  There is considerable interest in the application of quantum information
science to advance computations in plasma physics. Many of the topics in fusion
plasma physics are classical in nature. In order to implement them on quantum
computers it will require couching a classical problem in the language of
quantum mechanics. Electromagnetic waves are routinely used in fusion
experiments. The propagation of electromagnetic waves is described by Maxwell
equations with an appropriate description of the plasma as a dielectric medium.
Before advancing to the tensor dielectric of a magnetized plasma, this paper
considers wave propagation in a one-dimensional inhomogeneous scalar
dielectric.
  The classic theory of scattering of plane electromagnetic waves at a planar
interface, separating two different dielectric media, leads to Fresnel
equations for reflection and transmission coefficients. In contrast to plane
waves, this paper is on the reflection and transmission of a spatially confined
electromagnetic pulse. An analytical formulation for the scattering of a
Gaussian pulse shows that the maximum transmission coefficient is modified by
the square-root of the ratio of the two permittivities. The theory is
complemented by numerical simulations using a quantum lattice algorithm for
Maxwell equations. The algorithm, based on the Riemann-Silberstein-Weber
representation of the electromagnetic fields and expressed in term of qubits,
is an interleaved sequence of entangling operators at each lattice site and
unitary streaming operators which transmit information from one site to an
adjacent lattice site. Besides substantiating results from the theory for
Gaussian pulses, numerical simulations show their validity for non-Gaussian
pulses.
