  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 learn from measurements of a single quantum
state to reconstruct the state accurately enough to predict local observables.
Alternatively, classification and regression models can predict local
observables by learning from measurements on different but related states. 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,
learning shared structures of different quantum states from measurements. The
trained model enables us to predict arbitrary local properties of ground
states, even for states not included in the training data, without
necessitating further training for new observables. We first numerically
validate our approach on 2D random Heisenberg models using simulations of up to
45 qubits. Furthermore, we conduct quantum simulations on a neutral-atom
quantum computer and demonstrate that our method can accurately predict the
quantum phases of square lattices of 13$\times$13 Rydberg atoms.
