  Topological quantum computation based on Majorana objects is subject to a
significant challenge because at least some of the two-qubit quantum gates rely
on the fermion (either charge or spin) parity of the qubits. This dependency
renders the quantum operations involving these gates probabilistic when
attempting to advance quantum processes within the quantum circuit model. Such
an approach leads to significant information loss whenever measurements yield
the undesired fermion parity. To resolve the problem of wasting information, we
devise topological operations that allow for the non-dissipative correction of
information from undesired fermion parity to the desired one. We will use the
sparse-dense mixed encoding process for the controlled-NOT gate as an example
to explain how corrections can be implemented without affecting the quantum
information carried by the computational qubits. This correction process can be
applied {to} either the undesired input qubits or the fermion parity-dependent
quantum gates, and it works for both Majorana-zero-mode-based and
Majorana-edge-mode-based topological quantum computation.
