Absorption Spectra with Kernel Polynomial Neural Quantum States

The computational challenge of predicting optical absorption spectra for correlated quantum systems stems from the exponential scaling of many-body wave functions. We introduce kernel polynomial neural quantum states (KPNQS), a generative framework that unifies the kernel polynomial method (KPM) with autoregressive neural wave functions to compute spectral properties directly from the ground state. This approach inherently avoids the prohibitive cost of explicit excited-state calculations by efficiently evaluating the KPM moments governing linear response. KPNQS achieves exact agreement with full configuration interaction for molecules ranging from water to sodium carbonate (52 electrons) while maintaining effective polynomial scaling. Our architecture-agnostic framework establishes a broadly applicable and scalable paradigm for excited-state-free spectral modeling in correlated matter.