Convolutional Neural Network Wave Functions: learning quantum many-body physics

Convolutional neural networks (CNN) have become a staple of modern machine learning research, since they are ideally suited for applications with spatial and/or temporal features such as images, videos, and signals. The key feature of CNNs is their internal structure which is designed to prioritize local features and produce a result that it translational invariant. This has made them an ideal candidate for variational wave functions (VWF) to represent ground states of quantum many-body 2D systems. However, achieving results that improve on existing computational methods has been challenging, mainly due the difficulty of augmenting existing CNN architectures and training them. Here, we propose, discuss and benchmark novel strategies to improve and train CNNs as VWF for the frustrated 2D J1-J2 Heisenberg model on the square lattice with focus on the use of real or complex weights, choice of activation functions, the overall architecture, and enforcement of symmetries.