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Approximating Ground States by Neural Network Quantum States.

Ying Yang1,2, Chengyang Zhang1, Huaixin Cao1

  • 1School of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710119, China.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary
This summary is machine-generated.

This study introduces neural network quantum states to approximate unknown ground states of Hamiltonians. It analyzes how Hamiltonian properties affect approximation accuracy, offering insights into quantum state representation.

Keywords:
approximationground stateneural network quantum state

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Area of Science:

  • Quantum Mechanics
  • Computational Physics
  • Machine Learning

Background:

  • Neural network quantum states offer a powerful approach for representing complex quantum wavefunctions.
  • Approximating the ground state of a Hamiltonian is a fundamental problem in quantum many-body physics.

Purpose of the Study:

  • To approximate the unknown ground state of a Hamiltonian (H) using neural network quantum states.
  • To investigate the impact of Hamiltonian properties (sum, tensor product, local unitary) on approximation accuracy (best relative error).

Main Methods:

  • Employing neural network quantum states as variational wavefunctions.
  • Calculating the best relative error for ground state approximation.
  • Analyzing the influence of different Hamiltonian structures on the error.

Main Results:

  • Demonstrated the capability of neural network quantum states for ground state approximation.
  • Quantified the effect of sum, tensor product, and local unitary operations on the best relative error.
  • Provided illustrative examples validating the methodology.

Conclusions:

  • Neural network quantum states are effective for approximating ground states.
  • Hamiltonian structure significantly influences the accuracy of quantum state approximations.
  • The findings contribute to the development of advanced quantum simulation techniques.