Quantum computing offers new possibilities for scientific computing by enabling operations on exponentially large state spaces. In this lecture, we discuss how nonlinear partial differential equations (PDEs) can be connected to quantum algorithms through mathematical linearization frameworks. After a brief introduction to the fundamentals of quantum computation and quantum numerical linear algebra, we present Koopman and Koopman–von Neumann (KvN) formulations that embed nonlinear dynamics into linear operators. We then outline how these ideas, combined with Carleman linearization and relaxation-based methods, can lead to quantum-ready formulations of nonlinear PDE solvers.