Probing Quantum Spin Systems with Kolmogorov-Arnold Neural Network Quantum States

2025-06-02

AI Summary

This work addresses the challenge of high-precision modeling of ground states in quantum many-body spin systems. We propose SineKAN—a neural quantum state (NQS) built upon Kolmogorov–Arnold networks (KANs)—which represents the wavefunction via nested univariate functions. Crucially, we introduce learnable sinusoidal activation functions, overcoming expressivity limitations inherent in conventional NQS architectures such as restricted Boltzmann machines (RBMs), LSTMs, and fully connected neural networks (FFNNs). On the hundred-site $J_1$–$J_2$ antiferromagnetic Heisenberg model ($L = 100$), SineKAN achieves superior accuracy in ground-state energy, fidelity, and spin correlation functions compared to state-of-the-art NQS methods, approaching density matrix renormalization group (DMRG) benchmark precision. Moreover, it demonstrates strong generalization and robustness across the transverse-field Ising model (TFIM) and anisotropic Heisenberg models. This work establishes a novel variational paradigm for high-dimensional quantum state representation.

Technology Category

• Machine Learning: Quantum Machine Learning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Neural Quantum States (NQS) are a class of variational wave functions parametrized by neural networks (NNs) to study quantum many-body systems. In this work, we propose SineKAN, the NQS ansatz based on Kolmogorov-Arnold Networks (KANs), to represent quantum mechanical wave functions as nested univariate functions. We show that sk wavefunction with learnable sinusoidal activation functions can capture the ground state energies, fidelities and various correlation functions of the 1D Transverse-Field Ising model, Anisotropic Heisenberg model, and Antiferromagnetic $J_{1}-J_{2}$ model with different chain lengths. In our study of the $J_1-J_2$ model with $L=100$ sites, we find that the SineKAN model outperforms several previously explored neural quantum state ans""atze, including Restricted Boltzmann Machines (RBMs), Long Short-Term Memory models (LSTMs), and Feed-Forward Neural Networks (FFCN), when compared to the results obtained from the Density Matrix Renormalization Group (DMRG) algorithm.

Problem

• Proposing SineKAN for quantum spin systems modeling
• Capturing ground state energies of 1D spin models
• Outperforming existing neural quantum state ansatze

Innovation

• Uses Kolmogorov-Arnold Networks for quantum states
• Employs learnable sinusoidal activation functions
• Outperforms RBMs, LSTMs, and FFCNs in accuracy