Optimizing temperature distributions for training neural quantum states using parallel tempering

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.