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This work explores the representation of univariate and multivariate functions as matrix product states (MPS), also known as quantized tensor-trains (QTT).
A note on the summation of Chebyshev series
C. W. Clenshaw · 1955
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A good submatrix is hard to find
John J. Bartholdi · 1982
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Rigorous results on valence-bond ground states in antiferromagnets
Ian Affleck, Tom Kennedy, Elliott H. Lieb, and Hal Tasaki · 1987
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Chebyshev & Fourier Spectral Methods
John P. Boyd · 1989
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Exact Antiferromagnetic Ground States of Quantum Spin Chains
M Fannes, B Nachtergaele, and R. F Werner · 1989
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Density matrix formulation for quantum renormalization groups
Steven R. White · 1992
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Thermodynamic Limit of Density Matrix Renormalization
Stellan Östlund and Stefan Rommer · 1995
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Equivalence of the variational matrix product method and the density matrix renormalization group applied to spin chains
J Dukelsky, M. A Martín-Delgado, T Nishino, and G Sierra · 1998
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Chebyshev Polynomials
John C. Mason and David C. Handscomb · 2003
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Image compression and entanglement, October 2005
Jose I. Latorre · 2005
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Sequential Generation of Entangled Multiqubit States
C. Schön, E. Solano, F. Verstraete, J. I. Cirac, and M. M. Wolf · 2005
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Fast Construction of the Fejér and Clenshaw–Curtis Quadrature Rules
Jörg Waldvogel · 2006
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Entropy and Exact Matrix-Product Representation of the Laughlin Wave Function
S. Iblisdir, J. I. Latorre, and R. Orús · 2007
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How to Find a Good Submatrix
S. A. Goreinov, I. V. Oseledets, D. V. Savostyanov, E. E. Tyrtyshnikov, and N. L. Zamarashkin · 2010
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TT-cross approximation for multidimensional arrays
Ivan Oseledets and Eugene Tyrtyshnikov · 2010
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O(dlog N)-Quantics Approximation of N-d Tensors in High-Dimensional Numerical Modeling
Boris N. Khoromskij · 2011
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Tensor-Train Decomposition
I. V. Oseledets · 2011
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Fast adaptive interpolation of multi-dimensional arrays in tensor train format
Dmitry Savostyanov and Ivan Oseledets · 2011
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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
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Superfast Fourier Transform Using QTT Approximation
Sergey Dolgov, Boris Khoromskij, and Dmitry Savostyanov · 2012
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Constructive Representation of Functions in Low-Rank Tensor Formats
I. V. Oseledets · 2013
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A practical introduction to tensor networks: Matrix product states and projected entangled pair states
Román Orús · 2014
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Quasioptimality of maximum-volume cross interpolation of tensors
Dmitry V. Savostyanov · 2014
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Chebyshev matrix product state approach for time evolution
Jad C. Halimeh, Fabian Kolley, and Ian P. McCulloch · 2015
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Efficient Computation of Highly Oscillatory Integrals by Using QTT Tensor Approximation
Boris Khoromskij and Alexander Veit · 2016
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Multigrid Renormalization
Michael Lubasch, Pierre Moinier, and Dieter Jaksch · 2018
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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 state tomography with tensor train cross approximation, July 2022
Alexander Lidiak, Casey Jameson, Zhen Qin, Gongguo Tang, Michael B. Wakin, Zhihui Zhu, and Zhexuan Gong · 2022
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Learning Feynman Diagrams with Tensor Trains
Yuriel Núñez Fernández, Matthieu Jeannin, Philipp T. Dumitrescu, Thomas Kloss, Jason Kaye, Olivier Parcollet, and Xavier Waintal · 2022
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Functional Tensor-Train Chebyshev Method for Multidimensional Quantum Dynamics Simulations
Micheline B. Soley, Paul Bergold, Alex A. Gorodetsky, and Victor S. Batista · 2022
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TTOpt: A Maximum Volume Quantized Tensor Train-based Optimization and its Application to Reinforcement Learning, September 2022
Konstantin Sozykin, Andrei Chertkov, Roman Schutski, Anh-Huy Phan, Andrzej Cichocki, and Ivan Oseledets · 2022
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Rectangular maximum-volume submatrices and their applications
A. Mikhalev and I. V. Oseledets · 2018
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A continuous analogue of the tensor-train decomposition
Alex Gorodetsky, Sertac Karaman, and Youssef Marzouk · 2019
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Approximation Theory and Approximation Practice, Extended Edition
Lloyd N. Trefethen · 2019
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Entanglement and its relation to energy variance for local one-dimensional Hamiltonians
Mari Carmen Bañuls, David A. Huse, and J. Ignacio Cirac · 2020
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Approximation and sampling of multivariate probability distributions in the tensor train decomposition
Sergey Dolgov, Karim Anaya-Izquierdo, Colin Fox, and Robert Scheichl · 2020
Cited alongside, same era.
Parallel cross interpolation for high-precision calculation of high-dimensional integrals
Sergey Dolgov and Dmitry Savostyanov · 2020
Cited alongside, same era.
Quantum-inspired method for solving the Vlasov-Poisson equations
Erika Ye and Nuno F. G. Loureiro · 2022
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Challenging the Curse of Dimensionality in Multidimensional Numerical Integration by Using a Low-Rank Tensor-Train Format
Boian Alexandrov, Gianmarco Manzini, Erik W. Skau, Phan Minh Duc Truong, and Radoslav G. Vuchov · 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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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, and E. Gull · 2023
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Generative modeling via tensor train sketching
YoonHaeng Hur, Jeremy G. Hoskins, Michael Lindsey, E.M. Stoudenmire, and Yuehaw Khoo · 2023
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Efficient MPS representations and quantum circuits from the Fourier modes of classical image data, December 2023
Bernhard Jobst, Kevin Shen, Carlos A. Riofrío, Elvira Shishenina, and Frank Pollmann · 2023
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A Novel Method of Function Extrapolation Inspired by Techniques in Low-entangled Many-body Physics, August 2023
Lambert Lin and Steven R. White · 2023
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Multiscale interpolative construction of quantized tensor trains, November 2023
Michael Lindsey · 2023
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Quantum state preparation using tensor networks
Ar A Melnikov, A A Termanova, S V Dolgov, F Neukart, and M R Perelshtein · 2023
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Arithmetic circuit tensor networks, multivariable function representation, and high-dimensional integration
Ruojing Peng, Johnnie Gray, and Garnet Kin-Lic Chan · 2023
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Direct interpolative construction of the discrete Fourier transform as a matrix product operator, April 2024
Jielun Chen and Michael Lindsey · 2024
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Minimal matrix-product state algorithms library
Juan José García-Ripoll · 2024
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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 · 2024
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Simulations for the figures in the paper
Juan José Rodríguez-Aldavero · 2024
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