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arXiv · 2505.18711

Quantum simulation of elastic wave equations via Schrödingerisation

Shi Jin·Chundan Zhang
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Abstract

In this paper we study quantum simulation algorithms on the elastic wave equations using the Schrödingerisation method. The Schrödingerisation method transforms any linear PDEs into a system of Schrödinger-type PDEs -with unitary evolution-using the warped phase transformation that maps the equations in one higher dimension. This makes them suitable for quantum simulations. We expore the application in two forms of the elastic wave equations. For the velocity-stress equation in isotropic media, we explore the symmetric matrix form under the external forcing via Schrödingerisation combined with spectral method. For problems with variable medium parameters, we apply Schrödingerisation method based on the staggered grid method to simulate velocity and stress fields, and give the complexity estimates. For the wave displacement equation, we transform it into a hyperbolic system and apply the Schrödingerisation method, which is then discretized by the spectral method and central difference scheme. Details of the quantum algorithms will be provided, along with the complexity analysis which demontrate exponential quantum advantage in space dimensin over the classical algorithms.

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Shi Jin, Chundan Zhang. 2025-05-24. Quantum simulation of elastic wave equations via Schrödingerisation. https://arxiv.org/abs/2505.18711

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