  Universal quantum simulations of gauge field theories are exposed to the risk
of gauge symmetry violations when it is not known how to compile the desired
operations exactly using the available gate set. In this letter, we show how
time evolution can be compiled in an Abelian gauge theory -- if only
approximately -- without compromising gauge invariance, by graphically
motivating a block-diagonalization procedure. When gauge invariant interactions
are associated with a "spatial network" in the space of discrete quantum
numbers, it is seen that cyclically shearing the spatial network converts
simultaneous updates to many quantum numbers into conditional updates of a
single quantum number: ultimately, this eliminates any need to pass through
(and acquire overlap onto) unphysical intermediate configurations. Shearing is
explicitly applied to gauge-matter and magnetic interactions of lattice QED.
The features that make shearing successful at preserving Abelian gauge symmetry
may also be found in non-Abelian theories, bringing one closer to gauge
invariant simulations of quantum chromodynamics.
