  Formulating a lattice gauge theory using only physical degrees of freedom
generically leads to non-local interactions. A local Hamiltonian is desirable
for quantum simulation, and this is possible by treating the Hilbert space as a
subspace of a much larger Hilbert space in which Gauss's law is not automatic.
Digital quantum simulations of this local formulation will wander into
unphysical sectors due to errors from Trotterization or from quantum noise. In
this work, oracles are constructed that use local Gauss law constraints to
projectively distinguish physical and unphysical wave functions in Abelian
lattice gauge theories. Such oracles can be used to detect errors that break
Gauss's law.
