Predicting Properties of Quantum Systems with Conditional Generative Models

Classical machine learning has emerged recently as a powerful tool for predicting properties of quantum many-body systems. For many ground states of gapped Hamiltonians, generative models can reconstruct the state accurately enough to predict 1- and 2-body observables, given that they are trained on the output of repeated measurements on the same state. Alternatively, kernel methods can predict local observables after being trained on measurement outcomes on different but related quantum states, but effectively require a new model to be trained for each observable. In this work, we combine the benefits of both approaches and propose the use of conditional generative models to simultaneously represent a family of states, by learning shared structures of different quantum states from measurements. The trained model allows us to predict arbitrary local properties of ground states, even for states not present in the training data, and without necessitating further training for new observables. We numerically validate our approach (with simulation of up to 45 qubits) for two quantum many-body problems, 2D random Heisenberg models and Rydberg atom systems.