The semiclassically scaled time-dependent multi-particle Schrödinger equation describes,
inter alia, quantum dynamics of nuclei in a molecule. It poses the combined computational …

The Lie-Trotter formula, together with its higher-order generalizations, provides a direct
approach to decomposing the exponential of a sum of operators. Despite significant effort …

The phase diagram of strong interactions in nature at finite temperature and chemical
potential remains largely theoretically unexplored due to inadequacy of Monte-Carlo–based …

We consider simulating an n-qubit Hamiltonian with nearest-neighbor interactions evolving
for time t on a quantum computer. We show that this simulation has gate complexity (nt) 1+ o …

The accuracy of quantum dynamics simulation is usually measured by the error of the
unitary evolution operator in the operator norm, which in turn depends on certain norm of the …

Abstract Machine learning for differential equations paves the way for computationally
efficient alternatives to numerical solvers, with potentially broad impacts in science and …

In this work, the issue of favorable numerical methods for the space and time discretization
of low-dimensional nonlinear Schrödinger equations is addressed. The objective is to …

Recently, we have developed a generalized finite-difference time-domain (G-FDTD) method
for solving the time dependent linear Schrödinger equation. The G-FDTD is explicit and …

In this paper the error estimates are derived for Lie-Trotter operator splitting spectral method
for semiclassical linear fractional Schrödinger equation. We first establish a priori estimates …

The over-relaxation approach is an alternative to the Jin–Xin relaxation method in order to
apply the equilibrium source term in a more precise way. This is also a key ingredient of the …