Related papers: Numerical approximation of the Schr\"odinger equat…
Classical optimization is a cornerstone of the success of variational quantum algorithms, which often require determining the derivatives of the cost function relative to variational parameters. The computation of the cost function and its…
A new method of solution to the local spin density approximation to the electronic Schr\"{o}dinger equation is presented. The method is based on an efficient, parallel, adaptive multigrid eigenvalue solver. It is shown that adaptivity is…
Solving the time-dependent Schr\"odinger equation is an important application area for quantum algorithms. We consider Schr\"odinger's equation in the semi-classical regime. Here the solutions exhibit strong multiple-scale behavior due to a…
We propose an improved quantum algorithm to calculate the Green's function through real-time propagation, and use it to compute the retarded Green's function for the 2-, 3- and 4-site Hubbard models. This novel protocol significantly…
To approximate convolutions which occur in evolution equations with memory terms, a variable-stepsize algorithm is presented for which advancing N steps requires only O(N log(N)) operations and O(log(N)) active memory, in place of O(N^2)…
We study the effective approximation for a nonlocal stochastic Schrodinger equation with a rapidly oscillating, periodically time-dependent potential. We use the natural diffusive scaling of heterogeneous system and study the limit…
We propose quantum algorithms for projective ground-state preparation and calculations of the many-body Green's functions directly in frequency domain. The algorithms are based on the linear combination of unitary (LCU) operations and…
We study optimization problems that are neither approximable in polynomial time (at least with a constant factor) nor fixed parameter tractable, under widely believed complexity assumptions. Specifically, we focus on Maximum Independent…
We proposed a distributed approximating functional method for efficiently describing the electronic dynamics in atoms and molecules in the presence of the Coulomb singularities, using the kernel of a grid representation derived by using the…
We consider the study of a numerical scheme for an initial- and Dirichlet boundary- value problem for a nonlinear Schr\"odinger equation. We approximate the solution using a, local (non-uniform) two level scheme in time (see C. Besse [6]…
The radial Schrodinger equation for a spherically symmetric potential can be regarded as a one dimensional classical harmonic oscillator with a time-dependent spring constant. For solving classical dynamics problems, symplectic integrators…
We describe an exact and highly efficient numerical algorithm for solving a special but important class of convection-diffusion equations. These equations occur in many problems in physics, chemistry, or biology, and they are usually hard…
This paper concerns the numerical approximation of low-energy eigenstates of the linear random Schr\"odinger operator. Under oscillatory high-amplitude potentials with a sufficient degree of disorder it is known that these eigenstates…
We discuss a numerical algorithm for solving nonlinear integro-differential equations, and illustrate our findings for the particular case of Volterra type equations. The algorithm combines a perturbation approach meant to render a…
We propose an inexact variable-metric proximal point algorithm to accelerate gradient-based optimization algorithms. The proposed scheme, called QNing can be notably applied to incremental first-order methods such as the stochastic…
Computational fluid dynamics (CFD) is a cornerstone of classical scientific computing, and there is growing interest in whether quantum computers can accelerate such simulations. To date, the existing proposals for fault-tolerant quantum…
We introduce a numerical method for the solution of the time-dependent Schrodinger equation with a smooth potential, based on its reformulation as a Volterra integral equation. We present versions of the method both for periodic boundary…
This article presents a new high-order accurate algorithm for finding a particular solution to a linear, constant-coefficient partial differential equation (PDE) by means of a convolution of the volumetric source function with the Green's…
Recent breakthroughs have opened the possibility to intermediate-scale quantum computing with tens to hundreds of qubits, and shown the potential for solving classical challenging problems, such as in chemistry and condensed matter physics.…
We propose and apply the finite-element discrete variable representation to express the nonequilibrium Green's function for strongly inhomogeneous quantum systems. This method is highly favorable against a general basis approach with regard…