  We propose a discrete spacetime formulation of quantum electrodynamics in
one-dimension (a.k.a the Schwinger model) in terms of quantum cellular
automata, i.e. translationally invariant circuits of local quantum gates. These
have exact gauge covariance and a maximum speed of information propagation. In
this picture, the interacting quantum field theory is defined as a "convergent"
sequence of quantum cellular automata, parameterized by the spacetime lattice
spacing---encompassing the notions of continuum limit and renormalization, and
at the same time providing a quantum simulation algorithm for the dynamics.
