  We build exactly solvable lattice Hamiltonians for fermionic
symmetry-protected topological (SPT) phases in (3+1)D classified by group
supercohomology. A central benefit of our construction is that it produces an
explicit finite-depth quantum circuit (FDQC) that prepares the ground state
from an unentangled symmetric state. The FDQC allows us to clearly demonstrate
the characteristic properties of supercohomology phases - namely, symmetry
fractionalization on fermion parity flux loops - predicted by continuum
formulations. By composing the corresponding FDQCs, we also recover the
stacking relations of supercohomology phases. Furthermore, we derive
topologically ordered gapped boundaries for the supercohomology models by
extending the protecting symmetries, analogous to the construction of
topologically ordered boundaries for bosonic SPT phases. Our approach relies
heavily on dualities that relate certain bosonic 2-group SPT phases with
supercohomology SPT phases. We develop physical motivation for the dualities in
terms of explicit lattice prescriptions for gauging a 1-form symmetry and for
condensing emergent fermions. We also comment on generalizations to
supercohomology phases in higher dimensions and to fermionic SPT phases outside
of the supercohomology framework.
