  A simple probabilistic cellular automaton is shown to be equivalent to a
relativistic fermionic quantum field theory with interactions. Occupation
numbers for fermions are classical bits or Ising spins. The automaton acts
deterministically on bit configurations. The genuinely probabilistic character
of quantum physics is realized by probabilistic initial conditions. In turn,
the probabilistic automaton is equivalent to the classical statistical system
of a generalized Ising model. For a description of the probabilistic
information at any given time quantum concepts as wave functions and
non-commuting operators for observables emerge naturally. Quantum mechanics can
be understood as a particular case of classical statistics. This offers
prospects to realize aspects of quantum computing in the form of probabilistic
classical computing.
