Differentiable Programming of Isometric Tensor Networks

TL;DR

This paper extends differentiable programming to isometric tensor networks like MERA and TNR, demonstrating improved optimization stability and accuracy through auto-differentiation in quantum and classical models.

Contribution

It introduces gradient-based optimization methods for isometric tensor networks and compares their performance with existing techniques, showing superior stability and accuracy.

Findings

Auto-differentiation outperforms traditional methods in stability and accuracy.

Methods accurately compute ground state and internal energies.

Results agree well with theoretical predictions.

Abstract

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