  Quantum computing has emerged as a promising avenue for achieving significant
speedup, particularly in large-scale PDE simulations, compared to classical
computing. One of the main quantum approaches involves utilizing Hamiltonian
simulation, which is directly applicable only to Schr\"odinger-type equations.
To address this limitation, Schr\"odingerisation techniques have been
developed, employing the warped transformation to convert general linear PDEs
into Schr\"odinger-type equations. However, despite the development of
Schr\"odingerisation techniques, the explicit implementation of the
corresponding quantum circuit for solving general PDEs remains to be designed.
In this paper, we present detailed implementation of a quantum algorithm for
general PDEs using Schr\"odingerisation techniques. We provide examples of the
heat equation, and the advection equation approximated by the upwind scheme, to
demonstrate the effectiveness of our approach. Complexity analysis is also
carried out to demonstrate the quantum advantages of these algorithms in high
dimensions over their classical counterparts.
