Learning via Many-Body Localized Hidden Born Machine

Born Machines are novel generative models that leverage the probabilistic nature of the quantum states. While Born Machines based on tensor networks has shown great success learning both classical and quantum data, here, we use many-body localized states as a novel resource for learning. We present rigorous proof of expressibility of the MBL-Born Machine and show our numerical results that the driven quantum state via MBL dynamic is able to learn both MNIST data set and data from the quantum many-body state. At this end, we demonstrate that adding hidden unit boost the learnability power of the Born Machine . We further investigate the connection between disorder and the learnability power of the MBL phase by calculating various local quantities.