  Quantum simulations of fermionic many-body systems crucially rely on mappings
from indistinguishable fermions to distinguishable qubits. The non-local
structure of fermionic Fock space necessitates encodings that either map local
fermionic operators to non-local qubit operators, or encode the fermionic
representation in a long-range entangled code space. In this latter case, there
is an unavoidable trade-off between two desirable properties of the encoding:
low weight representations of local fermionic operators, and a high distance
code space. Here it is argued that despite this fundamental limitation,
fermionic encodings with low-weight representations of local fermionic
operators can still exhibit error mitigating properties which can serve a
similar role to that played by high code distances. In particular when
undetectable errors correspond to "natural" fermionic noise. We illustrate this
point explicitly for two fermionic encodings: the Verstraete-Cirac encoding,
and an encoding appearing in concurrent work by Derby and Klassen. In these
encodings many, but not all, single-qubit errors can be detected. However we
show that the remaining undetectable single-qubit errors map to local,
low-weight fermionic phase noise. We argue that such noise is natural for
fermionic lattice models. This suggests that even when employing low-weight
fermionic encodings, error rates can be suppressed in a similar fashion to high
distance codes, provided one is willing to accept simulated natural fermionic
noise in their simulated fermionic system.
