RTNI - A SYMBOLIC INTEGRATOR FOR HAAR-RANDOM TENSOR NETWORKS

RTNI is symbolic computer algebra package for MATHEMATICA and PYTHON. It computes averages of tensor networks containing multiple Haar-distributed random unitary matrices and symbolic tensors. Such tensor networks are represented as multigraphs, with vertices corresponding to tensors or random unitaries and edges corresponding to tensor contractions. Input and output spaces of random unitaries may be subdivided into arbitrary tensor factors, with dimensions treated symbolically. The algorithm implements the graphical Weingarten calculus and produces a weighted sum of tensor networks representing the average over the unitary group. Associated visualization routines are also provided.

A detailed description of the functionality of this package with examples of its usage is available at arXiv:1902.08539.

MATHEMATICA

• Follow the RTNI setup guide for MATHEMATICA to setup RTNI
• Look at the list of files and sample code for MATHEMATICA

PYTHON (A major update was made as PyRTNI2)

• Follow the RTNI setup guide for PYTHON to setup RTNI
• Look at the list of files and sample code for PYTHON
• A list of Weingarten functions for permutation size up to 20 can be found here

ONLINE

• A light, online version of the code implementing the main integration routine can be found here

LICENSE

This project is licensed under the terms of the GNU GENERAL PUBLIC LICENSE v3.0. When using this software, please include the following reference (also in BibTeX format)

• Motohisa Fukuda, Robert König, and Ion Nechita. RTNI - A symbolic integrator for Haar-random tensor networks. [ doi

  Journal of Physics A: Mathematical and Theoretical, Volume 52, Number 42, 2019 ].