Assigning Hamiltonians to Open Quantum Systems

Building on recent efforts illustrating that one may characterize a closed system of k-local interacting particles, we study the task of identifying a local-Hamiltonian in the presence of additional environmental interactions. Beginning with a candidate system consisting of an XX-interacting spin chain subject to thermal relaxation noise, we show how both the Hamiltonian and the underlying Lindbladian can models can be inferred. Moreover, we study open-systems learning in the settings where one is given i) access to steady states, ii) dynamical information, as well as iii) in the presence of stochastic noise on the measurement output.