Optimizing temperature distributions for training neural quantum states using parallel tempering

Smith, Conor; Campbell, Quinn T.; Albash, Tameem

doi:10.1103/PhysRevE.111.055306

Optimizing temperature distributions for training neural quantum states using parallel tempering

Journal Article · Thu May 22 00:00:00 EDT 2025 · Physical Review E

DOI:https://doi.org/10.1103/PhysRevE.111.055306· OSTI ID:2585667

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Univ. of New Mexico, Albuquerque, NM (United States); Flatiron Institute, New York, NY (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Parametrized artificial neural networks (ANNs) can be very expressive ansatzes for variational algorithms, reaching state-of-the-art energies on many quantum many-body Hamiltonians. Nevertheless, the training of the ANN can be slow and stymied by the presence of local minima in the parameter landscape. One approach to mitigate this issue is to use parallel tempering methods, and in this work, we focus on the role played by the temperature distribution of the parallel tempering replicas. Using an adaptive method that adjusts the temperatures in order to equate the exchange probability between neighboring replicas, we show that this temperature optimization can significantly increase the success rate of the variational algorithm with negligible computational cost by eliminating bottlenecks in the replicas' random walk. Furthermore, we demonstrate this using two different neural networks, a restricted Boltzmann machine and a feedforward network, which we use to study a toy problem based on a permutation invariant Hamiltonian with a pernicious local minimum and the 𝐽₁−𝐽₂ model on a rectangular lattice.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: Air Force Office of Scientific Research (AFOSR); National Science Foundation (NSF); USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Basic Energy Sciences (BES). Scientific User Facilities (SUF)

Grant/Contract Number:: NA0003525

OSTI ID:: 2585667

Report Number(s):: SAND--2025-06710J; 1762657

Journal Information:: Physical Review E, Journal Name: Physical Review E Journal Issue: 5 Vol. 111; ISSN 2470-0053; ISSN 2470-0045

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Optimizing temperature distributions for training neural quantum states using parallel tempering

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