Related papers: A novel multigrid method for electronic structure …
Unfitted finite element methods have emerged as a popular alternative to classical finite element methods for the solution of partial differential equations and allow modeling arbitrary geometries without the need for a boundary-conforming…
Density matrix electronic structure theory is used in many quantum chemistry methods to "alleviate" the computational cost that arises from directly using wave functions. Although density matrix based methods are computationally more…
Variational methods are highly valuable computational tools for solving high-dimensional quantum systems. In this paper, we explore the effectiveness of three variational methods: the density matrix renormalization group (DMRG), Boltzmann…
Density Matrix Renormalization Group (DMRG) or Matrix Product States (MPS) are widely acknowledged as highly effective and accurate methods for solving one-dimensional quantum many-body systems. However, the direct application of DMRG to…
It is known that the solution of a conservative steady-state two-sided fractional diffusion problem can exhibit singularities near the boundaries. As consequence of this, and due to the conservative nature of the problem, we adopt a finite…
The rectangular collocation approach makes it possible to solve the Schr\"odinger equation with basis functions that do not have amplitude in all regions in which wavefunctions have significant amplitude. Collocation points can be…
First quantized, grid-based methods for chemistry modelling are a natural and elegant fit for quantum computers. However, it is infeasible to use today's quantum prototypes to explore the power of this approach, because it requires a…
Quantum error mitigation (QEM) strategies are essential for improving the precision and reliability of quantum chemistry algorithms on noisy intermediate-scale quantum devices. Reference-state error mitigation (REM) is a cost-effective…
We present a polynomial multigrid method for the nodal interior penalty formulation of the Poisson equation on three-dimensional Cartesian grids. Its key ingredient is a weighted overlapping Schwarz smoother operating on element-centered…
The paper develops a Newton multigrid (MG) method for one- and two-dimensional steady-state shallow water equations (SWEs) with topography and dry areas.It solves the nonlinear system arising from the well-balanced finite volume…
Exceptional points are special parameter points in spectra of open quantum systems, at which resonance energies degenerate and the associated eigenvectors coalesce. Typical examples are Rydberg systems in parallel electric and magnetic…
Quotient regularization models (QRMs) are a class of powerful regularization techniques that have gained considerable attention in recent years, due to their ability to handle complex and highly nonlinear data sets. However, the nonconvex…
Implementing high-fidelity quantum control and reducing the effect of the coupling between a quantum system and its environment is a major challenge in developing quantum information technologies. Here, we show that there exists a…
A new mathematical model for the description of three electron quantum dots in 2D space is created, and ground states of this system in external magnetic field is investigated. The Schrodinger equation for three two-dimensional electrons is…
We formulate and implement a spectral method for solving the Schrodinger equation, as it applies to quasi-one-dimensional materials and structures. This allows for computation of the electronic structure of important technological materials…
All-photonic quantum repeaters use multi-qubit photonic graph states, called repeater graph states (RGS), instead of matter-based quantum memories, for protection against predominantly loss errors. The RGS comprises tree-graph-encoded…
Many problems in computational science and engineering involve partial differential equations and thus require the numerical solution of large, sparse (non)linear systems of equations. Multigrid is known to be one of the most efficient…
The numerical matrix Numerov algorithm is used to solve the stationary Schr\"odinger equation for central Coulomb potentials. An efficient approximation for accelerating the convergence is proposed. The Numerov method is error-prone if the…
We study efficient simulation of steady state for rarefied gas flow, which is modeled by the Boltzmann equation with BGK-type collision term. A nonlinear multigrid solver is proposed to resolve the efficiency issue by the following…
Quantum algorithms for molecular electronic structure have been developed with lower computational scaling than their classical counterparts, but emerging quantum hardware is far from being capable of the coherence,connectivity and gate…