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Quantized tensor trains (QTTs) have recently emerged as a framework for the numerical discretization of continuous functions, with the potential for widespread applications in numerical analysis.
A fast algorithm for chebyshev, fourier, and sinc interpolation onto an irregular grid
John P Boyd · 1992
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Finitely correlated states on quantum spin chains
M. Fannes, B. Nachtergaele, and R. F. Werner · 1992
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Groundstate properties of a generalized vbs-model
A. Klümper, A. Schadschneider, and J. Zittartz · 1992
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Density matrix formulation for quantum renormalization groups
S. R. White · 1992
Earlier work this paper cites.
Matrix product state representations
D. Perez-Garcia, F. Verstraete, M. M. Wolf, and J. I. Cirac · 2007
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Breaking the curse of dimensionality, or how to use svd in many dimensions
I. V. Oseledets and E. E. Tyrtyshnikov · 2009
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TT-cross approximation for multidimensional arrays
Ivan Oseledets and Eugene Tyrtyshnikov · 2010
Earlier work this paper cites.
QTT representation of the hartree and exchange operators in electronic structure calculations
V. Khoromskaia, B. Khoromskij, and R. Schneider · 2011
Earlier work this paper cites.
O(dlog n)-quantics approximation of n-d tensors in high-dimensional numerical modeling
Boris N. Khoromskij · 2011
Cited alongside, same era.
Tensor-train decomposition
Ivan V Oseledets · 2011
Cited alongside, same era.
Fast Solution of Parabolic Problems in the Tensor Train/Quantized Tensor Train Format with Initial Application to the Fokker–Planck Equation
S. V. Dolgov, B. N. Khoromskij, and I. V. Oseledets · 2012
Cited alongside, same era.
Superfast fourier transform using qtt approximation
Sergey Dolgov, Boris Khoromskij, and Dmitry Savostyanov · 2012
Cited alongside, same era.
Multilevel toeplitz matrices generated by tensor-structured vectors and convolution with logarithmic complexity
Vladimir A. Kazeev, Boris N. Khoromskij, and Eugene E. Tyrtyshnikov · 2013
Cited alongside, same era.
Constructive representation of functions in low-rank tensor formats
A quantum-inspired approach to exploit turbulence structures
Nikita Gourianov, Michael Lubasch, Sergey Dolgov, Quincy Y. van den Berg, Hessam Babaee, Peyman Givi, Martin Kiffner, and Dieter Jaksch · 2022
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Quantum-inspired method for solving the vlasov-poisson equations
Erika Ye and Nuno F. G. Loureiro · 2022
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Approximation theory of tree tensor networks: Tensorized multivariate functions, 2023
Mazen Ali and Anthony Nouy · 2023
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Approximation theory of tree tensor networks: Tensorized univariate functions
Mazen Ali and Anthony Nouy · 2023
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Quantum fourier transform has small entanglement
Jielun Chen, E.M. Stoudenmire, and Steven R. White · 2023
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Tensorized orbitals for computational chemistry, 2023
Nicolas Jolly, Yuriel Núñez Fernández, and Xavier Waintal · 2023
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I. V. Oseledets · 2013
Cited alongside, same era.
Approximation Theory and Approximation Practice, Extended Edition
Lloyd N. Trefethen · 2019
Cited alongside, same era.
On the compressibility of tensors
Tianyi Shi and Alex Townsend · 2021
Cited alongside, same era.
TT-Toolbox
Ivan Oseledets
Cited in the paper.
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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 · 2023
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Quantized tensor networks for solving the vlasov-maxwell equations, 2023
Erika Ye and Nuno Loureiro · 2023
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