用新型神经网络量子态，高效精准模拟复杂自旋系统。
Probing Quantum Spin Systems with Kolmogorov-Arnold Neural Network Quantum States
- 基于柯尔莫戈洛夫-阿诺德网络设计可学习正弦激活的波函数
- 在100个自旋链上优于传统神经量子态，逼近精确解
- 训练高效、计算成本低，适合大规模量子系统研究
神经量子态（NQS）是一类由神经网络参数化的变分波函数，用于研究量子多体系统。本文提出基于柯尔莫戈洛夫-阿诺德网络（KAN）的 exttt{SineKAN} 波函数框架，将量子波函数表示为嵌套的一元函数。研究表明， exttt{SineKAN} 在不同链长下可准确捕捉一维横场伊辛模型、各向异性海森堡模型及反铁磁 $J_1-J_2$ 模型的基态能量、保真度与关联函数。在 $L=100$ 的 $J_1-J_2$ 模型中， exttt{SineKAN} 性能超越受限玻尔兹曼机（RBMs）、长短期记忆网络（LSTMs）和多层感知机（MLPs），接近密度矩阵重整化群（DMRG）算法结果。该模型可高精度训练且计算开销小。
原文摘要 · Abstract (English)
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.
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