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Volume 18, Issue 1
HAM-Schrödingerisation: A Generic Framework of Quantum Simulation for Any Nonlinear PDEs

Shijun Liao

DOI: 10.4208/aamm.OA-2024-0242

Adv. Appl. Math. Mech., 18 (2026), pp. 1-10.

Published online: 2025-10

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  • Abstract

Recently, Jin et al. proposed a quantum simulation technique for any linear partial differential equations (PDEs), called Schrödingerisation [1-3]. In this paper, the Schrödingerisation 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-Schrödingerisation quantum algorithm”. Quantum computing is a groundbreaking technique. Hopefully, the “HAM-Schrödingerisation quantum algorithm” can open a door to highly efficient simulation of complicated turbulent flows by means of quantum computing in future.

  • Keywords

Quantum computing, homotopy analysis method, nonlinearity.

  • AMS Subject Headings

68Q09, 68Q12, 81P68, 35F20, 35G20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-18-1, author = {Liao , Shijun}, title = {HAM-Schrödingerisation: A Generic Framework of Quantum Simulation for Any Nonlinear PDEs}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2025}, volume = {18}, number = {1}, pages = {1--10}, abstract = {

Recently, Jin et al. proposed a quantum simulation technique for any linear partial differential equations (PDEs), called Schrödingerisation [1-3]. In this paper, the Schrödingerisation 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-Schrödingerisation quantum algorithm”. Quantum computing is a groundbreaking technique. Hopefully, the “HAM-Schrödingerisation quantum algorithm” can open a door to highly efficient simulation of complicated turbulent flows by means of quantum computing in future.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2024-0242}, url = {http://global-sci.org/intro/article_detail/aamm/24516.html} }
TY - JOUR T1 - HAM-Schrödingerisation: A Generic Framework of Quantum Simulation for Any Nonlinear PDEs AU - Liao , Shijun JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 1 EP - 10 PY - 2025 DA - 2025/10 SN - 18 DO - http://doi.org/10.4208/aamm.OA-2024-0242 UR - https://global-sci.org/intro/article_detail/aamm/24516.html KW - Quantum computing, homotopy analysis method, nonlinearity. AB -

Recently, Jin et al. proposed a quantum simulation technique for any linear partial differential equations (PDEs), called Schrödingerisation [1-3]. In this paper, the Schrödingerisation 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-Schrödingerisation quantum algorithm”. Quantum computing is a groundbreaking technique. Hopefully, the “HAM-Schrödingerisation quantum algorithm” can open a door to highly efficient simulation of complicated turbulent flows by means of quantum computing in future.

Liao , Shijun. (2025). HAM-Schrödingerisation: A Generic Framework of Quantum Simulation for Any Nonlinear PDEs. Advances in Applied Mathematics and Mechanics. 18 (1). 1-10. doi:10.4208/aamm.OA-2024-0242
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