# TensorNetwork on TensorFlow: Entanglement Renormalization for quantum critical lattice models

## TL;DR

This paper implements a tensor network optimization algorithm using TensorFlow to study quantum critical models, achieving significant speed-ups on GPUs for ground state approximations and conformal data extraction.

## Contribution

It introduces a GPU-accelerated tensor network optimization method for MERA using TensorFlow, enabling efficient analysis of quantum critical systems.

## Key findings

- GPU implementation speeds up optimization by up to 200 times
- Successfully approximates ground states of critical quantum models
- Extracts conformal data from optimized tensor networks

## Abstract

We use TensorNetwork [C. Roberts et al., arXiv: 1905.01330], a recently developed API for performing tensor network contractions using accelerated backends such as TensorFlow, to implement an optimization algorithm for the Multi-scale Entanglement Renormalization Ansatz (MERA). We use the MERA to approximate the ground state wave function of the infinite, one-dimensional transverse field Ising model at criticality, and extract conformal data from the optimized ansatz. Comparing run times of the optimization on CPUs vs. GPU, we report a very significant speed-up, up to a factor of 200, of the optimization algorithm when run on a GPU.