Isometric Tensor Network

This project is used for the paper "Differentiable Programming of Isometric Tensor Network". (arXiv:2110.03898)

Main features:

Auto-gradient based isometric tensor network construction (MERA and TNR).
Several built-in spin models
Multiple optimizers and retraction methods
Compatible with the graduate lifting bond dimension trick
Dynamically switching optimizers
Computing scaling dimensions

In future:

More models, optimizers and retraction methods
Layers for variation structures of MERA and TNR
Quantum machine learning and quantum computing
...

Dependencies

The code requires Python and PyTorch, with optional CUDA support.

Gallery

A Ternary MERA

Computation process of MERA

Computation process of TNR

Network layers of TNR

Efficiency comparing of these methods

Relative energy errors of Ising model as functions of time for conventional algorithm, differentiable programming with Evenbly-Vidal method in CPU, differentiable programming with Evenbly-Vidal method in GPU, and differentiable programming with random Mixing method in GPU.

Scaling dimensions

The scaling dimensions extracted from TNR.

XinLJ66/IsoTensor