Related papers: Quantum lower bounds for simulating fluid dynamics
Fault-tolerant quantum computing is a promising technology to solve linear partial differential equations that are classically demanding to integrate. It is still challenging to solve non-linear equations in fluid dynamics, such as the…
A computational fluid dynamics (CFD) simulation framework for fluid-flow prediction is developed on the Tensor Processing Unit (TPU) platform. The TPU architecture is featured with accelerated dense matrix multiplication, large high…
Algorithms are described for efficiently simulating quantum mechanical systems on quantum computers. A class of algorithms for simulating the Schrodinger equation for interacting many-body systems are presented in some detail. These…
Quantum computing has the potential to revolutionize multiple fields by solving complex problems that can not be solved in reasonable time with current classical computers. Nevertheless, the development of quantum computers is still in its…
The paper extends a stabilized fictitious domain finite element method initially developed for the Stokes problem to the incompressible Navier-Stokes equations coupled with a moving solid. This method presents the advantage to predict an…
A new model for Korteweg and de-Vries equation (KdV) is derived. The system under study is an open channel consisting of two concentric cylinders, rotating about their vertical axis, which is tilted by slope {\tau} from the inertial…
Fast and stable fluid simulations are an essential prerequisite for applications ranging from computer-generated imagery to computer-aided design in research and development. However, solving the partial differential equations of…
Fluid flow simulations marshal our most powerful computational resources. In many cases, even this is not enough. Quantum computers provide an opportunity to speed up traditional algorithms for flow simulations. We show that lattice-based…
The Vlasov-Maxwell system of equations, which describes classical plasma physics, is extremely challenging to solve, even by numerical simulation on powerful computers. By linearizing and assuming a Maxwellian background distribution…
Many current and near-future applications of quantum computing utilise parametric families of quantum circuits and variational methods to find optimal values for these parameters. Solving a quantum computational problem with such…
For more than 150 years the Navier-Stokes equations for thermodynamically quasi-equilibrium flows have been the cornerstone of modern computational fluid dynamics that underpins new fluid technologies. However, the applicable regime of the…
Several methods in nonadiabatic molecular dynamics are based on Madelung's hydrodynamic description of nuclear motion, while the electronic component is treated as a finite-dimensional quantum system. In this context, the quantum potential…
The aim of this manuscript is to study the influence of the vorticity on the existence time in fluid systems for which global smoothness and decay is known in the case of small irrotational data. We focus on two examples: the Euler-Korteweg…
Quantum Extreme Learning Machine (QELM) is an emerging hybrid quantum machine learning framework that leverages quantum system dynamics to enhance classical models. However, QELM can suffer from the exponential concentration problem, where…
An effective computer program for three dimensional relativistic hydrodynamical model has been developed. It implements a new approach to the early hot phase of relativistic heavy-ion collisions. The computer program simulates time-space…
Nonlinear differential equations model diverse phenomena but are notoriously difficult to solve. While there has been extensive previous work on efficient quantum algorithms for linear differential equations, the linearity of quantum…
Imaginary time evolution is a powerful tool for studying quantum systems. While it is possible to simulate with a classical computer, the time and memory requirements generally scale exponentially with the system size. Conversely, quantum…
We initiate the study of utilizing Quantum Langevin Dynamics (QLD) to solve optimization problems, particularly those non-convex objective functions that present substantial obstacles for traditional gradient descent algorithms.…
Simulating nonlinear classical dynamics on a quantum computer is an inherently challenging task due to the linear operator formulation of quantum mechanics. In this work, we provide a systematic approach to alleviate this difficulty by…
We consider the motion of several solids in a bounded cavity filled with a perfect incompressible fluid, in two dimensions. The solids move according to Newton's law, under the influence of the fluid's pressure, and the fluid dynamics is…