  Presented is a quantum lattice gas algorithm to efficiently model a system of
Dirac particles interacting through an intermediary gauge field. The algorithm
uses a fixed qubit array to represent both the spacetime and the particles
contained in the spacetime. Despite being a lattice based algorithm, Lorentz
invariance is preserved down to the grid scale, with the continuum Dirac
Hamiltonian generating the local unitary evolution even at that scale: there is
nonlinear scaling between the smallest observable time and that time measured
in the quantum field theory limit, a kind of time dilation effect that emerges
on small scales but has no effect on large scales. The quantum lattice gas
algorithm correctly accounts for the anticommutative braiding of
indistinguishable fermions---it does not suffer the Fermi-sign problem. It
provides a highly convergent numerical simulation for strongly-correlated
fermions equal to a covariant path integral, presented here for the case when a
Dirac particle's Compton wavelength is large compared to the grid scale of the
qubit array.
