A general frame of quantum simulation for nonlinear partial differential equations

• URL: http://arxiv.org/abs/2406.15821v1
• Date: Sat, 22 Jun 2024 11:33:09 GMT
• Title: A general frame of quantum simulation for nonlinear partial differential equations
• Authors: Shijun Liao,
• Abstract summary: The Schr"odingerisation technique of quantum simulation is expanded to any a nonlinear PDE. For simplicity, we call it the HAM-Schr"odingerisation quantum algorithm''
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Currently, Jin et al. proposed a quantum simulation technique for any a linear PDE, called Schr\"{o}dingerisation [1-3], which has been successfully applied to solve many non-Hamiltonian linear PDEs. In this paper, the Schr\"{o}dingerisation technique of quantum simulation is expanded to any a nonlinear PDE by means of combining the Schr\"{o}dingerisation technique with the homotopy analysis method (HAM) [4-6] that can transfer any a nonlinear PDE into a series of linear PDEs with convergence guarantee of series solution. In this way, a nonlinear PDE can be solved by quantum simulation using a quantum computer -- yet to be developed in the future. For simplicity, we call it ``the HAM-Schr\"{o}dingerisation quantum algorithm''.

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