Learning exotic phases of matter via hidden Born Machines

Quantum Inspired generative models are becoming one of the most appealing tools in machine learning.  Owning to the quantum nature they can express complex distributions which are intractable by a classical computer, leading to quantum advantage. However, their learning power and efficient training schemes are far from being understood and are an ongoing investigation. Here, we focus on Born machines as quantum-inspired generative models, which allow the parameterization of the joint probability distributions of target data via  Born probabilities of quantum states.  We first focus on the Complex Born Machine, harnessing already existing tools such as tensor Network as an efficient ansatz, and present our results in learning exotic phases of quantum states obtained from XY and Rysberg spin chain. We further introduce the periodic Born Machine and show that matching the boundary condition of the Born Machine and that of training data improves the performance when limited data is available. We finally comment on the power of learning of complex Born machines when data from a different base is obtained.