HAM-Schrodingerisation: 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  Schrodingerisation [1-3].  In this paper,   the Schrodingerisation 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-Schrodingerisation quantum algorithm''.   Quantum computing is a groundbreaking technique.  Hopefully, the  "HAM-Schrodingerisation quantum algorithm'' can open a door to highly efficient simulation  of complicated turbulent flows  by  means  of  quantum  computing  in future.