tensor4all

This website collects information from the tensor4all group which is working on tensor network methods based on tensor cross interpolation (TCI) and related tensor learning algorithms such as quantics/quantized tensor trains.

Literature

A pedagogical introduction to tensor network methods, which includes an overview of the existing literature and also new algorithms, can be found in:

Yuriel Núñez Fernández, Marc K. Ritter, Matthieu Jeannin, Jheng-Wei Li, Thomas Kloss, Thibaud Louvet, Satoshi Terasaki, Olivier Parcollet, Jan von Delft, Hiroshi Shinaoka, and Xavier Waintal, “Learning tensor networks with tensor cross interpolation: new algorithms and libraries”, arXiv:2407.02454.

Please check the reference page for more information on TCI and quantics tensor trains.

Code

We provide two software libraries that implement algorithms from the above manuscript for computing low-rank tensor representations. The code focuses on recent applications of tensor networks to objects that do not necessarily involve many-body quantum mechanics. It also contain known and new variants of the tensor cross interpolation (TCI) algorithm for unfolding tensors into tensor trains. One code is called Xfac (written in C++ with Python bindings), and a second implementation with similar functionality is based on Julia:

Monthly online meeting

We have a monthly online meeting to discuss the development of new methods and applications. Zoom links will be provided through a mailing list (49 registered users as of November 4th, 2024). Please contact us if you would like to join the mailing list.

Previous meetings:

Workshops

We organize workshops to discuss the development of new methods.

People

Check the about page to see who is involved in the tensor4all collaboration.

Frequently Asked Questions

We have a FAQ page to answer common questions.