Parent hamiltonians of restricted Boltzmann machine wavefunctions*

Wavefunctions based on the restricted Boltzmann machine (RBM) architecture have recently been found to be highly effective in variational calculations on interacting spin models. The promise of RBMs for compactly encoding quantum states motivates study of the structure underlying RBM wavefunctions. Here we tackle the question of what hamiltonians take RBM wavefunctions as eigenstates. Using a recently developed framework for identifying local hamiltonians from wavefunctions, we consider a select set of RBM states, and comment on the features of their parent hamiltonians.