生成式量子启发科莫哥洛夫-阿诺德特征求解器

Generative Quantum-inspired Kolmogorov-Arnold Eigensolver

May 6, 2026

作者: Yu-Cheng Lin, Yu-Chao Hsu, I-Shan Tsai, Chun-Hua Lin, Kuo-Chung Peng, Jiun-Cheng Jiang, Yun-Yuan Wang, Tzung-Chi Huang, Tai-Yue Li, Kuan-Cheng Chen, Samuel Yen-Chi Chen, Nan-Yow Chen

cs.AI

摘要

高性能计算（HPC）在耦合经典生成模型、量子电路模拟及选择性组态相互作用后处理的可扩展量子化学工作流中日益重要。我们提出生成式量子启发科摩哥洛夫-阿诺德特征求解器（GQKAE），这是针对量子化学的生成式量子特征求解器（GQE）的参数高效扩展方案。GQKAE采用混合量子启发科摩哥洛夫-阿诺德网络模块替代GPT风格生成式特征求解器中参数密集的前馈网络组件，形成紧凑的HQKANsformer主干架构。该方法在保持自回归算子选择与量子选择性组态相互作用评估流程的同时，利用单量子比特数据重上传激活模块实现表达性非线性映射。在H4、N2、LiH、C2H6、H2O及H2O二聚体上的数值基准测试表明，GQKAE在达到与基于GPT的GQE架构相当的化学精度时，可减少约66%的可训练参数与内存占用，并提升实时性能。对于N2、LiH等强关联体系，GQKAE还改善了收敛行为与最终能量误差。这些结果表明量子启发科摩哥洛夫-阿诺德网络能在保持电路生成质量的同时降低经典计算开销，为近量子平台上的HPC-量子协同设计提供了可扩展路径。

English

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.