Quantum Algorithm for Simulating the Wave Equation

TL;DR

This paper introduces a quantum algorithm that efficiently simulates wave equations, including Klein-Gordon and Maxwell's equations, by leveraging Hamiltonian simulation and specialized factorizations for better accuracy and scalability.

Contribution

It develops a novel quantum algorithm that improves simulation efficiency for wave equations using Laplacian factorizations and advanced Hamiltonian simulation techniques.

Findings

Enhanced scaling in truncation errors

Improved state preparation efficiency

Applicability to Klein-Gordon and Maxwell's equations

Abstract

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.