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Optimizing temperature distributions for training neural quantum states using parallel tempering.

Conor Smith1,2,3, Quinn T Campbell4, Tameem Albash4

  • 1University of New Mexico, Center for Quantum Information and Control, University of New Mexico, Albuquerque, New Mexico 87131, USA.

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|June 19, 2025
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Summary
This summary is machine-generated.

Optimizing the temperature distribution in parallel tempering for artificial neural networks (ANNs) significantly improves variational algorithm success rates. This adaptive method efficiently overcomes local minima in parameter landscapes with minimal computational overhead.

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Area of Science:

  • Quantum many-body physics
  • Machine learning in physics
  • Computational condensed matter

Background:

  • Parametrized artificial neural networks (ANNs) are powerful tools for studying quantum many-body systems.
  • Training ANNs can be challenging due to local minima in the parameter landscape.
  • Parallel tempering is a method used to mitigate training difficulties.

Purpose of the Study:

  • To investigate the impact of temperature distribution in parallel tempering for ANN training.
  • To develop an adaptive method for optimizing replica temperatures.
  • To enhance the success rate of variational algorithms using optimized parallel tempering.

Main Methods:

  • An adaptive temperature adjustment method was employed to equalize exchange probabilities between parallel tempering replicas.
  • The method was tested on two types of ANNs: restricted Boltzmann machines and feedforward networks.
  • Simulations were performed on a toy model with a permutation invariant Hamiltonian and the J1-J2 model on a rectangular lattice.

Main Results:

  • Optimized temperature distributions significantly increased the success rate of the variational algorithm.
  • The adaptive method effectively eliminated bottlenecks in the replica random walk.
  • Negligible additional computational cost was incurred by the temperature optimization.

Conclusions:

  • Adaptive temperature optimization in parallel tempering is a highly effective strategy for improving ANN training in variational algorithms.
  • This approach offers a computationally inexpensive way to enhance the performance of quantum many-body simulations.
  • The findings are applicable to various ANN architectures and quantum Hamiltonians.