Majorana qubit codes that also correct odd-weight errors

Abstract: The tetron architecture is a promising candidate for topological quantum computation. Each tetron Majorana island has four Majorana zero modes, and possible measurements are constrained to span zero or two Majoranas per tetron. Such measurements are known to be sufficient for correcting so-called "bosonic errors," which affect an even number of Majoranas per tetron. We demonstrate that such measurements are also sufficient for correcting "fermionic errors," which affect an odd number of Majoranas per tetron. In contrast, previous proposals for "fermionic error correction" on tetrons introduce more experimental challenges. We show that "fermionic codes" can be derived from traditional "bosonic codes" by inclusion of tetrons in the stabilizer group.