The Dirac Quantum Automaton: a preview
  Quantum Information and the new informational paradigm are entering the domain of quantum field theory and gravity, suggesting the quantum automata framework. The quantum automaton is the minimal-assumption extension to the Planck and ultrarelativistic scales of quantum field theory. It can describe localized states and measurements, which are unmanageable by quantum field theory. The automaton theory is a very promising framework for quantum gravity, since it is quantum ab-initio, with relativistic covariance as emergent and not assumed a priori, it is free from all the problems arising from the continuum, it doesn't suffer violations of causality, and has no divergences. It is the natural scenario to accommodate the quantum holographic principle. Lorentz covariance and all other symmetries are violated in the ultrarelativistic Planckian regime, but are perfectly recovered at the Fermi-scale.   In the present report, after briefly reviewing the fundamental principles at the basis of the quantum cellular automata extension of quantum field theory, I will present a preview of recent results on the Fermi scale limit [1] and on the Dirac automaton in two space-dimensions [2]. The automaton in three dimensions is under way. 
Giacomo Mauro D'Ariano
quant-ph gr-qc hep-th