Shutao Zhang

Qing-Hong Cao, Zong-Yue Hou, Ying-Ying Li et al.

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 \texttt{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 $n \ge 4$, 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.

Zhuo-Yang Song, Zeyu Cai, Shutao Zhang et al.

Symbolic regression (SR), the automated discovery of mathematical expressions from data, is a cornerstone of scientific inquiry. However, it is often hindered by the combinatorial explosion of the search space and a tendency to overfit. Popular methods, rooted in genetic programming, explore this space syntactically, often yielding overly complex, uninterpretable models. This paper introduces IdeaSearchFitter, a framework that employs Large Language Models (LLMs) as semantic operators within an evolutionary search. By generating candidate expressions guided by natural-language rationales, our method biases discovery towards models that are not only accurate but also conceptually coherent and interpretable. We demonstrate IdeaSearchFitter's efficacy across diverse challenges: it achieves competitive, noise-robust performance on the Feynman Symbolic Regression Database (FSReD), outperforming several strong baselines; discovers mechanistically aligned models with good accuracy-complexity trade-offs on real-world data; and derives compact, physically-motivated parametrizations for Parton Distribution Functions in a frontier high-energy physics application. IdeaSearchFitter is a specialized module within our broader iterated agent framework, IdeaSearch, which is publicly available at https://www.ideasearch.cn/.