Learning tensor networks with tensor cross interpolation: New algorithms and libraries

• DOI: 10.21468/scipostphys.18.3.104
• Publication Date: 2025-03-20T11:19:52Z
• Authors: Yuriel Núñez Fern...; Marc K Ritter; Matthieu Jeannin; Jheng-Wei Li; Thomas Kloss; Thibaud Louvet; Satoshi Terasaki; Olivier Parcollet; Jan von Delft; Hiroshi Shinaoka; Xavier Waintal
• Keywords: Interpolation

The tensor cross interpolation (TCI) algorithm is a rank-revealing for decomposing low-rank, high-dimensional tensors into trains/matrix product states (MPS). TCI learns compact MPS representation of the entire object from tiny training data set. Once obtained, large existing toolbox provides exponentially fast algorithms performing set operations. We discuss several improvements and variants TCI. In particular, we show that replacing by partially LU decomposition yields more stable flexible than original algorithm. also present two open source libraries, xfac in Python/C++ TensorCrossInterpolation.jl Julia, implement these improved algorithms, illustrate them on applications. These include sign-problem-free integration dimension, “superhigh-resolution” quantics functions, solution partial differential equations, superfast Fourier transform, computation partition construction matrix operators.