Introduction to the neural network-based variational Monte Carlo method

The construction of trial wave functions based on neural networks combined with the variational Monte Carlo method is discussed. The mathematical formulation for representing quantum states as neural networks is introduced. The advantages of employing such trial states and how machine learning works are considered. It is shown that the variational method is a kind of unsupervised learning algorithm, where the multiple minima landscape is used as an asset that leads to a stable optimization procedure. The feature representation plays an important role on interpretability and on extracting physical insights from nontrivial trial wave functions. The algorithm is illustrated for the Yukawa potential and the hydrogen molecule.