Related papers: An Optimally Accurate Lanczos Algorithm in the Mat…
We propose a new method for low-rank approximation of Moore-Penrose pseudoinverses (MPPs) of large-scale matrices using tensor networks. The computed pseudoinverses can be useful for solving or preconditioning of large-scale overdetermined…
A brief pedagogical overview of recent advances in tensor network state methods are presented that have the potential to broaden their scope of application radically for strongly correlated molecular systems. These include global fermionic…
Numerical linked-cluster expansions allow one to calculate finite-temperature properties of quantum lattice models directly in the thermodynamic limit through exact solutions of small clusters. However, full diagonalization is often the…
Understanding extreme non-locality in many-body quantum systems can help resolve questions in thermostatistics and laser physics. The existence of symmetry selection rules for Hamiltonians with non-decaying terms on infinite-size lattices…
In this paper, we propose a novel model to recover a low-rank tensor by simultaneously performing double nuclear norm regularized low-rank matrix factorizations to the all-mode matricizations of the underlying tensor. An block successive…
Learning-based low rank approximation algorithms can significantly improve the performance of randomized low rank approximation with sketch matrix. With the learned value and fixed non-zero positions for sketch matrices from learning-based…
Rank deficient Hankel matrices are at the core of several applications. However, in practice, the coefficients of these matrices are noisy due to e.g. measurements errors and computational errors, so generically the involved matrices are…
Recent work by Wu {\em et al.} [arXiv:1910.11011] proposed a numerical method, so-called matrix product operator-matrix product state (MPO-MPS) method, by which several types of quantum many-body wave functions, in particular, the projected…
We show that any matrix product state (MPS) can be exactly represented by a recurrent neural network (RNN) with a linear memory update. We generalize this RNN architecture to 2D lattices using a multilinear memory update. It supports…
By combining the continuous matrix product state (cMPS) representation for quantum fields in the continuum with standard optimization techniques for matrix product states (MPS) on the lattice, we obtain an approximation $|\Psi\rangle$,…
The density matrices are positively semi-definite Hermitian matrices of unit trace that describe the state of a quantum system. The goal of the paper is to develop minimax lower bounds on error rates of estimation of low rank density…
We present a method to apply the well-known matrix product state (MPS) formalism to partially separable states in solid state systems. The computational effort of our method is equal to the effort of the standard density matrix…
In this work, we propose a new randomized algorithm for computing a low-rank approximation to a given matrix. Taking an approach different from existing literature, our method first involves a specific biased sampling, with an element being…
We show that from the point of view of the generalized pairing Hamiltonian, the atomic nucleus is a system with small entanglement and can thus be described efficiently using a 1D tensor network (matrix-product state) despite the presence…
Tensor-network Born machines (TNBMs) are quantum-inspired generative models for learning data distributions. Using tensor-network contraction and optimization techniques, the model learns an efficient representation of the target…
The use of heuristics to assess the convergence and compress the output of Markov chain Monte Carlo can be sub-optimal in terms of the empirical approximations that are produced. Typically a number of the initial states are attributed to…
We present some exact results for the optimal Matrix Product State (MPS) approximation to the ground state of the infinite isotropic Heisenberg spin-1/2 chain. Our approach is based on the systematic use of Schmidt decompositions to reduce…
Large Language Models (LLMs) have demonstrated remarkable capabilities across diverse natural language tasks but suffer from extremely large memory footprints and computational costs. In this paper, we introduce a tensor compression…
We present randUBV, a randomized algorithm for matrix sketching based on the block Lanzcos bidiagonalization process. Given a matrix $\bf{A}$, it produces a low-rank approximation of the form ${\bf UBV}^T$, where $\bf{U}$ and $\bf{V}$ have…
Tensor network methods have progressed from variational techniques based on matrix-product states able to compute properties of one-dimensional condensed-matter lattice models into methods rooted in more elaborate states such as projected…