相关论文: Quantum Variational Solving of Nonlinear and Multi…

We present a parallel algorithm for solving backward stochastic differential equations (BSDEs in short) which are very useful theoretic tools to deal with many financial problems ranging from option pricing option to risk management. Our…

A focus of recent research in quantum computing has been on developing quantum algorithms for differential equations solving using variational methods on near-term quantum devices. A promising approach involves variational algorithms, which…

This paper proposes a novel non-iterative method to solve power system differential algebraic equations (DAEs) using the differential transformation, a mathematical tool that can obtain power series coefficients by transformation rules…

The main aim of this study is to introduce a 2-layered Artificial Neural Network (ANN) for solving the Black-Scholes partial differential equation (PDE) of either fractional or ordinary orders. Firstly, a discretization method is employed…

In this thesis we develop techniques to efficiently solve numerical Partial Differential Equations (PDEs) using Graphical Processing Units (GPUs). Focus is put on both performance and re--usability of the methods developed, to this end a…

In numerical approaches to solving differential equations on a lattice, a representation of the derivative operator that correctly matches the continuum behaviour of functions of momentum up to the band limit must be non-local. We present…

Whether integrable, partially integrable or nonintegrable, nonlinear partial differential equations (PDEs) can be handled from scratch with essentially the same toolbox, when one looks for analytic solutions in closed form. The basic tool…

We consider a least-squares variational kernel-based method for numerical solution of second order elliptic partial differential equations on a multi-dimensional domain. In this setting it is not assumed that the differential operator is…

This paper is concerned with the problem of counting solutions of stationary nonlinear Partial Differential Equations (PDEs) when the PDE is known to admit more than one solution. We suggest tackling the problem via a sampling-based…

This paper presents a numerical method based on the variational quantum algorithm to solve potential and Stokes flow problems. In this method, the governing equations for potential and Stokes flows can be respectively written in the form of…

In the present paper, we precisely conduct a q-calculus method for the numerical solutions of PDEs. A nonlinear Schrodinger equation is considered. Instead of the classical discretization methods we consider subdomains according to…

Quantum computing uses the physical principles of very small systems to develop computing platforms which can solve problems that are intractable on conventional supercomputers. There are challenges not only in building the required…

We introduce a variational quantum algorithm to solve unconstrained black box binary optimization problems, i.e., problems in which the objective function is given as black box. This is in contrast to the typical setting of quantum…

We overview a series of recent works addressing numerical simulations of partial differential equations in the presence of some elements of randomness. The specific equations manipulated are linear elliptic, and arise in the context of…

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…

Accurately solving high-dimensional partial differential equations (PDEs) remains a central challenge in computational mathematics. Traditional numerical methods, while effective in low-dimensional settings or on coarse grids, often…

We present a novel variational quantum framework for nonlinear partial differential equation (PDE) constrained optimization problems. The proposed work extends the recently introduced bi-level variational quantum PDE constrained…

For solving the Poisson equation it is usually possible to discretize it into solving the corresponding linear system $Ax=b$.Variational quantum algorithms (VQAs) for the discreted Poisson equation have been studied before. We give a VQA…

Nonlinear partial differential equations (PDEs) are used to model dynamical processes in a large number of scientific fields, ranging from finance to biology. In many applications standard local models are not sufficient to accurately…

The variational quantum eigensolver (or VQE) uses the variational principle to compute the ground state energy of a Hamiltonian, a problem that is central to quantum chemistry and condensed matter physics. Conventional computing methods are…