Related papers: A quantum algorithm for the linear Vlasov equation…
We present a new numerical scheme for solving the advection equation and its application to the Vlasov simulation. The scheme treats not only point values of a profile but also its zeroth to second order piecewise moments as dependent…
At the core of some of the most important problems in plasma physics -- from controlled nuclear fusion to the acceleration of cosmic rays -- is the challenge to describe nonlinear, multi-scale plasma dynamics. The development of reduced…
We consider the theory and application of a solution method for the inverse problem in collisionless equilibria, namely that of calculating a Vlasov-Maxwell equilibrium for a given macroscopic (fluid) equilibrium. Using Jeans' Theorem, the…
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…
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…
The Harrow-Hassidim-Lloyd (HHL) quantum algorithm for sampling from the solution of a linear system provides an exponential speed-up over its classical counterpart. The problem of solving a system of linear equations has a wide scope of…
We present a new algorithm for the discretization of the Vlasov-Maxwell system of equations for the study of plasmas in the kinetic regime. Using the discontinuous Galerkin finite element method for the spatial discretization, we obtain a…
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,…
The numerical solution of high dimensional Vlasov equation is usually performed by particle-in-cell (PIC) methods. However, due to the well-known numerical noise, it is challenging to use PIC methods to get a precise description of the…
Turbulence at kinetic scales is an unresolved and ubiquitous phenomenon that characterizes both space and laboratory plasmas. Recently, new theories, {\it in-situ} spacecraft observations and numerical simulations suggest a novel scenario…
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…
We propose a distinct approach to solving linear and nonlinear differential equations (DEs) on quantum computers by encoding the problem into ground states of effective Hamiltonian operators. Our algorithm relies on constructing such…
Harrow, Hassidim, and Lloyd showed that for a suitably specified $N \times N$ matrix $A$ and $N$-dimensional vector $\vec{b}$, there is a quantum algorithm that outputs a quantum state proportional to the solution of the linear system of…
Non-Hermitian physics has emerged as a rich field of study, with applications ranging from $PT$-symmetry breaking and skin effects to non-Hermitian topological phase transitions. Yet most studies remain restricted to small-scale or…
Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…
The aim of this work is to perform numerical simulations of the propagation of a laser in a plasma. At each time step, one has to solve a Helmholtz equation in a domain which consists in some hundreds of millions of cells. To solve this…
We derive the conductivity tensor for axisymmetric perturbations of a hot, collisionless, and charge-neutral plasma in the shearing sheet approximation. Our results generalize the well-known linear Vlasov theory for uniform plasmas to…
The accurate modeling of plasma-based accelerators relies on costly numerical simulations due to the complexity of laser-plasma and beam-plasma interactions. Several strategies can highly reduce the computational cost compared to 3D…
As industrial models and designs grow increasingly complex, the demand for optimal control of large-scale dynamical systems has significantly increased. However, traditional methods for optimal control incur significant overhead as problem…
Many claims of computational advantages have been made for quantum computing over classical, but they have not been demonstrated for practical problems. Here, we present algorithms for solving time-dependent PDEs, with particular reference…