HAM-Schrödingerisation: A Generic Framework of Quantum Simulation for Any Nonlinear PDEs

Abstract

Recently, Jin et al. proposed a quantum simulation technique for any linear partial differential equations (PDEs), called Schrödingerisation [1-3]. In this paper, the Schrödingerisation technique for quantum simulation is expanded to any nonlinear PDEs by combining it with the homotopy analysis method (HAM) [4-6]. The HAM can transfer a nonlinear PDE into a series of linear PDEs with guaranteeing convergence of the series. In this way, any nonlinear PDEs can be solved by quantum simulation using a 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.