Complete description of fault-tolerant quantum gate operations for topological Majorana qubit systems

Among the list of major threats to quantum computation, decoherence poses one largest because it generates losses environment within a computational system which cannot be recovered via error correction methods. These methods require assumption that environmental interaction forces qubit state into some linear combination eigenstates. In reality, causes enter mixed where original is no longer recoverable. A promising solution this problem bases states on low lying energy excitations topological materials. The existence these protected by global parameter Hamiltonian prevents from coupling locally and decohering. paper, based nonlocal, Majorana fermions (MF), gate operations are generated swapping or braiding positions said MF. algorithmic calculation for such well known, but, opposite gates-to-braid currently underdeveloped. Additionally, may choose number different possible definitions, resultant appear different. Here, calculations two- four-MF cases recapitulated sake logical flow. This set gates serves as foundation understanding construction six-MF cases. Using these, full characterization made completely generalizing transformations between definitions. complete description desirable will hopefully serve future iterations qubits.