Related papers: A higher-order accurate operator splitting spectra…
A coupled quantum-classical model describing the transport of electrons confined in nanoscale semiconductor devices is considered. Using the subband decomposition approach allows to separate the transport directions from the confinement…
Semi-Lagrangian schemes with various splitting methods, and with different reconstruction/interpolation strategies have been applied to kinetic simulations. For example, the order of spatial accuracy of the algorithms proposed in {[Qiu and…
We introduce a novel spectral element method based on the ultraspherical spectral method and the hierarchical Poincar\'{e}-Steklov scheme for solving second-order linear partial differential equations on polygonal domains with unstructured…
Dissipation and irreversibility are central to most physical processes, yet they lead to non-unitary dynamics that are challenging to realise on quantum processors. High-order operator splitting is an attractive approach for simulating…
Numerical solving the Schr\"odinger equation with incommensurate potentials presents a great challenge since its solutions could be space-filling quasiperiodic structures without translational symmetry nor decay. In this paper, we propose…
We study the tomography of propagators for spin systems in the context of finite-dimensional Wigner representations, which completely characterize and visualize operators using shapes assembled from linear combinations of spherical…
Precise modeling of extended sources is a central challenge in modern optical engineering, laser physics, and computational lithography. Unlike ideal point sources or completely incoherent thermal radiation sources, real-world light sources…
This work develops simulation methods that enable the application of the variational quantum linear solver (VQLS) to simulate quantum transport in nanoscale semiconductor devices. Most previous work on VQLS applications in semiconductor…
We consider the 2D quasi-periodic scattering problem in optics, which has been modelled by a boundary value problem governed by Helmholtz equation with transparent boundary conditions. A spectral collocation method and a tensor product…
The analysis of wave-packet dynamics may be greatly simplified when viewed in phase-space. While harmonic oscillators are often used as a convenient platform to study wave-packets, arbitrary state preparation in these systems is more…
Solving partial differential equations is crucial to analysing and predicting complex, large-scale physical systems but pushes conventional high-performance computers to their limits. Application specific photonic processors are an exciting…
The explicit split-operator algorithm is often used for solving the linear and nonlinear time-dependent Schr\"{o}dinger equations. However, when applied to certain nonlinear time-dependent Schr\"{o}dinger equations, this algorithm loses…
In this paper we develop a class of Implicit-Explicit Runge-Kutta schemes for solving the multi-scale semiconductor Boltzmann equation. The relevant scale which characterizes this kind of problems is the diffusive scaling. This means that,…
In this brief report we present a feasible scheme to split quantum information in the realm of traveling waves. An oversimplified scheme is also proposed for the generation of a class of W states useful for perfect teleportation and…
By taking the Weyl equation with external electro-magnetic potentials as the simplest representative for a system of PDOs, we give a new method of treating non-commutativity of coefficients matrices. More precisely, we construct a Fourier…
The solution to the Poisson equation arising from the spectral element discretization of the incompressible Navier-Stokes equation requires robust preconditioning strategies. One such strategy is multigrid. To realize the potential of…
In this paper, we develop two energy-preserving splitting methods for solving three-dimensional stochastic Maxwell equations driven by multiplicative noise. We use operator splitting methods to decouple stochastic Maxwell equations into…
We report on a high-fidelity digital quantum simulation of Wigner localisation in a quasi-one-dimensional (quasi-1D) electron system using a 6-qubit segment of the state-of-the-art \textbf{IBM\,Heron\,2} quantum processor. By mapping the…
We present a new multi-fluid, multi-temperature plasma solver with adaptive Cartesian mesh (ACM) based on a full-Newton (non-linear, implicit) scheme for collisional low-temperature plasma. The particle transport is described using the…
While symplectic integration methods based on operator splitting are well established in many branches of science, high order methods for Hamiltonian systems that split in more than two parts have not been studied in great detail. Here, we…