  Quantum Cellular Automaton (QCA) is a model for universal quantum computation
and a natural candidate for digital quantum simulation of relativistic quantum
fields. Here we introduce the first photonic platform for implementing
QCA-simulation of a free relativistic Dirac quantum field in 1+1 dimension,
through a Dirac Quantum Cellular Automaton (DQCA). Encoding the field position
degree of freedom in the Orbital Angular Momentum (OAM) of single photons, our
state-of-the-art setup experimentally realizes 8 steps of a DQCA, with the
possibility of having complete control over the input OAM state preparation and
the output measurement making use of two spatial light modulators. Therefore,
studying the distribution in the OAM space at each step, we were able to
reproduce the time evolution of the free Dirac field observing, the
Zitterbewegung, an oscillatory movement extremely difficult to see in real case
experimental scenario that is a signature of the interference of particle and
antiparticle states. The accordance between the expected and measured
Zitterbewegung oscillations certifies the simulator performances, paving the
way towards the application of photonic platforms to the simulation of more
complex relativistic effects.
