A quantum computing concept for 1-D elastic wave simulation with exponential speedup.

Quantum computing has attracted considerable attention in recent years because it promises speedups that conventional supercomputers cannot offer, at least for some applications. Though existing quantum computers (QCs) are, in most cases, still too small to solve significant problems, their future impact on domain sciences is already being explored now. Within this context, 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 QC. The method rests on a finite-difference approximation, followed by a sparsity-preserving transformation of the discrete elastic wave equation to a Schrödinger equation, which can be simulated directly on a gate-based QC. An implementation on an error-free quantum simulator verifies our approach and forms the basis of numerical experiments with small problems on the real QC IBM Brisbane. The latter produce simulation results that qualitatively agree with the error-free version but are contaminated by quantum decoherence and noise effects. Complementing the discrete transformation to the Schrödinger equation by a continuous version allows the replacement of finite differences by other spatial discretization schemes, such as the spectral-element method. Anticipating the emergence of error-corrected quantum chips, we analyse the computational complexity of the best quantum simulation algorithms for future QCs. This analysis suggests that our quantum computing approach may lead to wavefield simulations that run exponentially faster than simulations on classical computers. [ABSTRACT FROM AUTHOR]