Related papers: Quantum Circuits for partial differential equation…
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…
We analyze the Schr\"odingerization method for quantum simulation of a general class of non-unitary dynamics with inhomogeneous source terms. The Schr\"odingerization technique, introduced in [31], transforms any linear ordinary and partial…
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 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…
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…
We construct quantum circuits for solving one-dimensional Schr\"odinger equations. Simulations of three typical examples, i.e., harmonic oscillator, square-well and Coulomb potential, show that reasonable results can be obtained with eight…
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…
We propose an explicit, oracle-free quantum framework for numerically simulating general linear partial differential equations (PDEs), extending previous work to incorporate (a) Robin boundary conditions - which include Neumann and…
Recent demonstrations of superconducting quantum computers by Google and IBM and trapped-ion computers from IonQ fueled new research in quantum algorithms, compilation into quantum circuits, and empirical algorithmics. While online access…
Classical simulations of quantum computations are vital for the future development of this emerging technology. To this end, decision diagrams have been proposed as a complementary technique which frequently allows to tackle the inherent…
In this work, we develop a highly efficient representation of functions and differential operators based on Fourier analysis. Using this representation, we create a variational hybrid quantum algorithm to solve static, Schr\"odinger-type,…
Recent breakthroughs have opened the possibility to intermediate-scale quantum computing with tens to hundreds of qubits, and shown the potential for solving classical challenging problems, such as in chemistry and condensed matter physics.…
In this paper, we present a quantum implicit-explicit (IMEX) scheme for multiscale ordinary and partial differential equations whose discretization parameters are independent of the scaling parameter $\varepsilon$. A key ingredient of our…
The Helmholtz equation is a prototypical model for time-harmonic wave propagation. Numerical solutions become increasingly challenging as the wave number $k$ grows, due to the equation's elliptic yet noncoercive character and the highly…
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…
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…
Quantum dynamics, typically expressed in the form of a time-dependent Schr\"odinger equation with a Hermitian Hamiltonian, is a natural application for quantum computing. However, when simulating quantum dynamics that involves the emission…
Solving partial differential equations for extremely large-scale systems within a feasible computation time serves in accelerating engineering developments. Quantum computing algorithms, particularly the Hamiltonian simulations, present a…
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…
Partial differential equations (PDEs) are crucial for modeling various physical phenomena such as heat transfer, fluid flow, and electromagnetic waves. In computer-aided engineering (CAE), the ability to handle fine resolutions and large…