Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Quantum Neural Network States: A Brief Review of Methods and Applications

Quantum Neural Network States: A Brief Review of Methods and Applications One of the main challenges of quantum many‐body physics is the exponential growth in the dimensionality of the Hilbert space with system size. This growth makes solving the Schrödinger equation of the system extremely difficult. Nonetheless, many physical systems have a simplified internal structure that typically makes the parameters needed to characterize their ground states exponentially smaller. Many numerical methods then become available to capture the physics of the system. Among modern numerical techniques, neural networks, which show great power in approximating functions and extracting features of big data, are now attracting much interest. In this work, the progress in using artificial neural networks to build quantum many‐body states is reviewed. The Boltzmann machine representation is taken as a prototypical example to illustrate various aspects of the neural network states. The classical neural networks are also briefly reviewed, and it is illustrated how to use neural networks to represent quantum states and density operators. Some physical properties of the neural network states are discussed. For applications, the progress in many‐body calculations based on neural network states, the neural network state approach to tomography, and the classical simulation of quantum computing based on Boltzmann machine states are briefly reviewed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advanced Quantum Technologies Wiley

Quantum Neural Network States: A Brief Review of Methods and Applications

Download PDF
16 pages

Loading next page...
 
/lp/wiley/quantum-neural-network-states-a-brief-review-of-methods-and-t5wTbReVc9
Publisher
Wiley
Copyright
© 2019 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim
eISSN
2511-9044
DOI
10.1002/qute.201800077
Publisher site
See Article on Publisher Site

Abstract

One of the main challenges of quantum many‐body physics is the exponential growth in the dimensionality of the Hilbert space with system size. This growth makes solving the Schrödinger equation of the system extremely difficult. Nonetheless, many physical systems have a simplified internal structure that typically makes the parameters needed to characterize their ground states exponentially smaller. Many numerical methods then become available to capture the physics of the system. Among modern numerical techniques, neural networks, which show great power in approximating functions and extracting features of big data, are now attracting much interest. In this work, the progress in using artificial neural networks to build quantum many‐body states is reviewed. The Boltzmann machine representation is taken as a prototypical example to illustrate various aspects of the neural network states. The classical neural networks are also briefly reviewed, and it is illustrated how to use neural networks to represent quantum states and density operators. Some physical properties of the neural network states are discussed. For applications, the progress in many‐body calculations based on neural network states, the neural network state approach to tomography, and the classical simulation of quantum computing based on Boltzmann machine states are briefly reviewed.

Journal

Advanced Quantum Technologies – Wiley

Published: Aug 1, 2019

Keywords: ; ; ;

References

  • Reinforcement Learning: An Introduction
    Sutton, R. S.; Barto, A. G.
  • Perceptrons: An introduction to computational geometry
    Minsky, M.; Papert, S. A.
  • Neural Networks and Deep Learning
    Nielsen, M. A.
  • The Handbook of Brain Theory and Neural Networks
    LeCun, Y.; Bengio, Y.
  • Advances in Neural Information Processing Systems
    Krizhevsky, A.; Sutskever, I.; Hinton, G. E.
  • Proc. of the IEEE Conference on Computer Vision and Pattern Recognition
    Hinton, G. E.; Sejnowski, T. J.
  • Neural Networks for Pattern Recognition
    Bishop, C. M.
  • Fundamentals of Neural Networks: Architectures, Algorithms, and Applications
    Fausett, L. V.
  • Advances in Neural Information Processing Systems
    Stoudenmire, E.; Schwab, D. J.
  • Collected Works, Volume 1: Representations of Functions, Celestial Mechanics, and KAM Theory 1957–1965
    Arnold, V. I.
  • Proc. of the IEEE Int. Conf. on Neural Networks III
    Hecht‐Nielsen, R.
  • Quantum Computation and Quantum Information
    Nielsen, M. A.; Chuang, I. L.