  An important approach to the fault-tolerant quantum computation is protecting
the logical information using the quantum error correction. Usually, the
logical information is in the form of logical qubits, which are encoded in
physical qubits using quantum error correction codes. Compared with the qubit
quantum computation, the fermionic quantum computation has advantages in
quantum simulations of fermionic systems, e.g. molecules. In this paper, we
show that the fermionic quantum computation can be universal and fault-tolerant
if we encode logical Majorana fermions in physical Majorana fermions. We take a
color code as an example to demonstrate the universal set of fault-tolerant
operations on logical Majorana fermions, and we numerically find that the
fault-tolerance threshold is about 0.8%.
