  Known mappings that encode fermionic modes into a bosonic qubit system are
non-local transformations. In this paper we establish that this must
necessarily be the case, if the locality graph is complex enough (for example
for regular 2$d$ lattices). In particular we show that, in case of exact
encodings, a fully local mapping is possible if and only if the locality graph
is a tree. If instead we allow ourselves to also consider operators that only
act fermionically on a subspace of the qubit Hilbert space, then we show that
this subspace must be composed of long range entangled states, if the locality
graph contains at least two overlapping cycles. This implies, for instance,
that on 2$d$ lattices there exist states that are simple from the fermionic
point of view, while in any encoding require a circuit of depth at least
proportional to the system size to be prepared.
