Quantum Algorithm for Solving the Advection Equation using Hamiltonian Simulation
Abstract
A quantum algorithm for solving the advection equation by embedding the discrete time-marching operator into Hamiltonian simulations is presented. One-dimensional advection can be simulated directly since the central finite difference operator for first-order derivatives is anti-Hermitian. Here, this is extended to industrially relevant, multi-dimensional flows with realistic boundary conditions and arbitrary finite difference stencils. A single copy of the initial quantum state is required and the circuit depth grows linearly with the required number of time steps, the sparsity of the time-marching operator and the inverse of the allowable error. Statevector simulations of a scalar transported in a two-dimensional channel flow and lid-driven cavity configuration are presented as a proof of concept of the proposed approach.
Cite
@article{arxiv.2312.09784,
title = {Quantum Algorithm for Solving the Advection Equation using Hamiltonian Simulation},
author = {Peter Brearley and Sylvain Laizet},
journal= {arXiv preprint arXiv:2312.09784},
year = {2024}
}