Feedback-Based Learning of Ground State Properties using Tensor Cross Interpolation

The integration of machine learning with quantum computing is a vital pathway for accelerating scientific discovery in many-body physics. However, mapping out the properties of quantum materials over extended parameter regimes, such as required for identifying phase transitions, remains computationally expensive because individual evaluations, e.g., on a quantum computer, are expensive. We propose an active learning loop to explore parameter spaces of quantum models in a more sample-efficient way. We treat the quantum processor as a high-cost oracle and use tensor cross interpolation (TCI) as a classical agent to control it. TCI efficiently reconstructs a surrogate model by adaptively querying the oracle at informative parameter points and interpolating the remaining parameter space. We benchmark this approach on the transverse-field XY model, focusing on learning the energy gap across its phase diagram. Our results show that TCI autonomously concentrates its sampling budget near critical phase boundaries, where the structure of ground state properties is most complex. In these regions, our framework achieves higher accuracy than standard regression baselines with the same sampling budget, providing a scalable strategy for AI-driven materials discovery in the era of early fault-tolerant quantum computing.