Related papers: Hybrid Eigensolvers for Nuclear Configuration Inte…
We consider iterative methods for solving linear ill-posed problems with compact operator and right-hand side only available via noise-polluted measurements. Conjugate gradients (CG) applied to the normal equations with an appropriate…
A majority of numerical scientific computation relies heavily on handling and manipulating matrices, such as solving linear equations, finding eigenvalues and eigenvectors, and so on. Many quantum algorithms have been developed to advance…
We present a method of filter diagonalization for shell-model calculations. This method is based on the Sakurai and Sugiura (SS) method, but extended with help of the shifted complex orthogonal conjugate gradient (COCG) method. A salient…
We present for the first time an efficient iterative method to directly solve the four-component Dirac-Kohn-Sham (DKS) density functional theory. Due to the existence of the negative energy continuum in the DKS operator, the existing…
The local approach to computing electrostatic interactions proposed by Maggs and adapted by Pasichnyk for molecular dynamics simulations is extended to situations where the dielectric background medium is inhomogeneous. We furthermore…
This work considers large-scale Lyapunov matrix equations of the form $AX + XA = \boldsymbol{c}\boldsymbol{c}^T$, where $A$ is a symmetric positive definite matrix and $\boldsymbol{c}$ is a vector. Motivated by the need to solve such…
Solving the trust-region subproblem (TRS) plays a key role in numerical optimization and many other applications. Based on a fundamental result that the solution of TRS of size $n$ is mathematically equivalent to finding the rightmost…
The structure and reactions of light nuclei represent fundamental and formidable challenges for microscopic theory based on realistic strong interaction potentials. Several {\it ab initio} methods have now emerged that provide nearly exact…
Interior eigenvalue problems for large-scale sparse Hermitian matrices are fundamental in computational science. We propose an adaptive polynomial filtering strategy based on Chebyshev expansion of a step function, integrated into a…
We use the Lipkin-Meshkov-Glick (LMG) model and the valence-space nuclear shell model to examine the likely performance of variational quantum eigensolvers in nuclear-structure theory. The LMG model exhibits both a phase transition and…
We combine the adaptive and multilevel approaches to the BDDC and formulate a method which allows an adaptive selection of constraints on each decomposition level. We also present a strategy for the solution of local eigenvalue problems in…
Recent work found that an analysis formalism based on the Lanczos algorithm allows energy levels to be extracted from Euclidean correlation functions with faster ground-state convergence than effective masses, convergent estimators for…
We introduce a new algorithm for finding the eigenvalues and eigenvectors of Hermitian matrices within a specified region, based upon the LANSO algorithm of Parlett and Scott. It uses selective reorthogonalization to avoid the duplication…
Currently available noisy intermediate-scale quantum (NISQ) devices are limited by the number of qubits that can be used for quantum chemistry calculations on molecules. We show herein that the number of qubits required for simulations on a…
The power method and block Lanczos method are popular numerical algorithms for computing the truncated singular value decomposition (SVD) and eigenvalue decomposition problems. Especially in the literature of randomized numerical linear…
A novel parallel hybrid quantum-classical algorithm for the solution of the quantum-chemical ground-state energy problem on gate-based quantum computers is presented. This approach is based on the reduced density-matrix functional theory…
We present a heuristic algorithm designed to solve Quadratic Unconstrained Binary Optimization (QUBO) problems efficiently. The algorithm, referred to as IC-D2S, leverages a hybrid approach using Ising and classical machines to address very…
A new spectral type method for solving the one dimensional quantum-mechanical Lippmann-Schwinger integral equation in configuration space is described. The radial interval is divided into partitions, not necessarily of equal length. Two…
The theory of a novel bond-order potential, which is based on the block Lanczos algorithm, is presented within an orthogonal tight-binding representation. The block scheme handles automatically the very different character of sigma and pi…
The Lanczos method with implicit restarting is one of the most popular methods for finding a few exterior eigenpairs of a large symmetric matrix $A$. Usually based on polynomial filtering, restarting is crucial to limit memory and the cost…