Hamiltonian Tomography via Quantum Quench

We show that it is possible to uniquely reconstruct a generic many-body local Hamiltonian from a single pair of initial and final states related by time evolution with the Hamiltonian. We then propose a practical version of the protocol involving multiple pairs of such initial/final states. Using the eigenstate thermalization hypothesis, we provide bounds on the protocol's performance and stability against errors from measurements and in the ansatz of the Hamiltonian. The protocol is efficient (requiring experimental resources scaling polynomially with system size in general and constant with system size given translation symmetry) and thus enables analog and digital quantum simulators to verify implementation of a putative Hamiltonian.