HAM-Schrödingerisation: A Generic Framework of Quantum Simulation for Any Nonlinear PDEs (Advances in Applied Mathematics and Mechanics, 2025)
Recently, Jin et al. proposed a quantum simulation technique for any linearpartial differential equations (PDEs), called Schrödingerisation [1-3]. In this paper, the Schrödingerisation technique for quantum simulation is expanded to any nonlinearPDEs by combining it with the homotopy analysis method (HAM) [4-6]. The HAM cantransfer a nonlinear PDE into a series of linear PDEs with guaranteeing convergence ofthe series. In this way, any nonlinear PDEs can be solved by quantum simulation usinga quantum computer. For simplicity, we call the procedure “HAM-Schrödingerisation quantum algorithm”. Quantum computing is a groundbreaking technique. Hopefully,the “HAM-Schrödingerisation quantum algorithm” can open a door to highly efficient simulation of complicated turbulent flows by means of quantum computing in future.