Related papers: Solving Nonlinear Partial Differential Equations v…
The variational principle serves as a fundamental framework for describing equilibrium states of physical systems via the minimization or extremization of an energy-like functional. While quantum algorithms have demonstrated promising…
We present a quantum solver for partial differential equations based on a flexible matrix product operator representation. Utilizing mid-circuit measurements and a state-dependent norm correction, this scheme overcomes the restriction of…
We construct quantum algorithms to compute the solution and/or physical observables of nonlinear ordinary differential equations (ODEs) and nonlinear Hamilton-Jacobi equations (HJE) via linear representations or exact mappings between…
Implicit methods are attractive for hybrid quantum-classical CFD solvers as the flow equations are combined into a single coupled matrix that is solved on the quantum device, leaving only the CFD discretisation and matrix assembly on the…
A very simple and accurate numerical method which is applicable to systems of differentio-integral equations with quite general boundary conditions has been devised. Although the basic idea of this method stems from the Keller Box method,…
Quantum computing promises exponential improvements in solving large systems of partial differential equations (PDE), which forms a bottleneck in high-resolution computational fluid dynamics (CFD) simulations, in, among others, aerospace…
We present a quantum algorithm that analyzes time series data simulated by a quantum differential equation solver. The proposed algorithm is a quantum version of the dynamic mode decomposition algorithm used in diverse fields such as fluid…
We present a new method to solve nonlinear Hammerstein equations with weakly singular kernels. The process to approximate the solution, followed usually, consists in adapting the discretization scheme from the linear case in order to obtain…
Numerical investigations of partial differential equations with hysteresis have largely focused on simulations, leaving numerical error analysis unexplored and relying mainly on derivative-free nonlinear solvers. This work establishes…
We propose a numerical homogenization method for scalar linear partial differential equations with rough coefficients, that integrates classical coarse-scale solvers with quantum subroutines for fine-scale corrections. Inspired by the…
We present an efficient quantum algorithm to simulate nonlinear differential equations with polynomial vector fields of arbitrary degree on quantum platforms. Models of physical systems that are governed by ordinary differential equations…
Quantum computation offers a promising alternative to classical computing methods in many areas of numerical science, with algorithms that make use of the unique way in which quantum computers store and manipulate data often achieving…
The Poisson equation has many applications across the broad areas of science and engineering. Most quantum algorithms for the Poisson solver presented so far either suffer from lack of accuracy and/or are limited to very small sizes of the…
Accurately predicting response properties of molecules such as the dynamic polarizability and hyperpolarizability using quantum mechanics has been a long-standing challenge with widespread applications in material and drug design. Classical…
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…
Quantum Support Vector Machines (QSVM) play a vital role in using quantum resources for supervised machine learning tasks, such as classification. However, current methods are strongly limited in terms of scalability on Noisy Intermediate…
Finding the solution to linear systems is at the heart of many applications in science and technology. Over the years a number of algorithms have been proposed to solve this problem on a digital quantum device, yet most of these are too…
This paper focuses on discussing Newton's method and its hybrid with machine learning for the steady state Navier-Stokes Darcy model discretized by mixed element methods. First, a Newton iterative method is introduced for solving the…
The finite element method is used to approximately solve boundary value problems for differential equations. The method discretises the parameter space and finds an approximate solution by solving a large system of linear equations. Here we…
Quantum computers have the potential to efficiently solve a system of nonlinear ordinary differential equations (ODEs), which play a crucial role in various industries and scientific fields. However, it remains unclear which system of…