Scalable Quantum State Preparation via Large-Language-Model-Driven Discovery

TL;DR

A large language model (LLM)-assisted framework for quantum-circuit design that systematically scales state-preparation circuits to large lattice volumes is introduced, providing the first scalable ansatz for this class of 2+1d models.

Abstract

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.

Figures (9)

• Figure 1: Integrated workflow for quantum ansatz design.
• Figure 2: Best ansatz returned for the $XY$ model.
• Figure 3: Optimal parameters obtained for the ansatz in Fig. \ref{['fg:best-llm']} as a function of the system size $n$. The red lines correspond to the fitting functions shown in the legend.
• Figure 4: Ground-state energy for different system sizes. Blue dots show energies obtained from circuits using the fitted parameters in Fig. \ref{['fg:theta_XY']}, and red squares indicate the exact ground-state energies. The inset shows the relative energy deviation from the exact values.
• Figure 5: The geometry of the two-qubit meta-circuit $\rm MCZ (\theta)$ for the $2$+$1$d scalar field theory.