The Schrödingerization method, together with the autonomization technique in [13, 14], transforms general non-autonomous linear differential equations with non-unitary dynamics into time-independent Schrödinger-type systems via a warped phase transformation that lifts the problem to a higher-dimensional space. Despite their success and natural fit for continuous-variable analog simulation, Schrödingerization techniques are less direct on qubit-based hardware, as they often rely on black-box sparse-Hamiltonian simulation or block-encoding. For practical gate-based implementations, explicit quantum circuits are therefore needed. This paper explicitly constructs a quantum circuit for Maxwell’s equations with perfect electric conductor (PEC) boundary conditions and time-dependent source terms, based on Schrödingerization and autonomization, with corresponding computational complexity analysis. Through initial value smoothing and high-order approximation to the delta function, the increase in qubits from the extra dimensions only requires minor rise in computational complexity, almost \(\log \log {1/\varepsilon }\) where \(\varepsilon \) is the desired precision. Our analysis shows that, for three-dimensional electromagnetic simulations, the resulting Schrödingerization-based quantum algorithm has gate complexity \(\tilde{\mathcal {O}} \left( \varepsilon ^{-5/4}\right) \) , compared to \(\mathcal {O}\!\left( \varepsilon ^{-5/2}\right) \) for the classical finite-difference time-domain (FDTD) method. Here \(\tilde{\mathcal {O}}(\cdot )\) hides factors polylogarithmic in \(1/\varepsilon \) .
