Energy based models for tomography of quantum spin-lattice systems

We present a novel method to learn Energy-Based Models (EBM) from quantum tomography data. We represent quantum states via distributions generated by generalized measurements and use state-of-the-art algorithms for energy function learning to obtain a representation of these states as classical Gibbs distributions. Our results show that this method is especially well suited for learning quantum thermal states. For the case of ground states, we find that the learned EBMs often have an effective temperature that makes learning easier, especially in the paramagnetic phase.