  We point out a formal analogy between the Dirac equation in Majorana form and
the discrete-velocity version of the Boltzmann kinetic equation. By a
systematic analysis based on the theory of operator splitting, this analogy is
shown to turn into a concrete and efficient computational method, providing a
unified treatment of relativistic and non-relativistic quantum mechanics. This
might have potentially far-reaching implications for both classical and quantum
computing, because it shows that, by splitting time along the three spatial
directions, quantum information (Dirac-Majorana wavefunction) propagates in
space-time as a classical statistical process (Boltzmann distribution).
