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 - <p style="text-align: justify;">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.</p>