Agent-VQE: Learning Transferable Quantum Circuit Programs for Gradient-Free Deployment at Scale

The high measurement overhead of gradient-based optimization is a bottleneck for deploying the variational quantum eigensolver at scale. We introduce Agent-VQE, an AI-assisted framework that learns transferable quantum circuit programs from small systems for gradient-free deployment. The agent analyzes local Hamiltonian features to propose circuit architectures and parameter-sharing rules, then iteratively refines these designs through small-system optimization and energy evaluation. The resulting circuit programs encode reusable circuit-building rules and shared circuit parameters. Larger circuits directly reuse these rules and coefficients without target-side gradient evaluations or parameter updates. Across six spin and fermionic many-body benchmarks spanning chain, ladder, and fully connected interaction structures, we fit circuit programs for ground-state energy estimation on systems of at most 16 qubits and evaluate the resulting circuits in noiseless simulations with 100–1000 qubits. Relative differences from reference energies remain below $1\%$ for five of the six benchmarks, while Fermi–Hubbard has the largest difference of $5.31\%$. We further execute the learned one-dimensional transverse-field Ising model (TFIM) circuits on an OriginQ quantum computer. Measurements from 4–16-qubit circuits support measured-energy extrapolation up to 38 qubits. A separate comparison shows that the learned 32-qubit circuit achieves lower measured energy than randomized circuits of the same logical depth, despite hardware noise. These results support small-system circuit learning as a route to scalable ground-state energy estimation without costly target-side optimization.