  The core concept of quantum simulation is the mapping of an inaccessible
quantum system onto a controllable one by identifying analogous dynamics. We
map the Dirac equation of relativistic quantum mechanics in 3+1 dimensions onto
a multi-level superconducting Josephson circuit. Resonant drives determine the
particle mass and momentum and the quantum state represents the internal spinor
dynamics, which are cast in the language of multi-level quantum optics. The
degeneracy of the Dirac spectrum corresponds to a degeneracy of bright/dark
states within the system and particle spin and helicity are employed to
interpret the multi-level dynamics. We simulate the Schwinger mechanism of
electron-positron pair production by introducing an analogous electric field as
a doubly degenerate Landau-Zener problem. All proposed measurements can be
performed well within typical decoherence times. This work opens a new avenue
for experimental study of the Dirac equation and provides a tool for control of
complex dynamics in multi-level systems.
