Primitive gates for fermions in lattice gauge theory: A highly efficient general method for fermions coupled to finite groups

General methods for writing down primitive quantum gates for lattice gauge theories coupled to fermions is important for ab initio quantum simulations of QCD. Currently nearly all encodings require a designer gate construction for these terms depending on the encoding and truncation of the gauge field register. We provide a rigorous, efficient, and group agnostic construction of the fermion hopping operator. We discuss fault tolerant resource costs and compare them to existing work.