Generative Quantum-inspired Kolmogorov-Arnold Eigensolver
Authors: name: Yu-Cheng Lin, name: Yu-Chao Hsu, name: I-Shan Tsai, name: Chun-Hua Lin, name: Kuo-Chung Peng, name: Jiun-Cheng Jiang, name: Yun-Yuan Wang, name: Tzung-Chi Huang, name: Tai-Yue Li, name: Kuan-Cheng Chen, name: Samuel Yen-Chi Chen, name: Nan-Yow Chen

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.