Differentiable programming of isometric tensor networks

Abstract Differentiable programming is a new paradigm which enables large scale optimization through automatic calculation of gradients also known as auto-differentiation. This concept emerges from deep learning, and has been generalized to tensor network optimizations. Here, we extend the differentiable networks with isometric constraints applications multiscale entanglement renormalization ansatz (MERA) (TNR). By introducing several gradient-based methods for comparing Evenbly–Vidal method, show that auto-differentiation better performance both stability accuracy. We numerically tested our on 1D critical quantum Ising spin chain 2D classical model. calculate ground state energy model internal model, scaling dimensions operators find they all agree theory well.