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AKPIK: Arbeitskreis Physik, moderne Informationstechnologie und Künstliche Intelligenz

AKPIK 1: Reservoir Computing & Neural Networks

AKPIK 1.5: Vortrag

Dienstag, 19. März 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 Vicentini^2,1, Michel Ferrero^2,1, and Antoine Georges^1,2,3 — 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