Related papers: Spectral-based Propagation Schemes for Time-Depend…
Quantum systems governed by time-dependent Hamiltonians pose significant challenges for the accurate computation of unitary time-evolution operators, which are essential for predicting quantum state dynamics. In this work, we introduce a…
Adaptive second-order Crank-Nicolson time-stepping methods using the recent scalar auxiliary variable (SAV) approach are developed for the time-fractional Molecular Beam Epitaxial models with Caputo's derivative. Based on the piecewise…
Simulation of unsteady creeping flows in complex geometries has traditionally required the use of a time-stepping procedure, which is typically costly and unscalable. To reduce the cost and allow for computations at much larger scales, we…
Complex computer codes are often too time expensive to be directly used to perform uncertainty propagation studies, global sensitivity analysis or to solve optimization problems. A well known and widely used method to circumvent this…
The controls enacting logical operations on quantum systems are described by time-dependent Hamiltonians that often include rapid oscillations. In order to accurately capture the resulting time dynamics in numerical simulations, a very…
The dynamics of quantum systems can be approximated by the time propagation of Gaussian wave packets. Applying a time dependent variational principle, the time evolution of the parameters of the coupled Gaussian wave packets can be…
The multi-layer multi-configurational time-dependent Hartree (MCTDH) in optimized second quantization representation (oSQR) approach combines the tensor contraction scheme of the multi-layer MCTDH approach with the use of an optimized…
In the preceding paper [T. Fabcic et al., preprint] "restricted Gaussian wave packets" were introduced for the regularized Coulomb problem in the four-dimensional Kustaanheimo-Stiefel coordinates, and their exact time propagation was…
We present a new numerical scheme to solve the transfer of diffuse radiation on three-dimensional mesh grids which is efficient on processors with highly parallel architecture such as recently popular GPUs and CPUs with multi- and many-core…
The growing field of large-scale time domain astronomy requires methods for probabilistic data analysis that are computationally tractable, even with large datasets. Gaussian Processes are a popular class of models used for this purpose…
Ray tracing is a widely used deterministic method for radio propagation simulations, capable of producing physically accurate multipath components. The accuracy depends on the quality of the environment model and its electromagnetic…
A propagation method for time-dependent Schr\"odinger equations with an explicitly time-dependent Hamiltonian is developed where time ordering is achieved iteratively. The explicit time-dependence of the time-dependent Schr\"odinger…
Simulating time evolution of quantum systems is one of the most promising applications of quantum computing and also appears as a subroutine in many applications such as Green's function methods. In the current era of NISQ machines we…
Solving multiscale diffusion problems is often computationally expensive due to the spatial and temporal discretization challenges arising from high-contrast coefficients. To address this issue, a partially explicit temporal splitting…
In this paper, a compact high-order gas-kinetic scheme (GKS) with spectral resolution will be presented and used in the simulation of acoustic and shock waves. For accurate simulation, the numerical scheme is required to have excellent…
Parameterized quantum circuits are a promising technology for achieving a quantum advantage. An important application is the variational simulation of time evolution of quantum systems. To make the most of quantum hardware, variational…
Simulation and analysis of multidimensional dynamics of a quantum non-Hmeritian system is a challenging problem. Gaussian wavepacket dynamics has proven to be an intuitive semiclassical approach to approximately solving the dynamics of…
A potential approach for demonstrating quantum advantage is using quantum computers to simulate fermionic systems. Quantum algorithms for fermionic system simulation usually involve the Hamiltonian evolution and measurements. However, in…
The extent to which quantum computers can simulate physical phenomena and solve the partial differential equations (PDEs) that govern them remains a central open question. In this work, one of the most fundamental PDEs is addressed: the…
In the time-dependent simulation of pure states dealing with transport in open quantum systems, the initial state is located outside of the active region of interest. Using the superposition principle and the analytical knowledge of the…