A quantum computing concept for 1-D elastic wave simulation with exponential speedup
arxiv(2023)
摘要
Quantum computing has attracted considerable attention in recent years
because it promises speed-ups that conventional supercomputers cannot offer, at
least for some applications. Though existing quantum computers 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 quantum computer. 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 quantum computer. An implementation on an error-free quantum
simulator verifies our approach and forms the basis of numerical experiments
with small problems on the real quantum computer 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
discretisation schemes, such as the spectral-element method. Anticipating the
emergence of error-corrected quantum chips, an analogy between our method and
analyses of coupled mass-spring systems suggests that our quantum computing
approach may lead to wave field simulations that run exponentially faster than
simulations on classical computers.
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