  We propose an efficient variation of the fermionic swap network scheme used
to efficiently simulate n-dimensional Fermi-Hubbard-model Hamiltonians encoded
using the Jordan-Wigner transform. For the two-dimensional versions, we show
that our choices minimize swap depth and number of Hamiltonian interaction
layers. The proofs, along with the choice of swap network, rely on
isoperimetric inequality results from the combinatorics literature, and are
closely related to graph bandwidth problems. The machinery has the potential to
be extended to maximize swap network efficiency for other types of lattices.
