Related papers: Quantum simulation of Maxwell's equations via Schr…
In this paper, we propose a quantum algorithm that combines the momentum accelerated gradient method with Schr\"odingerization [S. Jin, N. Liu and Y. Yu, Phys. Rev. Lett, 133 (2024), 230602][S. Jin, N. Liu and Y. Yu, Phys. Rev. A, 108…
A novel unified Hamiltonian approach is proposed to solve Maxwell-Schrodinger equation for modeling the interaction between classical electromagnetic (EM) fields and particles. Based on the Hamiltonian of electromagnetics and quantum…
We develop a quantum algorithm for linear algebraic equations $ A\bb{x} = \bb{b} $ from the perspective of Schr\"odingerization-form problems, which are characterized by a system of linear convection equations in one higher dimension. When…
Partial differential equation (PDE) models with multiple temporal/spatial scales are prevalent in several disciplines such as physics, engineering, and many others. These models are of great practical importance but notoriously difficult to…
In this paper, we present efficient quantum algorithms that are exponentially faster than classical algorithms for solving the quantum optimal control problem. This problem involves finding the control variable that maximizes a physical…
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…
We introduce a simple and stable computational method for ill-posed partial differential equation (PDE) problems. The method is based on Schr\"odingerization, introduced in [S. Jin, N. Liu and Y. Yu, arXiv:2212.13969][S. Jin, N. Liu and Y.…
Quantum computers are known for their potential to achieve up-to-exponential speedup compared to classical computers for certain problems. To exploit the advantages of quantum computers, we propose quantum algorithms for linear stochastic…
Recently, Jin et al. proposed a quantum simulation technique for ANY linear partial differential equations (PDEs), called Schr\"{o}dingerisation [1,2,3]. In this paper, the Schr\"{o}dingerisation technique for quantum simulation is expanded…
To simulate plasma phenomena, large-scale computational resources have been employed in developing high-precision and high-resolution plasma simulations. One of the main obstacles in plasma simulations is the requirement of computational…
We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators. To our knowledge, this is the first quantum algorithm…
This paper presents a quantum algorithm for solving the fractional Poisson equation \((-\Delta)^s u = f\) with \(s \in (0,1)\) on bounded domains. The proposed approach combines rational approximation techniques with quantum linear system…
We present a general framework for simulating quantum systems in the Heisenberg picture on quantum hardware. Based on the vectorization map, our framework fully exploits the mapping between operators and quantum states, allowing any task…
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…
The Vlasov-Maxwell system of equations, which describes classical plasma physics, is extremely challenging to solve, even by numerical simulation on powerful computers. By linearizing and assuming a Maxwellian background distribution…
Quantum computers have the potential for an exponential speedup of classical molecular computations. However, existing algorithms have limitations; quantum phase estimation (QPE) algorithms are intractable on current hardware while…
It is well known that Maxwell equations can be expressed in a unitary Schrodinger-Dirac representation for homogeneous media. However, difficulties arise when considering inhomogeneous media. A Dyson map points to a unitary field qubit…
Accurate computation of multiple eigenvalues of quantum Hamiltonians is essential in quantum chemistry, materials science, and molecular spectroscopy. Estimating excited-state energies is challenging for classical algorithms due to…
We develop a quantum algorithm for solving high-dimensional fractional Poisson equations. By applying the Caffarelli-Silvestre extension, the $d$-dimensional fractional equation is reformulated as a local partial differential equation in…
We present a quantum algorithm for simulating the wave equation under Dirichlet and Neumann boundary conditions. The algorithm uses Hamiltonian simulation and quantum linear system algorithms as subroutines. It relies on factorizations of…