Neural-network quantum states (NQS) are powerful neural-network ansätzes that have emerged as promising tools for studying quantum many-body physics through the lens of the variational principle. These architectures are known to be systematically improvable by increasing the number of parameters. Here we demonstrate an Adaptive scheme to optimize NQSs, through the example of recurrent neural networks (RNN), using a fraction of the computation cost while reducing training fluctuations and improving the quality of variational calculations targeting ground states of prototypical models in one- and two-spatial dimensions. This Adaptive technique reduces the computational cost through training small RNNs and reusing them to initialize larger RNNs. This work opens up the possibility for optimizing graphical processing unit (GPU) resources deployed in large-scale NQS simulations.

Optimization problems involve the identification of the best possible solution among several possibilities. These problems can be encountered in real-world settings, as well as in most scientific research fields. In recent years, computer scientists have developed increasingly advanced computational methods for solving optimization problems. Some of the most promising techniques developed so far are based on artificial neural networks (ANNs). Researchers at the Vector Institute, University of Waterloo and Perimeter Institute for Theoretical Physics in Canada have recently developed variational neural annealing, a new optimization method that merges recurrent neural networks (RNNs) with the principle of annealing.