HAM-Schr\"{o}dingerisation: 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 Schr\"{o}dingerisation [1,2,3]. In this paper, the Schr\"{o}dingerisation technique for quantum simulation is expanded to ANY nonlinear PDEs by combining it with the homotopy analysis method (HAM). 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-Schr\"{o}dingerisation quantum algorithm''. Quantum computing is a groundbreaking technique. Hopefully, the ``HAM-Schr\"{o}dingerisation quantum algorithm'' can open a door to highly efficient simulation of complicated turbulent flows by means of quantum computing in future.