References

We provide a list of references to the literature related to tensor cross interpolation and quantics tensor networks.

Please feel to contact us if you would like to add a relevant paper to this list or make a pull request here.

• Learning low-rank tensor train representations: new algorithms and libraries
  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
  arXiv:2407.02454
  This paper provides a pedagogical introduction to tensor network methods, which includes an overview of the existing literature and also new algorithm.

• Learning parameter dependence for Fourier-based option pricing with tensor trains
  Rihito Sakurai, Haruto Takahashi, Koichi Miyamoto
  arXiv:2405.00701
  This paper discusses applications of Tensor Cross Interpolation (TCI) to financial problems, such as Fourier-based option pricing.

• Learning tensor trains from noisy functions with application to quantum simulation
  Kohtaroh Sakaue, Hiroshi Shinaoka, Rihito Sakurai
  arXiv:2405.12730
  TCI-based approaches for learning tensor trains from noisy functions, with applications to quantum simulation.

• Low-rank quantics tensor train representations of Feynman diagrams for multiorbital electron-phonon models
  Hirone Ishida, Natsuki Okada, Shintaro Hoshino, Hiroshi Shinaoka
  arXiv:2405.06440
  Applications of Quantics Tensor Cross Interpolaiton (QTCI) to multiorbital electron-phonon impurity models.

• Compactness of quantics tensor train representations of local imaginary-time propagators Haruto Takahashi, Rihito Sakurai, Hiroshi Shinaoka
  arXiv:2403.09161
  Numerical invetigation of compactness of QTT representations of local imaginary-time propagators, showing the saturation of the bond dimension at low temperature.

• Multiscale interpolative construction of quantized tensor trains
  Michael Lindsey
  arXiv:2311.12554
  This paper introduces a multiscale polynomial interpolation method for constructing qunatics/quantized tensor trains.

• A Tensor Train Continuous Time Solver for Quantum Impurity Models
  A. Erpenbeck, W.-T. Lin, T. Blommel, L. Zhang, S. Iskakov, L. Bernheimer, Y. Núñez-Fernández, G. Cohen, O. Parcollet, X. Waintal, E. Gull
  Phys. Rev. B 107, 245135 (2023)
  arXiv:2303.11199
  Applications of TCI to the single-impurity Anderson model at equilibrium by calculating the systematic expansion in power of the hybridization of the impurity with the bath.

• Quantics Tensor Cross Interpolation for High-Resolution Parsimonious Representations of Multivariate Functions
  Marc K. Ritter, Yuriel Núñez Fernández, Markus Wallerberger, Jan von Delft, Hiroshi Shinaoka, and Xavier Waintal
  Phys. Rev. Lett. 132, 056501 (2024)
  arXiv:2303.11819
  This paper introduces quantics tensor cross interpolation (QTCI) for high-resolution parsimonious representations of multivariate functions.

• Multiscale Space-Time Ansatz for Correlation Functions of Quantum Systems Based on Quantics Tensor Trains
  Hiroshi Shinaoka, Markus Wallerberger, Yuta Murakami, Kosuke Nogaki, Rihito Sakurai, Philipp Werner, and Anna Kauch
  Phys. Rev. X 13, 021015 (2023)
  This paper discusses compressing correlation functions of quantum systems using quantics tensor trains on a multiscale space-time ansatz.

• Quantum Fourier Transform Has Small Entanglement
  Jielun Chen, E.M. Stoudenmire, Steven R. White
  PRX Quantum 4, 040318 (2023)
  This paper reveals the low-entanglement structure of the quantum Fourier transform.

• Learning Feynman Diagrams with Tensor Trains
  Yuriel Núñez Fernández, Matthieu Jeannin, Philipp T. Dumitrescu, Thomas Kloss, Jason Kaye, Olivier Parcollet, and Xavier Waintal
  Phys. Rev. X 12, 041018 (2022)
  This paper introduces Tensor Cross Interpolation (TCI) for learning Feynman diagrams.