quantum system is a
vexing problem that underlies a range of problems in experimental physics and
quantum information theory. Recently, a method called quantum Hamiltonian
learning has been proposed by the present authors that uses quantum simulation
as a resource for modeling an unknown quantum system. This approach can, under
certain circumstances, allow such models to be efficiently identified. A major
caveat of that work is the assumption of that all elements of the protocol are
noise-free. Here, we show that quantum Hamiltonian learning can tolerate
substantial amounts of depolarizing noise and show numerical evidence that it
can tolerate noise drawn from other realistic models. We further provide
evidence that the learning algorithm will find a model that is maximally close
to the true model in cases where the hypothetical model lacks terms present in
the true model. Finally, we also provide numerical evidence that the algorithm
works for non-commuting models. This work illustrates that quantum Hamiltonian
learning can be performed using realistic resources and suggests that even
imperfect quantum resources may be valuable for characterizing quantum systems.
