Convolutional Neural Networks and Symmetries of Quantum 1D Spin Chains*

Using neural network architectures that employ quantum variational Monte Carlo methods has opened up a new method of studying quantum many body systems. We discuss previous work in using a deep convolutional neural network for studying a 1D SU(N) spin chain, and our use of Importance Sampling Gradient Optimization (ISGO) method to speed up the learning from the Variational Quantum Monte Carlo. We further discuss how symmetries of this spin-chain model play a role in the training and how they can be exploited to accelerate the training. Finally, we compare the neural network to other families of wavefunction ansatzes.