Quantum Machine Learning with Quantum-Probabilistic Generative Models

In this work we explore the task of generatively modelling mixed quantum states using hybridizations of classical probabilistic machine learning models and quantum neural networks (QNNs). More specifically, we explore applications of these models to the tasks of either learning to replicate a mixed quantum state from a collection of measurements outcomes for a set of local observables or direct coherent quantum-access to copies of the quantum state. We focus on a particular class of quantum-probabilistic models called quantum Hamiltonian-based models, which are a composition of a classical energy-based model (EBM) with a parameterized unitary QNN. We show how one can tractably sample from this class of hybrid model via classical MCMC sampling and conditional sampling through a QNN running on a quantum computer. Furthermore, we derive analytic expressions for unbiased estimators of both the gradients of the quantum relative entropy and the Quantum Fisher information metric for the full hybrid model. We demonstrate how this enables scalable training of such models via global natural gradient descent. Finally, we discuss implementation of sampling and training algorithms for such models via a combination of TensorFlow Probability and TensorFlow Quantum.