Quantum Hamiltonian Simulation of Time-Domain Electromagnetic Fields

In this work, we present a quantum-computing framework for time-domain simulation of Maxwell's equations. By defining the Riemann-Silberstein vector, Maxwell's curl equations reduce to a single Schrödinger-like evolution equation. The solution requires computing the exponential of the curl (Hamiltonian). On quantum hardware, matrix exponentials correspond to sequences of unitary gates. Therefore decomposing the Hamiltonian using the Trotter-Suzuki decomposition it is possible to simulate electrodynamics. To validate the method, we simulate the propagation of transverse-magnetic (TM) waves in a two-dimensional free-space domain. Results show accurate field propagation highlighting the potential advantage of quantum computing for solving electromagnetic problems.