Solving the quantum many-body problem with artificial neural networks
Machine learning and quantum physics
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.
Abstract
The 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.
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Science
Volume 355 | Issue 6325
10 February 2017
10 February 2017
Copyright
Copyright © 2017, American Association for the Advancement of Science.
Submission history
Received: 7 June 2016
Accepted: 12 January 2017
Published in print: 10 February 2017
Acknowledgments
We acknowledge discussions with F. Becca, J. F. Carrasquilla, M. Dolfi, J. Osorio, D. Patané, and S. Sorella. The time-dependent MPS results have been obtained with the open-source implementation available as a part of the Algorithms and Libraries for Physics Simulations (ALPS) project (33, 42). This work was supported by the European Research Council (ERC) through ERC Advanced Grant SIMCOFE, by the Swiss National Science Foundation through National Center of Competence in Research Quantum Science and Technology (QSIT), and by Microsoft Research. This paper is based on work supported in part by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA) via Massachusetts Institute of Technology Lincoln Laboratory Air Force contract no. FA8721-05-C-0002. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of ODNI, IARPA, or the U.S. government. The U.S. government is authorized to reproduce and distribute reprints for governmental purposes, notwithstanding any copyright annotation thereon. The authors agree to making the code used in this paper available upon reasonable request.
Authors
Funding Information
Microsoft Research: award287221
Lincoln Laboratory: award287222
Swiss National Science Foundation: award287223
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