Related papers: Computing vibrational energy levels by solving lin…
In single-reference coupled-cluster (CC) methods, one has to solve a set of non-linear polynomial equations in order to determine the so-called amplitudes which are then used to compute the energy and other properties. Although it is of…
Observations in various applications are frequently represented as a time series of multidimensional arrays, called tensor time series, preserving the inherent multidimensional structure. In this paper, we present a factor model approach,…
Choosing a basis set is the first step of a quantum chemistry calculation and it sets its maximum accuracy. This choice of orbitals is limited by strong technical constraints as one must be able to compute a large number of six dimensional…
In this paper, we suggest a new method for a given tensor to find CP decompositions using a less number of rank $1$ tensors. The main ingredient is the Least Absolute Shrinkage and Selection Operator (LASSO) by considering the decomposition…
The so-called block-term decomposition (BTD) tensor model has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of \emph{blocks} of rank higher than one, a…
The calculation time for the energy of atoms and molecules scales exponentially with system size on a classical computer but polynomially using quantum algorithms. We demonstrate that such algorithms can be applied to problems of chemical…
This article covers few selected aspects of quantum theory of molecular rotations and vibrations. Triatomic molecules are the simplest systems, which show qualitative characteristics of larger polyatomic molecules. On the minimal example of…
We consider the problem of decomposing a real-valued symmetric tensor as the sum of outer products of real-valued vectors. Algebraic methods exist for computing complex-valued decompositions of symmetric tensors, but here we focus on…
We present how to compute vibrational eigenstates with tree tensor network states (TTNSs), the underlying ansatz behind the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method. The eigenstates are computed with an…
Tensors play a central role in many modern machine learning and signal processing applications. In such applications, the target tensor is usually of low rank, i.e., can be expressed as a sum of a small number of rank one tensors. This…
In this paper we show that every combinatorial problem has an exact explicit equation that returns its solution. We present a method to obtain an equation that solves exactly any combinatorial problem, both inversion, constraint…
We are concerned with the tensor equation with an M-tensor or Z-tensor, which we call the M- tensor equation or Z-tensor equation respectively. We derive a necessary and sufficient condition for a Z (or M)-tensor equation to have…
Controllability and observability energy functions play a fundamental role in model order reduction and are inherently connected to optimal control problems. For linear dynamical systems the energy functions are known to be quadratic…
Tensor decomposition is a fundamental method used in various areas to deal with high-dimensional data. \emph{Tensor power method} (TPM) is one of the widely-used techniques in the decomposition of tensors. This paper presents a novel tensor…
In this paper, we extend a method recently reported [Phys. Rev. E 87, 042921 (2012)] for the calculation of the eigestates of classically highly chaotic systems to cases of mixed dynamics, i.e. those presenting regular and irregular motions…
A method based on separated integration to estimate anharmonic corrections to energy and vibration of molecules in a second-order diagrammatic vibrational many-body Green's function formalism has already been presented. A severe bottleneck…
A very accurate, (HF)$_2$ potential energy surface (PES) due to Huang et al. (J. Chem. Phys., 150, 154302 (2019)) is used to calculate the energy levels of the HF dimer by solving the nuclear-motion Schr\"{o}dinger equation using…
The various ways to reduce number of vectors describing condition of particles for high energy physics problems are presented. In particular decomposition of any vector with respect to the basis, consisting of any four linearly independent…
The tensor self energy is computed at one loop order in a model in which a vector and tensor interact in a way that eliminates all tensor degrees of freedom. Divergencies arise which cannot be eliminated without introducing a kinetic term…
We introduce a family of numerical algorithms for the solution of linear system in higher dimensions with the matrix and right hand side given and the solution sought in the tensor train format. The proposed methods are rank--adaptive and…