  Digital quantum simulation of fermionic systems is important in the context
of chemistry and physics. Simulating fermionic models on general purpose
quantum computers requires imposing a fermionic algebra on spins. The
previously studied Jordan-Wigner and Bravyi-Kitaev transformations are two
techniques for accomplishing this task. Here we re-examine an auxiliary fermion
construction which maps fermionic operators to local operators on spins. The
local simulation is performed by relaxing the requirement that the number of
spins should match the number of fermionic modes. Instead, auxiliary modes are
introduced to enable non-consecutive fermionic couplings to be simulated with
constant low-rank tensor products on spins. We connect the auxiliary fermion
construction to other topological models and give examples of the construction.
