Ground State Wave Function of Helium using Artificial Neural Network

Finding a wave function for any quantum mechanical system involves solving the famous Schrodinger equation which has analytical solutions for a few simple Hamiltonians. Solutions for more useful and complicated Hamiltonians are obtained by numerical methods which are greatly limited by computational resources. Recent advancement in the field of machine learning provides a very useful tool known as Artificial Neural Networks (ANN). The application of ANN to many-body quantum problems has recently been pointed out in the pioneering work by Carleo and Troyer. In this work, we solve the ground state wave function for Helium atom using the reinforcement learning method. Variational Monte Carlo (VMC) method in conjugation with Metropolis-Hastings algorithm will be used to numerically compute the expectation of various operators involved in the optimization of the trial wave function by using Stochastic Reconfiguration (SR). This work sheds light on the applicability of ANNs to quantum systems with spatial variable, rather than spin states as in the work of Carleo and Troyer.