Variational optimization of two-dimensional MERA with GPGPU

Our study focuses on the potential of Multi-scale Entanglement Renormalization Ansatz (MERA) to describe the ground state of quantum matter, particularly at quantum critical points. Most numerical calculations are limited to one-dimensional models because working with two-dimensional lattices is difficult due to the large space and time complexity. In this study, we utilize a near-optimal contraction tree optimization and slicing technique to distribute computation over multiple GPGPUs. This approach significantly enhances the speed of evaluating various two-dimensional MERA ansatz and provides promising insights into the potential of MERA for understanding quantum matter.