Resources

I. Oseledets. Tensor-Train Decomposition. SIAM Journal on Scientific Computing 33, 2295–2317 (2011). ↩¹

U. Schollwöck. The density-matrix renormalization group in the age of matrix product states. Annals of Physics 326, 96–192 (2011). ↩¹

B. N. Khoromskij. Tensor Numerical Methods in Scientific Computing (De Gruyter, Berlin, Boston, 2018). ↩¹ ↩² ↩³

B. Khoromskij. O(d log N)-Quantics Approximation of N - d Tensors in High-Dimensional Numerical Modeling. Constructive Approximation 34 (2009). ↩¹

L. Devos, M. Van Damme and J. Haegeman. TensorOperations.jl (2023). ↩¹

A. A. Michailidis, C. Fenton and M. Kiffner. Tensor Train Multiplication (2024), arXiv:2410.19747 [physics.comp-ph]. ↩¹

V. A. Kazeev and B. N. Khoromskij. Low-rank explicit QTT representation of the Laplace operator and its inverse. SIAM Journal on Matrix Analysis and Applications 33, 742–758 (2012). ↩¹

M. Lindsey. Multiscale interpolative construction of quantized tensor trains, arXiv preprint arXiv:2311.12554 (2023). ↩¹

S. Dolgov, B. Khoromskij and D. Savostyanov. Superfast Fourier Transform Using QTT Approximation. Journal of Fourier Analysis and Applications 18, 915–953 (2012).

J. Chen and M. Lindsey. Direct interpolative construction of the discrete Fourier transform as a matrix product operator (2024), arXiv:2404.03182 [quant-ph].

J. Chen, E. M. Stoudenmire and S. R. White. Quantum Fourier transform has small entanglement. PRX Quantum 4, 040318 (2023). ↩¹

S. Holtz, T. Rohwedder and R. Schneider. The Alternating Linear Scheme for Tensor Optimization in the Tensor Train Format. SIAM Journal on Scientific Computing 34, A683–A713 (2012). ↩¹

S. R. White. Density matrix formulation for quantum renormalization groups. Physical Review Letters 69, 2863–2866 (1992). ↩¹

S. V. Dolgov and D. V. Savostyanov. Alternating Minimal Energy Methods for Linear Systems in Higher Dimensions. SIAM Journal on Scientific Computing 36, A2248-A2271 (2014). ↩¹

D. Kressner, M. Steinlechner and A. Uschmajew. Low-Rank Tensor Methods with Subspace Correction for Symmetric Eigenvalue Problems. SIAM Journal on Scientific Computing 36, A2346-A2368 (2014). ↩¹

M. Lubasch, P. Moinier and D. Jaksch. Multigrid renormalization. Journal of Computational Physics 372, 587–602 (2018). ↩¹

J. Haegeman, C. Lubich, I. Oseledets, B. Vandereycken and F. Verstraete. Unifying time evolution and optimization with matrix product states. Physical Review B 94, 165116 (2016). ↩¹

L. Vanderstraeten, J. Haegeman and F. Verstraete. Tangent-space methods for uniform matrix product states. SciPost Physics Lecture Notes (2019). ↩¹

D. V. Savostyanov. Quasioptimality of maximum-volume cross interpolation of tensors. Linear Algebra and its Applications 458, 217–244 (2014). ↩¹

D. Savostyanov and I. Oseledets. Fast adaptive interpolation of multi-dimensional arrays in tensor train format. In: The 2011 International Workshop on Multidimensional (nD) Systems (2011); pp. 1–8.

L. I. Vysotsky, A. V. Smirnov and E. E. Tyrtyshnikov. Tensor-train numerical integration of multivariate functions with singularities. Lobachevskii Journal of Mathematics 42, 1608–1621 (2021). ↩¹