A general frame of quantum simulation for nonlinear partial differential equations
Abstract
Currently, Jin et al. proposed a quantum simulation technique for any a linear PDE, called Schrödingerisation [1-3], which has been successfully applied to solve many non-Hamiltonian linear PDEs. In this paper, the Schrödingerisation technique of quantum simulation is expanded to any a nonlinear PDE by means of combining the Schrödingerisation 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-Schrödingerisation quantum algorithm''.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2024
- DOI:
- 10.48550/arXiv.2406.15821
- arXiv:
- arXiv:2406.15821
- Bibcode:
- 2024arXiv240615821L
- Keywords:
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- Quantum Physics
- E-Print:
- 11 pages