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Quantum algorithm for simulating the wave equation



Pedro C. Costa, Stephen P. Jordan, Aaron Ostrander


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 in state preparation relative to general purpose linear differential equation algorithms. We also consider using Hamiltonian simulation for Klein- Gordon equations and Maxwell's equations.
Quantum Information & Computation


quantum algorithm, partial differential equations


Costa, P. , Jordan, S. and Ostrander, A. (2019), Quantum algorithm for simulating the wave equation, Quantum Information & Computation, [online],, (Accessed June 12, 2024)


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Created January 14, 2019, Updated October 12, 2021