Work

Quantum algorithm for simulating the wave equation

Year: 2019

Type: article

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 polynomially improved scaling in truncation errors and improved scaling for state preparation relative to general purpose quantum algorithms for solving linear differential equations. Relative to classical algorithms for simulating the $D$-dimensional wave equation, our quantum algorithm achieves exponential space savings and achieves a speedup which is polynomial for fixed $D$ and exponential in $D$. We also consider using Hamiltonian simulation for Klein-Gordon equations and Maxwell's equations.

Source: Physical Review A

DOI: 10.1103/physreva.99.012323

Authors: Pedro C. S. Costa, Stephen Jordan, Aaron Ostrander

Institutions: Centro Brasileiro de Pesquisas Físicas, Microsoft (United States), University of Maryland, College Park, Joint Center for Quantum Information and Computer Science

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: U.S. Department of Energy, National Institute of Standards and Technology

Award: QUANTUM COMPLEXITY THEORY AND HIGH ENERGY PHYSICS