Generative Quantum-inspired Kolmogorov-Arnold Eigensolver
Abstract
High-performance computing (HPC) is increasingly important for scalable quantum chemistry workflows that couple classical generative models, quantum circuit simulation, and selected configuration interaction postprocessing. We present the generative quantum-inspired Kolmogorov-Arnold eigensolver (GQKAE), a parameter-efficient extension of the generative quantum eigensolver (GQE) for quantum chemistry. GQKAE replaces the parameter-heavy feed-forward network components in GPT-style generative eigensolvers with hybrid quantum-inspired Kolmogorov-Arnold network modules, forming a compact HQKANsformer backbone. The method preserves autoregressive operator selection and the quantum-selected configuration interaction evaluation pipeline, while using single-qubit DatA Re-Uploading ActivatioN modules to provide expressive nonlinear mappings. Numerical benchmarks on H4, N2, LiH, C2H6, H2O, and the H2O dimer show that GQKAE achieves chemical accuracy comparable to the GPT-based GQE architecture, while reducing trainable parameters and memory by approximately 66% and improving wall-time performance. For strongly correlated systems such as N2 and LiH, GQKAE also improves convergence behavior and final energy errors. These results indicate that quantum-inspired Kolmogorov-Arnold networks can reduce classical-side overhead while preserving circuit-generation quality, offering a scalable route for HPC-quantum co-design on near-term quantum platforms.
Cite
@article{arxiv.2605.04604,
title = {Generative Quantum-inspired Kolmogorov-Arnold Eigensolver},
author = {Yu-Cheng Lin and Yu-Chao Hsu and I-Shan Tsai and Chun-Hua Lin and Kuo-Chung Peng and Jiun-Cheng Jiang and Yun-Yuan Wang and Tzung-Chi Huang and Tai-Yue Li and Kuan-Cheng Chen and Samuel Yen-Chi Chen and Nan-Yow Chen},
journal= {arXiv preprint arXiv:2605.04604},
year = {2026}
}