TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.18.3.104
TI  - Learning tensor networks with tensor cross interpolation: New algorithms and libraries
PY  - 2025/03/20
UR  - https://scipost.org/SciPostPhys.18.3.104
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 18
IS  - 3
SP  - 104
A1  - Núñez Fernández, Yuriel
AU  - Ritter, Marc K
AU  - Jeannin, Matthieu
AU  - Li, Jheng-Wei
AU  - Kloss, Thomas
AU  - Louvet, Thibaud
AU  - Terasaki, Satoshi
AU  - Parcollet, Olivier
AU  - von Delft, Jan
AU  - Shinaoka, Hiroshi
AU  - Waintal, Xavier
AB  - The tensor cross interpolation (TCI) algorithm is a rank-revealing algorithm for decomposing low-rank, high-dimensional tensors into tensor trains/matrix product states (MPS). TCI learns a compact MPS representation of the entire object from a tiny training data set. Once obtained, the large existing MPS toolbox provides exponentially fast algorithms for performing a large set of operations. We discuss several improvements and variants of TCI. In particular, we show that replacing the cross interpolation by the partially rank-revealing LU decomposition yields a more stable and more flexible algorithm than the original algorithm. We also present two open source libraries, xfac in Python/C++ and TensorCrossInterpolation.jl in Julia, that implement these improved algorithms, and illustrate them on several applications. These include sign-problem-free integration in large dimension, the "superhigh-resolution" quantics representation of functions, the solution of partial differential equations, the superfast Fourier transform, the computation of partition functions, and the construction of matrix product operators.
ER  -

@Article{10.21468/SciPostPhys.18.3.104,
	title={{Learning tensor networks with tensor cross interpolation: New algorithms and libraries}},
	author={Yuriel Núñez Fernández and Marc K. Ritter and Matthieu Jeannin and Jheng-Wei Li and Thomas Kloss and Thibaud Louvet and Satoshi Terasaki and Olivier Parcollet and Jan von Delft and Hiroshi Shinaoka and Xavier Waintal},
	journal={SciPost Phys.},
	volume={18},
	pages={104},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.18.3.104},
	url={https://scipost.org/10.21468/SciPostPhys.18.3.104},
}

Authors / Affiliations: mappings to Contributors and Organizations

• ^{1 2 3 4 5 6 7} Yuriel Núñez Fernández,
• ^{8 9 10 11} Marc K Ritter,
• ^{1 2 3 4 7} Matthieu Jeannin,
• ^{1 2 3 4 7} Jheng-Wei Li,
• ^{2 5 6} Thomas Kloss,
• ^{1 2 3 4 7} Thibaud Louvet,
• ¹² Satoshi Terasaki,
• ^{5 10 13 14 15} Olivier Parcollet,
• ^{8 9 11} Jan von Delft,
• ¹⁶ Hiroshi Shinaoka,
• ^{1 2 3 4 7} Xavier Waintal

• ¹ Centre d'études nucléaires de Grenoble / CEA Grenoble [CENG]
• ² Université Grenoble Alpes / Grenoble Alpes University [UGA]
• ³ Institut polytechnique de Grenoble / Grenoble Institute of Technology
• ⁴ PHotonique ELectronique et Ingénierie QuantiqueS / PHotonique ELectronique et Ingénierie QuantiqueS [PHELIQS]
• ⁵ Centre National de la Recherche Scientifique / French National Centre for Scientific Research [CNRS]
• ⁶ Institut Néel [NEEL]
• ⁷ Institut de Recherche Interdisciplinaire de Grenoble / Institut de Recherche Interdisciplinaire de Grenoble [IRIG]
• ⁸ Center for NanoScience [CeNS]
• ⁹ Munich Center for Quantum Science and Technology [MCQST]
• ¹⁰ Flatiron Institute
• ¹¹ Arnold Sommerfeld Center / Arnold Sommerfeld Center for Theoretical Physics [ACS]
• ¹² AtelierArith
• ¹³ L'Institut de physique théorique [IPhT]
• ¹⁴ Université Paris-Saclay / University of Paris-Saclay
• ¹⁵ Commissariat à l'énergie atomique / CEA Saclay [CEA Saclay]
• ¹⁶ 埼玉大学 / Saitama University