Quantum computing is considered a promising alternative to classical computational methods and a potential building block for expanding CSE capabilities to answer important future questions using simulation technology. Although industrial applications are still primarily based on classical simulation methods, some research teams have begun to build conceptual algorithmic bridges between the capabilities of new hardware and established simulation methods. This mini-symposium brings together experts in flow simulation technology with developers of quantum algorithms for solving nonlinear fluid dynamic PDE problems. The goal is to exchange ideas and discuss the latest findings on efficient PDE solution methods based on (a) quantum and (b) quantum-inspired strategies, e.g. tensor network methods, as well as their hardware requirements.