QuMUSE: Generative Pretraining from Local Measurements for Characterizing Quantum Many-Body Ground States

Characterizing quantum many-body ground states is fundamental to understanding quantum matter and advancing quantum technologies. However, most existing learning methods remain specialized to a particular Hamiltonian family, system size, or tasks, limiting knowledge reuse across physical systems. We introduce QuMUSE, a local measurement-native generative foundation model that learns unified, reusable representations of many-body ground states from local observables, targeting Hamiltonian families of variable scales and lattice geometries. QuMUSE consists of a variational autoencoder that compresses variable-dimensional measurement data into a fixed-size, physical system-aware latent state representation that decodes local observables, and a conditional latent flow model that generates state representations from physical specifications alone. Therefore, one unified representation supports both characterization from measurements and prediction without target-state measurements. Jointly pretrained on five 1D and 2D Hamiltonian families with up to 100 qubits, QuMUSE achieves the best overall observable-reconstruction and conditional-generation performance among baselines. Despite training only on local observables, the representations support predicting nonlinear and global properties, data-efficient adaptation to unseen Hamiltonian families, and unsupervised phase boundary witnessing. These results demonstrate the potential of measurement-native generative pretraining to reuse physical information across quantum systems and learning tasks.