  It is shown that discrete-time quantum walks can be used to digitize, i.e.,
to time discretize fermionic models of continuous-time lattice gauge theory.
The resulting discrete-time dynamics is thus not only manifestly unitary, but
also ultralocal, i.e. the particle's speed is upper bounded, as in standard
relativistic quantum field theories. The lattice chiral symmetry of staggered
fermions, which corresponds to a translational invariance, is lost after the
requirement of ultralocality of the evolution; this fact is an instance of
Meyer's 1996 no-go lemma stating that no non-trivial one-dimensional scalar
quantum cellular automaton can be translationally invariant [1]. All results
are presented in a single-particle framework and for a (1+1)-dimensional
spacetime.
