  The toric code is known to be equivalent to free fermions. This paper
presents explicit local unitary transformations that map the $\mathbb{Z}_2$
toric and surface code --- the open boundary equivalent of the toric code ---
to fermions. Through this construction it is shown that the surface code can be
mapped to a set of free fermion modes, while the toric code requires additional
fermionic symmetry operators. Finally, it is demonstrated how the anyonic
statistics of these codes are encoded in the fermionic representations.
