  We study the error correcting properties of Majorana Surface Codes (MSC),
topological quantum codes constructed out of interacting Majorana fermions,
which can be used to store quantum information and perform quantum computation.
These quantum memories suffer from purely "fermionic" errors, such as
quasiparticle poisoning (QP), that have no analog in conventional platforms
with bosonic qubits. In physical realizations where QP dominates, we show that
errors can be corrected provided that the poisoning rate is below a threshold
of $\sim11\%$. When QP is highly suppressed and fermionic bilinear ("bosonic")
errors become dominant, we find an error threshold of $\sim16\%$, which is much
higher than the threshold for spin-based topological memories like the Surface
code or the Color code. In addition, we derive new lattice gauge theories to
account for measurement errors. These results, together with the inherent error
suppression provided by the superconducting gap in physical realizations of the
MSC, makes this a strong candidate for a robust topological quantum memory.
