Quantum algorithm for simulating the wave equation

Journal Article · 15 January 2019 · Physical Review A

DOI: https://doi.org/10.1103/physreva.99.012323 · OSTI ID:1612549

Costa, Pedro C. S. ^[1]; Jordan, Stephen ^[2]; Ostrander, Aaron ^[3]

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1. Brazilian Center for Research in Physics-CBPF, Rio de Janeiro (Brazil); DOE/OSTI
2. Microsoft Quantum Architectures and Computation Group, Redmond, WA (United States); Univ. of Maryland, College Park, MD (United States)
3. Univ. of Maryland, College Park, MD (United States); Joint Center for Quantum Information and Computer Science, College Park, MD (United States)

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. Furthermore, we also consider using Hamiltonian simulation for Klein-Gordon equations and Maxwell's equations.

• Research Organization: Univ. of Maryland, College Park, MD (United States)
• Sponsoring Organization: USDOE; USDOE Office of Science (SC)
• Grant/Contract Number: SC0016431
• OSTI ID: 1612549
• Journal Information: Physical Review A, Journal Name: Physical Review A Journal Issue: 1 Vol. 99; ISSN 2469-9926
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English