Schrödingerization gives a quantum algorithm for indefinite Helmholtz systems with query complexity O(κ^2 polylog(1/ε)), reduced to O(κ polylog(1/ε)) with a simple shifted-Laplacian preconditioner.
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Quantum simulation of Helmholtz equations via Schr{\"o}dingerization
Schrödingerization gives a quantum algorithm for indefinite Helmholtz systems with query complexity O(κ^2 polylog(1/ε)), reduced to O(κ polylog(1/ε)) with a simple shifted-Laplacian preconditioner.