PT - JOURNAL ARTICLE
AU - Carleo, Giuseppe
AU - Troyer, Matthias
TI - Solving the quantum many-body problem with artificial neural networks
AID - 10.1126/science.aag2302
DP - 2017 Feb 10
TA - Science
PG - 602--606
VI - 355
IP - 6325
4099 - http://science.sciencemag.org/content/355/6325/602.short
4100 - http://science.sciencemag.org/content/355/6325/602.full
SO - Science2017 Feb 10; 355
AB - Elucidating the behavior of quantum interacting systems of many particles remains one of the biggest challenges in physics. Traditional numerical methods often work well, but some of the most interesting problems leave them stumped. Carleo and Troyer harnessed the power of machine learning to develop a variational approach to the quantum many-body problem (see the Perspective by Hush). The method performed at least as well as state-of-the-art approaches, setting a benchmark for a prototypical two-dimensional problem. With further development, it may well prove a valuable piece in the quantum toolbox.Science, this issue p. 602; see also p. 580The challenge posed by the many-body problem in quantum physics originates from the difficulty of describing the nontrivial correlations encoded in the exponential complexity of the many-body wave function. Here we demonstrate that systematic machine learning of the wave function can reduce this complexity to a tractable computational form for some notable cases of physical interest. We introduce a variational representation of quantum states based on artificial neural networks with a variable number of hidden neurons. A reinforcement-learning scheme we demonstrate is capable of both finding the ground state and describing the unitary time evolution of complex interacting quantum systems. Our approach achieves high accuracy in describing prototypical interacting spins models in one and two dimensions.