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Machine learning has emerged recently as a powerful tool for predictingproperties of quantum many-body systems. For many ground states of gappedHamiltonians, generative models can learn from measurements of a single quantumstate to reconstruct the state accurately enough to predict local observables.Alternatively, kernel methods can predict local observables by learning frommeasurements on different but related states. In this work, we combine thebenefits of both approaches and propose the use of conditional generativemodels to simultaneously represent a family of states, by learning sharedstructures of different quantum states from measurements. The trained modelallows us to predict arbitrary local properties of ground states, even forstates not present in the training data, and without necessitating furthertraining for new observables. We numerically validate our approach (withsimulations of up to 45 qubits) for two quantum many-body problems, 2D randomHeisenberg models and Rydberg atom systems.

Predicting Properties of Quantum Systems with Conditional Generative Models