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  Role of stochastic noise and generalization error in the time propagation of neural-network quantum states

Hofmann, D., Fabiani, G., Mentink, J. H., Carleo, G., & Sentef, M. A. (2021). Role of stochastic noise and generalization error in the time propagation of neural-network quantum states.

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2105.01054.pdf (Preprint), 3MB
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https://arxiv.org/abs/2105.01054 (Preprint)
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 Creators:
Hofmann, D.1, Author              
Fabiani, G.2, Author
Mentink, J. H.2, Author
Carleo, G.3, Author
Sentef, M. A.1, Author              
Affiliations:
1Theoretical Description of Pump-Probe Spectroscopies in Solids, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society, ou_3012828              
2Radboud University, Institute for Molecules and Materials, ou_persistent22              
3Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), ou_persistent22              

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 Abstract: Neural-network quantum states (NQS) have been shown to be a suitable variational ansatz to simulate out-of-equilibrium dynamics in two-dimensional systems using time-dependent variational Monte Carlo (t-VMC). In particular, stable and accurate time propagation over long time scales has been observed in the square-lattice Heisenberg model using the Restricted Boltzmann machine architecture. However, achieving similar performance in other systems has proven to be more challenging. In this article, we focus on the two-leg Heisenberg ladder driven out of equilibrium by a pulsed excitation as a benchmark system. We demonstrate that unmitigated noise is strongly amplified by the nonlinear equations of motion for the network parameters, which by itself is sufficient to cause numerical instabilities in the time-evolution. As a consequence, the achievable accuracy of the simulated dynamics is a result of the interplay between network expressiveness and regularization required to remedy these instabilities. Inspired by machine learning practice, we propose a validation-set based diagnostic tool to help determining the optimal regularization hyperparameters for t-VMC based propagation schemes. For our benchmark, we show that stable and accurate time propagation can be achieved in regimes of sufficiently regularized variational dynamics.

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Language(s): eng - English
 Dates: 2021-05-03
 Publication Status: Published online
 Pages: 27
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 Table of Contents: -
 Rev. Type: No review
 Identifiers: arXiv: 2105.01054
 Degree: -

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