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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | https://arxiv.org/abs/2506.01891 |
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| _version_ | 1866918074284769280 |
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| author | Shamim, Mahmud Ashraf Reinhardt, Eric A F Chowdhury, Talal Ahmed Gleyzer, Sergei Araujo, Paulo T |
| author_facet | Shamim, Mahmud Ashraf Reinhardt, Eric A F Chowdhury, Talal Ahmed Gleyzer, Sergei Araujo, Paulo T |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_01891 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Probing Quantum Spin Systems with Kolmogorov-Arnold Neural Network Quantum States Shamim, Mahmud Ashraf Reinhardt, Eric A F Chowdhury, Talal Ahmed Gleyzer, Sergei Araujo, Paulo T Quantum Physics Disordered Systems and Neural Networks Strongly Correlated Electrons Machine Learning 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. |
| title | Probing Quantum Spin Systems with Kolmogorov-Arnold Neural Network Quantum States |
| topic | Quantum Physics Disordered Systems and Neural Networks Strongly Correlated Electrons Machine Learning |
| url | https://arxiv.org/abs/2506.01891 |