Hamiltonian assignment for open quantum systems

We investigate the problem of determining the Hamiltonian of a locally interacting open quantum system. To do so, we construct Hamiltonian estimators based on inverting a set of stationary, or dynamical, Heisenberg-Langevin equations of motion which rely on a polynomial number of measurements and model parameters. To validate our Hamiltonian assignment methods we numerically simulate one-dimensional XX-interacting spin chains coupled to thermal reservoirs. We provide general bounds on the scalability and assignment error in the presence of noise. In addition to discussing some details of practical implementations we find that, in a dynamical setting, the Hamiltonian estimator's accuracy increases when relaxing the environment's physicality constraints.