  Quasiparticle poisoning errors in Majorana-based qubits are not suppressed by
the underlying topological properties, which undermines the usefulness of this
proposed platform. This work tackles the issue via quasiparticle measurement.
Error-detecting Majorana stabilizer codes are constructed whose stabilizers can
be measured by means of Wannier position operators. For a logical qubit encoded
in one of these codes, the Pauli error rates are exponentially suppressed in
the code distance, a result tied to the exponential localization of Wannier
functions. The benefit comes at the cost of a qubit loss rate that increases
linearly with the distance, but these can be readily compensated for by a
suitable outer code. The framework developed here serves as a basis for
understanding how realistic measurements, such as conductance measurements,
could be utilized for achieving fault tolerance in these systems. The work also
demonstrates that the theory of Wannier functions could lead to error
correcting codes beyond the standard stabilizer codes, uncovering another
fruitful connection between condensed matter physics and quantum information
theory.
