Related papers: Sample-based quantum diagonalization as parallel f…
Understanding strongly correlated systems is essential for advancing quantum chemistry and materials science, yet conventional methods like Density Functional Theory (DFT) often fail to capture their complex electronic behavior. To address…
In this paper, we propose two time-splitting finite element methods to solve the semiclassical nonlinear Schr\"odinger equation (NLSE) with random potentials. We then introduce the multiscale finite element method (MsFEM) to reduce the…
A novel overlapping domain decomposition splitting algorithm based on a Crank-Nisolson method is developed for the stochastic nonlinear Schroedinger equation driven by a multiplicative noise with non-periodic boundary conditions. The…
This paper improves the convergence and robustness of a multigrid-based solver for the cross sections of the driven Schroedinger equation. Adding an Coupled Channel Correction Step (CCCS) after each multigrid (MG) V-cycle efficiently…
Density matrix embedding theory (DMET) is a fully quantum-mechanical embedding method which shows great promise as a method of defeating the inherent exponential cost scaling of multiconfigurational wave function-based calculations by…
Quantum Selected Configuration Interaction (QSCI) methods (also known as Sample-based Quantum Diagonalization, SQD) have emerged as promising near-term approaches to solving the electronic Schr{\"o}dinger equation with quantum computers. In…
We have developed a Scalable Linear Augmented Slater-Type Orbital (LASTO) method for electronic-structure calculations on free-standing atomic clusters. As with other linear methods we solve the Schr\"odinger equation using a mixed basis…
Quantum computers have the potential for an exponential speedup of classical molecular computations. However, existing algorithms have limitations; quantum phase estimation (QPE) algorithms are intractable on current hardware while…
Quantum computers hold immense potential in the field of chemistry, ushering new frontiers to solve complex many body problems that are beyond the reach of classical computers. However, noise in the current quantum hardware limits their…
We investigate fully self-consistent multiscale quantum-classical algorithms on current generation superconducting quantum computers, in a unified approach to tackle the correlated electronic structure of large systems in both quantum…
Stochastic Gradient Descent (SGD) and its variants underpin modern machine learning by enabling efficient optimization of large-scale models. However, their local search nature limits exploration in complex landscapes. In this paper, we…
We present and analyze a multiscale method for wave propagation problems, posed on spatial networks. By introducing a coarse scale, using a finite element space interpolated onto the network, we construct a discrete multiscale space using…
Fractional evolution equations lack generally accessible and well-converged codes excepting anomalous diffusion. A particular equation of strong interest to the growing intersection of applied mathematics and quantum information science and…
A contracted quantum eigensolver (CQE) finds a solution to the many-electron Schr\"odinger equation by solving its integration (or contraction) to the 2-electron space -- a contracted Schr\"odinger equation (CSE) -- on a quantum computer.…
We extend the publicly available quantumfdtd code. It was originally intended for solving the time-independent three-dimensional Schr\"odinger equation via the finite-difference time-domain (FDTD) method and for extracting the ground,…
We consider solving nonlinear optimization problems with a stochastic objective and deterministic equality constraints, assuming that only zero-order information is available for both the objective and constraints, and that the objective is…
We present a new stochastic extended Lagrangian solution to charge equilibration that eliminates self-consistent field (SCF) calculations, eliminating the computational bottleneck in solving the many-body solution with standard SCF solvers.…
We discuss stationary solutions of the discrete nonlinear Schr\"odinger equation (DNSE) with a potential of the $\phi^{4}$ type which is generically applicable to several quantum spin, electron and classical lattice systems. We show that…
The quantum mechanical ground state of electrons is described by Density Functional Theory, which leads to large minimization problems. An efficient minimization method uses a selfconsistent field (SCF) solution of large eigenvalue…
We present a novel numerical method and algorithm for the solution of the 3D axially symmetric time-dependent Schr\"odinger equation in cylindrical coordinates, involving singular Coulomb potential terms besides a smooth time-dependent…