Logical gates on odd Majorana codes

Majorana based hardware has gained prominence as a promising platform to encode qubits and protect them against noise. To run computations on such devices, a fully fault tolerant scheme is needed for preparation and measurement, as well as to perform gates during the computation. To perform operations on odd codes, one needs calls to a quantum reference system in order to violate parity super selection, which can be thought of as a resource. We explore the challenges of executing gates on such codes and provide techniques to simplify logical circuits on such odd codes. We also connect this to known ideas in quantum resource theory, which gives an interesting connection between quantum resource theory and quantum error correction.