Related papers: Towards Solving the Navier-Stokes Equation on Quan…
Quantum adiabatic algorithm is of vital importance in quantum computation field. It offers us an alternative approach to manipulate the system instead of quantum gate model. Recently, an interesting work arXiv:1805.10549 indicated that we…
The large deformations and break up of circular 2D liquid patches in a high Reynolds number (Re=1000) gas flow are investigated numerically. The 2D, plane flow Navier--Stokes equations are directly solved with explicit tracking of the…
We introduce quantum algorithms able to sample equilibrium water solvent molecules configurations within proteins thanks to analog quantum computing. To do so, we combine a quantum placement strategy to the 3D Reference Interaction Site…
Governing equations of motion for a viscous incompressible material surface are derived from the balance laws of continuum mechanics. The surface is treated as a time-dependent smooth orientable manifold of codimension one in an ambient…
We explore the applicability of quantum annealing to the approximation task of curve fitting. To this end, we consider a function that shall approximate a given set of data points and is written as a finite linear combination of…
Quantum computers hold the promise of solving certain problems that lie beyond the reach of conventional computers. However, establishing this capability, especially for impactful and meaningful problems, remains a central challenge. Here,…
A number of recent studies have proposed that linear representations are appropriate for solving nonlinear dynamical systems with quantum computers, which fundamentally act linearly on a wave function in a Hilbert space. Linear…
This article introduces, and reviews recent work using, a simple optimisation technique for analysing the nonlinear stability of a state in a dynamical system. The technique can be used to identify the most efficient way to disturb a system…
There have been multiple attempts to demonstrate that quantum annealing and, in particular, quantum annealing on quantum annealing machines, has the potential to outperform current classical optimization algorithms implemented on CMOS…
We lay the foundation for a benchmarking methodology for assessing current and future quantum computers. We pose and begin addressing fundamental questions about how to fairly compare computational devices at vastly different stages of…
Great progress has been made in quantum computing in recent years, providing opportunities to overcome computation resource poverty in many scientific computations like computational fluid dynamics (CFD). In this work, efforts are made to…
The one-dimensional Navier-Stokes equations are used to derive analytical expressions for the relation between pressure and volumetric flow rate in capillaries of five different converging-diverging axisymmetric geometries for Newtonian…
Quantum computing provides a powerful framework for tackling computational problems that are classically intractable. The goal of this paper is to explore the use of quantum computers for solving relevant problems in systems and control…
Tensor network algorithms can efficiently simulate complex quantum many-body systems by utilizing knowledge of their structure and entanglement. These methodologies have been adapted recently for solving the Navier-Stokes equations, which…
The theoretical investigation of non-adiabatic processes is hampered by the complexity of the coupled electron-nuclear dynamics beyond the Born-Oppenheimer approximation. Classically, the simulation of such reactions is limited by the…
In this work the existence of weak solutions for a class of non-Newtonian viscous fluid problems is analyzed. The problem is modeled by the steady case of the generalized Navier-Stokes equations, where the exponent $q$ that characterizes…
We have developed dynamic manifold solutions for the Navier-Stokes equations using an extension of differential geometry called the calculus for moving surfaces. Specifically, we have shown that the geometric solutions to the Navier-Stokes…
Unsupervised visual clustering has garnered significant attention in recent times, aiming to characterize distributions of unlabeled visual images through clustering based on a parameterized appearance approach. Alternatively, clustering…
Classical Navier-Stokes equations fail to describe some flows in both the compressible and incompressible configurations. In this article, we propose a new methodology based on transforming the fluid mass velocity vector field to obtain a…
This article explores the current state and future prospects of quantum computing in industrial environments. Firstly, it describes three main paradigms in this field of knowledge: gate-based quantum computers, quantum annealers, and tensor…