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Diabatic errors in Majorana braiding with bosonic bath

TitleDiabatic errors in Majorana braiding with bosonic bath
Publication TypeJournal Article
Year of Publication2019
AuthorsA. Nag, and J. D. Sau
JournalPhys. Rev. B
Date PublishedJUL 12
Type of ArticleArticle

Majorana mode based topological qubits are potentially subject to diabatic errors that in principle can limit the utility of topological quantum computation. Using a combination of analytical and numerical methods we study the diabatic errors in Majorana-based topological Y junction that are coupled to a Bosonic bath in the Markovian approximation. We find that in the absence of a bath, the error can be made exponentially small with increasing braiding time, only when the time variation in the Hamiltonian is completely smooth. The presence of a dominantly dissipative Markovian bath is found to eliminate this exponential scaling of error to a power-law scaling as T-1 with T being the braiding time. However, the inclusion of relaxation improves this scaling slightly to go as T-2. Thus, coupling of topological systems to Bosonic baths can lead to power law in braiding time diabatic errors that might limit the speed of topologically protected operations using Majorana modes.