Related papers: Low-rank decomposition for quantum simulations wit…

We introduce a new low-dimensional model of high-dimensional numerical simulation data based on low-rank tensor decompositions. Our new model aims to minimize differences between the model data and simulation data as well as functions of…

A primary interest in dynamic inverse problems is to identify the underlying temporal behaviour of the system from outside measurements. In this work we consider the case, where the target can be represented by a decomposition of spatial…

Matrix decompositions are fundamental tools in the area of applied mathematics, statistical computing, and machine learning. In particular, low-rank matrix decompositions are vital, and widely used for data analysis, dimensionality…

Low-rank plus diagonal (LRPD) decompositions provide a powerful structural model for large covariance matrices, simultaneously capturing global shared factors and localized corrections that arise in covariance estimation, factor analysis,…

We present a natural generalization of the recent low rank + sparse matrix decomposition and consider the decomposition of matrices into components of multiple scales. Such decomposition is well motivated in practice as data matrices often…

We present a method for improving a Non Local Means operator by computing its low-rank approximation. The low-rank operator is constructed by applying a filter to the spectrum of the original Non Local Means operator. This results in an…

Low-rank approximation is a technique to approximate a tensor or a matrix with a reduced rank to reduce the memory required and computational cost for simulation. Its broad applications include dimension reduction, signal processing,…

Decomposing weight matrices into quantization and low-rank components ($\mathbf{W} \approx \mathbf{Q} + \mathbf{L}\mathbf{R}$) is a widely used technique for compressing large language models (LLMs). Existing joint optimization methods…

It is well known that the Schmidt decomposition exists for all pure states of a two-party quantum system. We demonstrate that there are two ways to obtain an analogous decomposition for arbitrary rank-1 operators acting on states of a…

We consider different Linear Combination of Unitaries (LCU) decompositions for molecular electronic structure Hamiltonians. Using these LCU decompositions for Hamiltonian simulation on a quantum computer, the main figure of merit is the…

Many data-analysis problems involve large dense matrices that describe the covariance of stationary noise processes; the computational cost of inverting these matrices, or equivalently of solving linear systems that contain them, is often a…

Composite quantum systems can be decomposed into subsystems in many different inequivalent ways. We call a particular decomposition a meronomic reference frame for the system. We apply the ideas of quantum reference frames to characterize…

We propose a general method for constructing system-dependent basis functions for correlated quantum chemical calculations. Our construction combines features from several traditional approaches: plane waves, localized basis functions, and…

The first discussion of basis sets consisting of exponentially decaying Coulomb Sturmian functions for modelling electronic structures is presented. The proposed basis set construction selects Coulomb Sturmian functions using separate upper…

A key task in quantum computation is the application of a sequence of gates implementing a specific unitary operation. However, the decomposition of an arbitrary unitary operation into simpler quantum gates is a nontrivial problem. Here we…

We study the decomposition of the Coulomb integrals of periodic systems into a tensor contraction of six matrices of which only two are distinct. We find that the Coulomb integrals can be well approximated in this form already with small…

We construct an efficient classical analogue of the quantum matrix inversion algorithm (HHL) for low-rank matrices. Inspired by recent work of Tang, assuming length-square sampling access to input data, we implement the pseudoinverse of a…

We study Sigma-Delta quantization methods coupled with appropriate reconstruction algorithms for digitizing randomly sampled low-rank matrices. We show that the reconstruction error associated with our methods decays polynomially with the…

In this paper, we introduce a method for multivariate function approximation using function evaluations, Chebyshev polynomials, and tensor-based compression techniques via the Tucker format. We develop novel randomized techniques to…

For the antisymmetric tensors the paper examines a low-rank approximation which is represented via only three vectors. We describe a suitable low-rank format and propose an alternating least squares structure-preserving algorithm for…