Berlin 2024 – scientific programme
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AKPIK: Arbeitskreis Physik, moderne Informationstechnologie und Künstliche Intelligenz
AKPIK 1: Reservoir Computing & Neural Networks
AKPIK 1.5: Talk
Tuesday, March 19, 2024, 10:30–10:45, MAR 0.002
Performance of RBM neural quantum states from the perspective of the quantum geometric tensor — •Sidhartha Dash1, Filippo Vicentini2,1, Michel Ferrero2,1, and Antoine Georges1,2,3 — 1Collège de France, Université PSL, 11 place Marcelin Berthelot, 75005 Paris, France — 2CPHT, CNRS, École polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France — 3Center for Computational Quantum Physics, Flatiron Institute, New York, New York, 10010, USA
There have been a lot of recent advances in using artificial neural networks, as variational ansätze (Neural quantum states), to approximate the ground states of quantum systems. Various neural network architectures including RBMs, RNNs, CNNs, and Transformers have been successfully used to approximate the ground states of many quantum spin models with a reasonable accuracy. However, the practical limit of the representation power of such ansätze is far from being understood. The universal approximation theorems only guarantee that the RBM can represent any distribution with an arbitrary accuracy, given a sufficient number of hidden units which is exponential in system size. In this work, we systematically study the accuracy of RBMs for representing the groundstate of spin-1 models. We use the quantum geometric tensor at convergence to characterize the performance of the ansatz for various spin-1 models, and for various densities of the network.
Keywords: neural quantum states; restricted boltzmann machines; variational Monte Carlo