  Quantum mechanics allows for a consistent formulation of particles that are
neither bosons nor fermions. These para-particles are rather indiscernible in
nature. Recently, we showed that strong coupling between a qubit and two field
modes is required to simulate even order para-Bose oscillators. Here, we show
that finite-dimensional representations of even order para-Fermi oscillators
are feasible of quantum simulation under weak coupling. This opens the door to
their potential implementation in different contemporaneous quantum
electrodynamics platforms. We emphasize the intrinsic value of para-particles
for the quantum state engineering of bichromatic field modes. In particular, we
demonstrate that binomial two field mode states result from the evolution of
para-Fermi vacuum states in the quantum simulation of these oscillators.
