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.
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.
Variational optimization of neural-network quantum state representations has achieved FCI-level accuracy for ground state calculations, yet computing optical properties involving excited states remains challenging. In this work, we present a neural-network-based variational quantum Monte Carlo approach for ab-initio absorption spectra. We leverage parallel batch autoregressive sampling and GPU-supported local energy parallelism to efficiently compute ground states of complex systems. By integrating neural quantum ground states with the kernel polynomial method, our approach accurately calculates absorption spectra for large molecules with over 50 electrons, achieving FCI-level precision. The proposed algorithm demonstrates superior scalability and reduced runtime compared to FCI, marking a significant step forward in optical property calculations for large-scale quantum systems.
Computing finite temperature properties of a quantum many-body system is key to describing a broad range of correlated quantum many-body physics from quantum chemistry and condensed matter to thermal quantum field theories. Quantum computing, which has seen rapid developments in recent years, has a huge potential to impact the computation of quantum thermodynamics. To fulfill these potential impacts, it is crucial to design quantum algorithms that utilize the computation power of quantum computing devices. Here, we present a quantum kernel function expansion (QKFE) algorithm for solving thermodynamic properties of quantum many-body systems. In this quantum algorithm, the many-body density of states is approximated by a kernel Fourier expansion, whose expansion moments are obtained by random state sampling and quantum interferometric measurements. Compared to its classical counterpart, namely, the kernel polynomial method (KPM), QKFE has an exponential advantage in the cost of both time and memory. In computing low temperature properties, QKFE becomes inefficient, similar to classical KPM. To resolve this difficulty, we further construct a thermal ensemble iteration (THEI) protocol which starts from the trivial limit of an infinite temperature ensemble and approaches the low temperature regime step by step. For quantum Hamiltonians, whose ground states are preparable with polynomial quantum circuits, THEI has an overall polynomial complexity. We demonstrate its efficiency with applications to one- and two-dimensional quantum spin models and a fermionic lattice. With our analysis of the realization with digital and analog quantum devices, we believe the quantum algorithm is accessible to current quantum technology.
Abstract Dynamical correlation functions are essential for revealing emergent phenomena in quantum matter, since they measure the frequency-resolved response of a system at equilibrium to a perturbation and thereby probe its full spectrum. While neural quantum states provide an accurate and flexible description of correlated ground states, accessing real-frequency dynamical correlators from them remains a major challenge. Here we introduce a general and systematically improvable framework to compute real-frequency linear-response functions directly from neural quantum state ground states. Our method performs the Lanczos subspace construction through an operator recursion and controls operator growth with a suited truncation scheme. We benchmark it on demanding quantum impurity models, where high precision is required close to the Fermi energy, and show that rich spectral structure and the self-energy can be resolved over several orders of magnitude. The approach generalizes straightforwardly, for example providing a direct path toward more broadly applicable dynamical mean-field theory solvers.
Accurate electronic spectra require both a flexible description of electron correlation and a tractable treatment of the many states contributing to the response. We combine neural network wave functions with the Lorentz integral transform to calculate electronic spectra directly in continuous coordinates, without truncation error from a fixed one-electron basis and with polynomial computational cost per optimization step. Instead of constructing a prescribed set of excited states, the method solves an inhomogeneous Schrödinger equation at a chosen complex energy. This formulation gives access, in principle, to the entire spectrum coupled to a perturbation, including bound excitations and the ionization continuum, without explicitly determining all lower-lying eigenstates. A finite imaginary energy controls the resolution and keeps the response square integrable. Near an isolated bound excitation, the normalized response also recovers the corresponding eigenstate as the width tends to zero. A helium application illustrates the extraction of an excitation energy and oscillator strength. The formulation provides a route from neural descriptions of electronic correlation to spectra beyond a small manifold of low-lying states.
In this work, we use neural quantum states (NQS) to describe the high-dimensional wave functions of electron-phonon coupled systems. We demonstrate that NQS can accurately and systematically learn the underlying physics of such problems through a variational Monte Carlo optimization of the energy with minimal incorporation of physical information, even in highly challenging cases. We assess the ability of our approach across various lattice model examples featuring different types of couplings. The flexibility of our NQS formulation is demonstrated via application to ab initio models parametrized by density functional perturbation theory consisting of electron or hole bands coupled linearly to dispersive phonons. We compute accurate real-frequency spectral properties of electron-phonon via a response formalism based on NQS. Our work establishes a general framework for exploring diverse ground-state and dynamical phenomena arising in electron-phonon systems, including the nonperturbative interplay of correlated electronic and electron-phonon effects in systems ranging from simple lattice models to realistic models of materials parametrized by ab initio calculations.
Understanding dynamical properties of quantum many-body systems remains a central challenge because excitations generally require information beyond a ground-state wave function. Here we introduce a neural polaron ansatz that represents quasiparticle excitations by neural many-body operators acting on a correlated ground state. Instead of learning an independent excited-state wave function, the method parameterizes a local dressing operator through a compact neural head defined on the feature map of a pretrained ground-state network. This operator-based construction builds in translation symmetry, momentum resolution, and quasiparticle locality, while separating ground-state correlations from excitation-specific dressing. We benchmark the method on the square-lattice J1-J2 Heisenberg model, where it accurately reproduces magnon dispersions and spectral weights over a broad range of frustration. In particular, it captures nontrivial many-body features including the (π,0) anomaly and its progressive softening with increasing J2/J1. These results establish neural operators as a physically transparent route for extending neural quantum states from ground-state properties to dynamical response.