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Quantum computing has attracted considerable attention in recent yearsbecause it promises speed-ups that conventional supercomputers cannot offer, atleast for some applications. Though existing quantum computers are, in mostcases, still too small to solve significant problems, their future impact ondomain sciences is already being explored now. Within this context, we presenta quantum computing concept for 1-D elastic wave propagation in heterogeneousmedia with two components: a theoretical formulation and an implementation on areal quantum computer. The method rests on a finite-difference approximation,followed by a sparsity-preserving transformation of the discrete elastic waveequation to a Schr\"{o}dinger equation, which can be simulated directly on agate-based quantum computer. An implementation on an error-free quantumsimulator verifies our approach and forms the basis of numerical experimentswith small problems on the real quantum computer IBM Brisbane. The latterproduce simulation results that qualitatively agree with the error-free versionbut are contaminated by quantum decoherence and noise effects. Complementingthe discrete transformation to the Schr\"{o}dinger equation by a continuousversion allows the replacement of finite differences by other spatialdiscretisation schemes, such as the spectral-element method. Anticipating theemergence of error-corrected quantum chips, an analogy between our method andanalyses of coupled mass-spring systems suggests that our quantum computingapproach may lead to wave field simulations that run exponentially faster thansimulations on classical computers.

A quantum computing concept for 1-D elastic wave simulation