Temperature Optimization for Parallel Tempering in Neural Networks

We benchmark a parallel tempering method for the variational optimization of neural networks to approximate ground states of many-body quantum systems. We study the role played by two parameters in this method that play the role of temperature in the standard parallel tempering approach. The first is the temperature associated with the entropy term added to the local energy samples, which acts to flatten the energy landscape. The second is the temperature in the swap rule used to determine whether or not two neighboring replicas exchange their neural network configurations. We explore the effect of optimizing or fixing these two different temperatures on the performance of the variational algorithm for approximating the ground state of the two-dimensional J1-J2 model.