Overparametrization and optimization landscape of neural-network quantum states

Neural-network wave functions serve as powerful and flexible tools for the solution of quantum many-body problems. However, obtaining an accurate approximation of the ground-state wave-function can be a daunting task with highly model-specific results. While the underlying reason for this behavior is not well-understood, most evidence so far points to issues in generalizability and trainability of the neural network quantum state. At the same time, the field of modern machine learning presents a seemingly simple solution to this challenge: Increasing the number of parameters beyond the interpolation threshold into an overparametrized regime has been found to improve both generalizability and trainability of neural networks.

Here we investigate to which extend these findings are transferrable to the ground state search with neural network quantum states. We devise a simple supervised learning setup and compare the general task of learning a quantum wave-function to classical problems such as image-based prediction. We then extend our findings to systematically probe the optimization landscape when energy minimization is employed for Hamiltonians exhibiting long-range correlations or different degrees of frustration.