We present quantum algorithms of the PML method for solving the time harmonic electromagnetic scattering problems. The algorithms are based on the Schr\”ödingerisation approach, which transforms any linear PDEs and ODEs with non-unitary dynamics into a system evolving under unitary dynamics, via a warped phase transformation that maps the equation into one higher dimension. In this paper, we extend the schr"ödingerisation method for general OED systems and obtain the nearly optimal cost. Our quantum algorithms are based on either a direct approximation of Maxwell’s equations combined with Yee’s algorithm, or a matrix representation in terms of Riemann-Silberstein vectors combined with a spectral approach. Several numerical experiments are performed to demonstrate the validity of this approach. In addition, instead of qubits, the quantum algorithms can also be formulated in the continuous variable quantum framework, which allows the quantum simulation of the PML method for Maxwell’s equations in analog quantum simulation.