Scalable quantum state preparation via large-language-model-driven discovery

Efficient quantum state preparation remains a central challenge in first-principles quantum simulations of dynamics in quantum field theories, where the Hilbert space is intrinsically infinite-dimensional. Here, we introduce a large language model (LLM)-assisted framework for quantum-circuit design that systematically scales state-preparation circuits to large lattice volumes. Applied to a 1+1d XY spin chain, the LLM autonomously discovers a compact 4-parameter circuit that captures boundary-induced symmetry breaking with sub-percent energy deviation, enabling successful validation on the Zuchongzhi quantum processor. Guided by this insight, we extend the framework to 2+1d quantum field theories, where scalable variational ansätze have remained elusive. For a scalar field theory, the search yields a symmetry-preserving, 3-parameter shallow-depth ansatz whose optimized parameters converge to size-independent constants for lattices n ≥ 4, providing, to our knowledge, the first scalable ansatz for this class of 2+1d models. Our results establish a practical route toward AI-assisted, human-guided discovery in quantum simulation.