  Fermions, as a major class of quantum particles, provide platforms for
quantum information processing beyond the possibilities of spins or bosons
which have been studied more extensively. One particularly interesting model to
study, in view of recent progress in manipulating ultracold fermion gases, is
the fermionic version of measurement-based quantum computation (MBQC), which
implements full quantum computation with only single site measurements on a
proper fermionic many-body resource state. However, it is not known which
fermionic states can be used as the resource states for MBQC and how to find
them. In this paper, we generalize the framework of spin MBQC to fermions. In
particular, we provide a general formalism to construct many-body entangled
fermion resource states for MBQC based on the fermionic projected entangled
pair state representation. We give a specific fermionic state which enables
universal MBQC and demonstrate that the non-locality inherent in fermion
systems can be properly taken care of with suitable measurement schemes. Such a
framework opens up possibilities of finding MBQC resource states which can be
more readily realized in the lab.
