Probing Quantum Spin Systems with Kolmogorov-Arnold Neural Network Quantum States
This work addresses the challenge of efficiently simulating quantum spin systems for researchers in quantum physics and computational science, representing an incremental improvement over prior neural quantum state methods.
The authors tackled the problem of representing quantum many-body systems by proposing SineKAN, a neural quantum state ansatz based on Kolmogorov-Arnold Networks, and showed it outperforms existing methods like RBMs, LSTMs, and MLPs in capturing ground state energies and correlations for models such as the J1-J2 model with L=100 sites, achieving high precision with minimal computational cost.
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 \texttt{SineKAN}, a NQS \textit{ansatz} based on Kolmogorov-Arnold Networks (KANs), to represent quantum mechanical wave functions as nested univariate functions. We show that \texttt{SineKAN} wavefunction with learnable sinusoidal activation functions can capture the ground state energies, fidelities and various correlation functions of the one dimensional 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 \texttt{SineKAN} model outperforms several previously explored neural quantum state \textit{ansätze}, including Restricted Boltzmann Machines (RBMs), Long Short-Term Memory models (LSTMs), and Multi-layer Perceptrons (MLP) \textit{a.k.a.} Feed Forward Neural Networks, when compared to the results obtained from the Density Matrix Renormalization Group (DMRG) algorithm. We find that \texttt{SineKAN} models can be trained to high precisions and accuracies with minimal computational costs.