Neural-network quantum states at finite temperature

@article{Irikura2020NeuralnetworkQS,
  title={Neural-network quantum states at finite temperature},
  author={Naoki Irikura and Hiroki Saito},
  journal={Physical Review Research},
  year={2020}
}
We propose a method to obtain the thermal-equilibrium density matrix of a many-body quantum system using artificial neural networks. The variational function of the many-body density matrix is represented by a convolutional neural network with two input channels. We first prepare an infinite-temperature state, and the temperature is lowered by imaginary-time evolution. We apply this method to the one-dimensional Bose-Hubbard model and compare the results with those obtained by exact… 

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References

SHOWING 1-10 OF 41 REFERENCES

Method to Solve Quantum Few-Body Problems with Artificial Neural Networks

  • H. Saito
  • Physics, Computer Science
    Journal of the Physical Society of Japan
  • 2018
TLDR
A machine learning technique to obtain the ground states of quantum few-body systems using artificial neural networks is developed and is applied to the Calogero-Sutherland model in one-dimensional space and Efimov bound states in three- dimensional space.

Variational Neural-Network Ansatz for Steady States in Open Quantum Systems.

TLDR
A general variational approach to determine the steady state of open quantum lattice systems via a neural-network approach is presented and applied to the dissipative quantum transverse Ising model.

Constructing neural stationary states for open quantum many-body systems

TLDR
A new variational scheme based on the neural-network quantum states to simulate the stationary states of open quantum many-body systems, which is dubbed as the neural stationary state ansatz, and shown to simulate various spin systems efficiently.

Machine Learning Technique to Find Quantum Many-Body Ground States of Bosons on a Lattice

TLDR
A variational method to obtain many-body ground states of the Bose–Hubbard model using feedforward artificial neural networks is developed and it is shown that many- body ground states with different numbers of particles can be generated by a single network.

Machine learning technique to find quantum many-body ground states of bosons on a lattice

TLDR
A variational method to obtain many-body ground states of the Bose-Hubbard model using feedforward artificial neural networks is developed and it is shown that many- body ground states with different numbers of atoms can be generated by a single network.

Solving the Bose–Hubbard Model with Machine Learning

Motivated by the recent successful application of artificial neural networks to quantum many-body problems [G. Carleo and M. Troyer, Science 355, 602 (2017)], a method to calculate the ground state

Symmetries and Many-Body Excitations with Neural-Network Quantum States.

TLDR
Interestingly, it is found that deep networks typically outperform shallow architectures for high-energy states, and an algorithm to compute low-lying excited states without symmetries is given.

Variational Quantum Monte Carlo Method with a Neural-Network Ansatz for Open Quantum Systems.

TLDR
A variational method to efficiently simulate the nonequilibrium steady state of Markovian open quantum systems based on variational Monte Carlo methods and on a neural network representation of the density matrix is developed.

Restricted Boltzmann machine learning for solving strongly correlated quantum systems

TLDR
The combined method substantially improves the accuracy beyond that ever achieved by each method separately, in the Heisenberg as well as Hubbard models on square lattices, thus proving its power as a highly accurate quantum many-body solver.

Neural-Network Approach to Dissipative Quantum Many-Body Dynamics.

TLDR
This work represents the mixed many-body quantum states with neural networks in the form of restricted Boltzmann machines and derive a variational Monte Carlo algorithm for their time evolution and stationary states based on machine-learning techniques.