Quantum Algorithm for Simulating the Wave Equation

TitleQuantum Algorithm for Simulating the Wave Equation
Publication TypeJournal Article
Year of Publication2019
AuthorsCosta, PCS, Jordan, SP, Ostrander, A
JournalPhys. Rev. A
Date Published03/24/2019

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 discretized Laplacian operators to allow for improved scaling in truncation errors and improved scaling for state preparation relative to general purpose linear differential equation algorithms. We also consider using Hamiltonian simulation for Klein-Gordon equations and Maxwell's equations.