21 papers · ranked by Valyu relevance
Yann Garniron, Thomas Applencourt, Kevin Gasperich, Anouar Benali + 15 more
Quantum Package is an open-source programming environment for quantum chemistry specially designed for wave function methods. Its main goal is the development of determinant-driven selected configuration interaction (sCI) methods and multi-reference second-order perturbation theory (PT2). The determinant-driven…
Daniel Miller, Laurin E. Fischer, Kyano Levi, Eric J. Kuehnke + 4 more
A central building block of many quantum algorithms is the diagonalization of Pauli operators. Although it is always possible to construct a quantum circuit that simultaneously diagonalizes a given set of commuting Pauli operators, only resource-efficient circuits can be executed reliably on near-term quantum…
Haoze He, Daniel Kressner
We present and analyze a simple numerical method that diagonalizes a complex normal matrix A by diagonalizing the Hermitian matrix obtained from a random linear combination of the Hermitian and skew-Hermitian parts of A.
Petr Tichavský, Anh Huy Phan, Andrzej Cichocki
Tensor diagonalization means transforming a given tensor to an exactly or nearly diagonal form through multiplying the tensor by non-orthogonal invertible matrices along selected dimensions of the tensor. It is generalization of approximate joint diagonalization (AJD) of a set of matrices. In particular, we derive (1)…
M. H. S. Amin, Anatoly Yu. Smirnov, Neil G. Dickson, Marshall Drew-Brook
'Marshall Drew-Brook'] An approximate diagonalization method is proposed that combines exact diagonalization and perturbation expansion to calculate low energy eigenvalues and eigenfunctions of a Hamiltonian. The method involves deriving an effective Hamiltonian for each eigenvalue to be calculated, using perturbation…
Eric Hermes, Khachik Sargsyan, Habib Najm, Judit Zádor
We present a new algorithm for the optimization of molecular structures to saddle points on the potential energy surface using a redundant internal coordinate system. This algorithm automates the procedure of defining the internal coordinate system, including the handling of linear bending angles, e.g. through the…
Marco Congedo, Bijan Afsari, Alexandre Barachant, Maher Moakher + 1 more
'Jesus Malo'] We explore the connection between two problems that have arisen independently in the signal processing and related fields: the estimation of the geometric mean of a set of symmetric positive definite (SPD) matrices and their approximate joint diagonalization (AJD). Today there is a considerable interest…
Théo Trouillon, Christopher R. Dance, Éric Gaussier, Guillaume Bouchard
'Guillaume Bouchard'] Diagonalization, or eigenvalue decomposition, is very useful in many areas of applied mathematics, including signal processing and quantum physics. Matrix decomposition is also a useful tool for approximating matrices as the product of a matrix and its transpose, which relates to unitary…
Xiao-Feng Gong, Ke Wang, Qiu-Hua Lin, Zhi-Wen Liu + 1 more
Joint estimation of direction-of-arrival (DOA) and polarization with electromagnetic vector-sensors (EMVS) is considered in the framework of complex-valued non-orthogonal joint diagonalization (CNJD). Two new CNJD algorithms are presented, which propose to tackle the high dimensional optimization problem in CNJD via a…
Alexre Urzhumtsev, Pavel V. Afonine, Andrew H. Van Benschoten, James S. Fraser + 1 more
The widely used Translation Libration Screw (TLS) approximation describes concerted motions of atomic groups in X-ray refinement. TLS refinement often provides a better interpretation of diffraction data and the resulting rigid body motions may subsequently be assigned biochemical significance. In TLS refinement, three…
Authors not listed
One of the main applications for which quantum computers are hoped to find utility is in simulating ground state energies and other observables of molecular chemical systems. The recently proposed sample-based diagonalization method is a readily implementable method for this task on current-day hardware using short…
Wei Pan, Jing Wang, Deyan Sun
The diagonalization of matrices may be the top priority in the application of modern physics. In this paper, we numerically demonstrate that, for real symmetric random matrices with non-positive off-diagonal elements, a universal scaling relationship between the eigenvector and matrix elements exists. Namely, each…
Zongyuan Han, Wenhao Li, Shengxin Zhu
In this paper, we investigate diagonal estimation for large or implicit matrices, aiming to develop a novel and efficient stochastic algorithm that incorporates adaptive parameter selection. We explore the influence of different eigenvalue distributions on diagonal estimation and analyze the necessity of introducing…
Robert A. Baston, Yuji Nakatsukasa
We study the problem of estimating the diagonal of an implicitly given matrix A. For such a matrix we have access to an oracle that allows us to evaluate the matrix vector product Av. For random variable v drawn from an appropriate distribution, this may be used to return an estimate of the diagonal of the matrix A.…
Davoud Mirzaei
These lecture notes focus on some numerical linear algebra algorithms in scientific computing. We assume that students are familiar with elementary linear algebra concepts such as vector spaces, systems of equations, matrices, norms, eigenvalues, and eigenvectors. In the numerical part, we do not pursue Gaussian…
Abd‐Krim Seghouane, Yousef Saad
Given a set of p symmetric (real) matrices, the Orthogonal Joint Diagonalization (OJD) problem consists of finding an orthonormal basis in which the representation of each of these p matrices is as close as possible to a diagonal matrix. We argue that when the matrices are of large dimension, then the natural…
Authors not listed
We present a comprehensive theoretical analysis of quantum subspace diagonalization methods for molecular electronic structure calculations, establishing rigorous complexity bounds and convergence guarantees. Building on recent developments in adaptive quantum algorithms for chemical systems, we formulate a general…
Authors not listed
Ongoing research involving electronic spin-dependent dynamics, such as chiral- induced spin selectivity, is providing impetus to revise our understanding of nuclear en- tanglement with electronic spatial and spin degrees of freedom. In a spin-independent setting, non-adiabatic couplings are well-known mediators of…
Evan D. Gorman, Manuel E. Lladser
Ultrametric matrices have a rich structure that is not apparent from their definition. Notably, the subclass of strictly ultrametric matrices are covariance matrices of certain weighted rooted binary trees. In applications, these matrices can be large and dense, making them difficult to store and handle. In this…
Authors not listed
This article is the second in a two-part tutorial review on electronic spin-dependent dynamics. In Part I, we presented the fundamental theory within the adiabatic Born– Huang framework that describes the interaction between nuclear motion and the elec- tronic (spin and spatial) degrees of freedom. In particular, we…
Rafael G. Viegas, Ingrid B. S. Martins, Murilo N. Sanches, Antonio B. Oliveira + 3 more
Molecular dynamics (MD) simulations provide a powerful means to explore the dynamic behavior of biomolecular systems at the atomic level. However, analyzing the vast datasets generated by MD simulations poses significant challenges. This manuscript discusses the Energy Landscape Visualization Method (ELViM), a…