HAM-Schrödingerisation: a generic framework of quantum simulation for any nonlinear PDEs

• URL: http://arxiv.org/abs/2406.15821v2
• Date: Fri, 11 Apr 2025 06:25:49 GMT
• Title: HAM-Schrödingerisation: a generic framework of quantum simulation for any nonlinear PDEs
• Authors: Shijun Liao,
• Abstract summary: Jin et al. proposed a quantum simulation technique for ANY linear partial differential equations (PDEs)<n>In this paper, Schr"odingerisation technique for quantum simulation is expanded to ANY nonlinear PDEs.<n>For simplicity, we call the procedure HAM-Schr"odingerisation quantum algorithm''
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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