Searching for degenerate ground spaces in quantum many-body systems is central to understanding spontaneous symmetry breaking and topological order. Although existing numerical methods can approximate individual ground states with high accuracy, recovering the full degenerate space remains a substantial challenge. Here, we address this problem using a hybrid generative quantum circuit that combines a classical generative model with an expressive parametrized quantum circuit (PQC). The classical model learns a distribution over PQC parameters, enabling the generation of an ensemble of ground states, while the PQC ensures compatibility with quantum hardware. To promote both low energy and state diversity, we define an energy-diversity objective composed of an energy-minimization term and cosine-similarity penalties derived from local observable correlators. These local descriptors provide a scalable, measurement-efficient means of distinguishing different ground-state directions. We benchmark the framework on the Majumdar-Ghosh model, the Affleck-Kennedy-Lieb-Tasaki model, and the spin-1 XXZ chain, which realize distinct mechanisms of degeneracy. In all cases the method produces diverse ensembles whose linear spans accurately reproduce the target ground spaces, and in some instances it identifies approximately orthogonal bases within the learned ensembles. Finite-shot simulations on small MG chains further show that the training protocol remains stable under sampling noise, preserving the recovered ground-space span.

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• Deep learning
• Quantum algorithms
• Quantum circuits