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Differentiable Programming Tensor Networks

Requirements

• PyTorch 1.0+
• A good GPU card if you are impatient or ambitious

Higher order gradient of free energy

Run this to compute the energy and specific heat of the 2D classical Ising model using Automatic Differentiation through the Tensor Renormalization Group contraction.

$ cd 1_ising_TRG
$ python ising.py 

Variational optimization of iPEPS

Run this to optimize an iPEPS wave function for 2D quantum Heisenberg model. Here, we use Corner Transfer Matrix Renormalization Group for contraction, and L-BFGS for optimization.

$ cd 2_variational_iPEPS
$ python variational.py -D 3 -chi 30 

You can supply the command line argument -use_checkpoint to reduce the memory usage. To make use of the GPU, you can add -cuda <GPUID>. You will reach the state-of-the-art variational energy and staggered magnetization using this code. You can also supply your own Hamiltonian of interest. In case of a question, you can type python variational.py -h.

What is under the hood ?

Reverse mode AD computes gradient accurately and efficiently for you! Check the codes in adlib for backward functions which propagate gradients through tensor network contractions.

To Cite

@article{PhysRevX.9.031041,
  title = {Differentiable Programming Tensor Networks},
  author = {Liao, Hai-Jun and Liu, Jin-Guo and Wang, Lei and Xiang, Tao},
  journal = {Phys. Rev. X},
  volume = {9},
  issue = {3},
  pages = {031041},
  numpages = {12},
  year = {2019},
  month = {Sep},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevX.9.031041},
  url = {https://link.aps.org/doi/10.1103/PhysRevX.9.031041}
}

Explore more

https://github.com/under-Peter/TensorNetworkAD.jl