  A reformulation of Maxwell equations for an inhomogeneous, anisotropic,
passive and non-dispersive medium results in a quantum-like Dirac equation that
admits unitary time evolution. In contrast to other approaches, there is no
a-priori introduction of the Riemann-Silberstein-Weber (RSW) vector but the
Maxwell equations are considered in their standard fields, with given
constitutive relations. From the electromagnetic conservation quantities a
pseudo-Hermitian dynamics is found together with a Dyson map that recovers the
full Hermicity of the dynamics in an extended Hilbert space that describes the
physical notion of unitary evolution. As an example, a uniaxial tensor
dielectric medium is considered, with the explicit Dyson map yielding an
optimal representation in a set of generalized RSW vectors. In this newly
discovered form, a Quantum Computing (QC) implementation for simulation of
electromagnetic wave propagation in complex media can be made, with further
extension into plasmas.
