A quantum computing concept for 1-D elastic wave simulation

We present a quantum computing concept for 1-D elastic wave propagation in heterogeneous media with two components: a theoretical formulation and an implementation on a real quantum computer. The method rests on a finite-difference approximation, followed by a transformation of the discrete elastic wave equation to the Schrödinger equation, which can be simulated directly on a gate-based quantum computer. An implementation on an error-free quantum simulator verifies our approach and forms the basis of numerical experiments with small problems on an actual quantum computer. As the presented approach promises exponential speedup compared to classical numerical wave propagation methods, it has the potential to significantly push the limits of global full-waveform inversion, particularly maximum feasible frequencies, on future quantum computers.