  Exterior calculus with its three operations meet, join and hodge star
complement, is used for the representation of fermion-hole systems and for
fermionic analogues of logical gates. Two different schemes that implement
fermionic quantum computation, are proposed. The first scheme compares
fermionic gates with Boolean gates, and leads to novel electronic devices that
simulate fermionic gates. The second scheme usesa well known map between
fermionic and multi-qubit systems, to simulate fermionic gates within
multi-qubit systems.
