Although quantum computing offers a promising solution for strongly correlated system simulation, existing algorithms face significant bottlenecks on current noisy intermediate-scale quantum (NISQ) devices. Here, we introduce QiankunNet-QSCI, a hybrid quantum-classical framework that addresses this challenge by combining efficient quantum-sampling with a transformer neural network. An efficient unitary selected configuration Interaction (USCI) ansatz especially designed for quantum sampling is proposed to identify the most chemically significant electronic configurations on the Zuchongzhi 3.1 quantum processor. Subsequently, the transformer model QiankunNet learns from these sparse yet critical quantum data to infer and reconstruct the complete electronic wavefunction with high fidelity. Simulation of the challenging 40-qubit [2Fe-2S] ferredoxin active center achieves chemical accuracy. Simulation of the nitrogenase P-cluster in a 114-electron 73-orbital active space also reaches 12 milli-Hartree-level agreement with the best density matrix renormalization group (DMRG) result. QiankunNet-QSCI thus offers a practical route to accurate quantum-assisted electronic structure calculations on current devices.
@article{arxiv.2605.24617,
title = {Transformer refined quantum sampling for strongly correlated electronic structure},
author = {Xiongzhi Zeng and Ming Gong and Bowen Kan and Yi Fan and Huan Ma and Jianbin Cai and Yancheng Liu and Naibin Zhou and Tao Jiang and Shaojun Guo and Zhijie Fan and Zongkang Zhang and Yuan Li and Sirui Cao and Kai Yan and Xiaobo Zhu and Yi Luo and Honghui Shang and Zhenyu Li and Jian-Wei Pan and Jinlong Yang},
journal= {arXiv preprint arXiv:2605.24617},
year = {2026}
}