Generative Quantum-inspired Kolmogorov-Arnold Eigensolver

TL;DR

The paper introduces GQKAE, a quantum-inspired eigensolver that reduces classical computational overhead while maintaining accuracy, enhancing quantum chemistry simulations on near-term quantum hardware.

Contribution

It presents a novel hybrid quantum-inspired network architecture that improves efficiency and convergence in quantum chemistry calculations compared to existing methods.

Findings

GQKAE achieves chemical accuracy comparable to GPT-based GQE.

It reduces trainable parameters and memory by approximately 66%.

GQKAE improves convergence and energy errors for strongly correlated systems.

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.