<p>Many problems in classical physics and engineering, such as turbulence, are governed by nonlinear differential equations, which typically require high-performance computing to be solved. Over the past decade, however, the growth of classical computing power has slowed because the miniaturization of chips is approaching the atomic scale. This development calls for a new computing paradigm: quantum computing is a prime candidate. In this Perspective, we offer a view on the challenges that need to be overcome in order to use quantum computing to simulate nonlinear dynamics. We discuss progress in the development of both quantum algorithms for nonlinear equations and quantum hardware. We propose synergies between quantum algorithms for nonlinear equations and quantum hardware concepts that could bear fruit in the near to mid-term future for the simulation of nonlinear systems and turbulence.</p>