Generative Quantum-inspired Kolmogorov-Arnold Eigensolver

• URL: http://arxiv.org/abs/2605.04604v1
• Date: Wed, 06 May 2026 07:53:55 GMT
• Title: Generative Quantum-inspired Kolmogorov-Arnold Eigensolver
• Abstract summary: We present the generative quantum-inspired Kolmogorov-Arnold eigensolver (GQKAE) for quantum chemistry.<n>GQKAE replaces the parameter-heavy feed-forward network components in GPT-style generative eigensolvers with hybrid quantum-inspired Kolmogorov-Arnold network modules.
• Score: 12.645057942348794
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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.

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