Time Domain Field Simulations on Quantum Computers via Riemann-Silberstein Formulation

This work presents a novel approach for simulating electromagnetic (EM) wave propagation by leveraging quantum computing techniques. By reformulating Maxwell's equations through the Riemann-Silberstein formalism, we cast the problem into a Schrödinger-like framework, enabling the application of Hamiltonian simulation methods. In particular, we employ the Trotter-Suzuki decomposition to approximate the time evolution operator, facilitating efficient quantum simulation of EM wave generated by a Gaussian pulse propagating within a two-dimensional metallic cavity. Our results illustrate the potential of quantum algorithms to address complex electrodynamics problems, offering promising avenues for future advancements in electromagnetics engineering.