We build a quantum cellular automaton (QCA) which coincides with [Formula: see text] QED on its known continuum limits. It consists in a circuit of unitary gates driving the evolution of particles on a one dimensional lattice, and having them interact with the gauge field on the links. The particles are massive fermions, and the evolution is exactly U(1) gauge-invariant. We show that, in the continuous-time discrete-space limit, the QCA converges to the Kogut-Susskind staggered version of [Formula: see text] QED. We also show that, in the continuous spacetime limit and in the free one particle sector, it converges to the Dirac equation-a strong indication that the model remains accurate in the relativistic regime.
© 2022. The Author(s).