Related papers: Quantum Iterative Methods for Solving Differential…
One of the central difficulties in the quantization of the gravitational interactions is that they are described by a set of constraints. The standard strategy for dealing with the problem is the Dirac quantization procedure, which leads to…
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…
In this study, we propose the Quantum Gradient Flow Algorithm (QGFA), a novel quantum algorithm for solving symmetric positive definite (SPD) linear systems based on the variational formulation and time-evolution dynamics. Conventional…
The aim of this paper is to present a first evaluation of a dynamic partition strategy associated to the recently proposed asynchronous distributed computation scheme based on the D-iteration approach. The D-iteration is a fluid diffusion…
Numerous scientific and engineering applications require numerically solving systems of equations. Classically solving a general set of polynomial equations requires iterative solvers, while linear equations may be solved either by direct…
Linear equations play a pivotal role in many areas of science and engineering, making efficient solutions to linear systems highly desirable. The development of quantum algorithms for solving linear systems has been a significant…
A new model of nonlinear charged quantum relativistic fluids is presented. This model can be discretized into Discrete Time Quantum Walks (DTQWs), and a new hybrid (quantum-classical) algorithm for implementing these walks on NISQ devices…
We present and experimentally realize a quantum algorithm for efficiently solving the following problem: given an $N\times N$ matrix $\mathcal{M}$, an $N$-dimensional vector $\textbf{\emph{b}}$, and an initial vector $\textbf{\emph{x}}(0)$,…
Path integral-based simulation methodologies play a crucial role for the investigation of nuclear quantum effects by means of computer simulations. However, these techniques are significantly more demanding than corresponding classical…
The numerical solution of partial differential equations by discretization techniques is ubiquitous in computational physics. In this work we benchmark this approach in the quantum realm by solving the heat equation for a square plate…
Differential equations are ubiquitous in models of physical phenomena. Applications like steady-state analysis of heat flow and deflection in elastic bars often admit to a second order differential equation. In this paper, we discuss the…
We discuss the Carleman linearization approach to the quantum simulation of classical fluids based on Grad's generalized hydrodynamics and compare it to previous investigations based on lattice Boltzmann and Navier-Stokes formulations. We…
Applied problems of oil and gas recovery are studied numerically using the mathematical models of multiphase fluid flows in porous media. The basic model includes the continuity equations and the Darcy laws for each phase, as well as the…
Multiphysics systems are driven by multiple processes acting simultaneously, and their simulation leads to partitioned systems of differential equations. This paper studies the solution of partitioned systems of differential equations using…
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…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
We consider a new splitting based on the Sherman-Morrison-Woodbury formula, which is particularly effective with iterative methods for the numerical solution of large linear systems. These systems involve matrices that are perturbations of…
This work proposes a higher-order iterative framework for solving matrix equations, inspired by the structure and functionality of neural networks. A modification of the classical Jacobi iterative method is introduced to compute…
In this work, we introduce a new way to quantify information flow in quantum systems, especially for parameterized quantum circuits. We use a graph representation of the circuits and propose a new distance metric using the mutual…
In this paper we describe a quantum algorithm to solve sparse systems of nonlinear differential equations whose nonlinear terms are polynomials. The algorithm is nondeterministic and its expected resource requirements are polylogarithmic in…