Related papers: An HHL-Based Quantum-Classical Solver for the Inco…
Quantum computational fluid dynamics (QCFD) offers a promising alternative to classical computational fluid dynamics (CFD) by leveraging quantum algorithms for higher efficiency. This paper introduces a comprehensive QCFD method, including…
This work presents a hybrid pressure face-centred finite volume (FCFV) solver to simulate steady-state incompressible Navier-Stokes flows. The method leverages the robustness, in the incompressible limit, of the hybridisable discontinuous…
Quantum computing enables the efficient resolution of complex problems, often outperforming classical methods across various applications. In 2009, Harrow, Hassidim and Lloyd proposed an algorithm for solving linear systems of equations,…
Despite the successful enhancement to the Harrow-Hassidim-Lloyd algorithm by Childs et al., who introduced the Fourier approach leveraging linear combinations of unitary operators, our research has identified non-trivial redundancies within…
The prosperous development of both hardware and algorithms for quantum computing (QC) potentially prompts a paradigm shift in scientific computing in various fields. As an increasingly active topic in QC, the variational quantum algorithm…
After learning basic quantum computing concepts, it is desirable to reinforce the learning using an important and relatively complex algorithm through which the students can observe and appreciate how the qubits evolve and interact with…
Computational fluid dynamics (CFD) simulations of viscous fluids described by the Navier-Stokes equations are considered. Depending on the Reynolds number of the flow, the Navier-Stokes equations may exhibit a highly nonlinear behavior. The…
Accurately modeling the dynamics of high-density ratio ($\mathcal{O}(10^5)$) two-phase flows is important for many material science and manufacturing applications. This work considers numerical simulations of molten metal oscillations in…
In this paper, we explore using the Harrow-Hassidim-Lloyd (HHL) algorithm to address scientific and engineering problems through quantum computing, utilizing the NWQSim simulation package on a high-performance computing platform. Focusing…
This work presents a new approach for simulating the HHL linear systems of equations solver algorithm with tensor networks. First, a novel HHL in the qudits formalism, the generalization of qubits, is developed, and then its operations are…
The limited capabilities of current quantum hardware significantly constrain the scale of experimental demonstrations of most quantum algorithmic primitives. This makes it challenging to perform benchmarking of the current hardware using…
We propose two Hybrid High-Order (HHO) methods for the incompressible Navier-Stokes equations and investigate their robustness with respect to the Reynolds number. While both methods rely on a HHO formulation of the viscous term, the…
Solving systems of linear equations is a key subroutine in many quantum algorithms. In the last 15 years, many quantum linear solvers (QLS) have been developed, competing to achieve the best asymptotic worst-case complexity. Most QLS assume…
Efficient algorithms for solving high-dimensional partial differential equations (PDEs) has been an exceedingly difficult task for a long time, due to the curse of dimensionality. We extend the forward-backward stochastic neural networks…
The simulation of fluid flow problems, specifically incompressible flows governed by the Navier-Stokes equations (NSE), holds fundamental significance in a range of scientific and engineering applications. Traditional numerical methods…
The Vlasov-Maxwell equations provide kinetic simulations of collisionless plasmas, but numerically solving them on classical computers is often impractical. This is due to the computational resource constraints imposed by the time evolution…
We present the components of a high-order accurate Navier-Stokes solver designed to simulate high-Reynolds-number stratified flows. The proposed numerical model addresses some of the numerical and computational challenges that…
Quantum computers hold promise for solving problems intractable for classical computers, especially those with high time or space complexity. Practical quantum advantage can be said to exist for such problems when the end-to-end time for…
In this work we propose a novel Hybrid High-Order method for the incompressible Navier--Stokes equations based on a formulation of the convective term including Temam's device for stability. The proposed method has several advantageous…
This paper presents a robust, adaptive numerical scheme for simulating high density ratio and high shear multiphase flows on locally refined Cartesian grids that adapt to the evolving interfaces and track regions of high vorticity. The…