Title | Diabatic errors in Majorana braiding with bosonic bath |
Publication Type | Journal Article |
Year of Publication | 2019 |
Authors | A. Nag, and J. D. Sau |
Journal | Phys. Rev. B |
Volume | 100 |
Pagination | 014511 |
Date Published | JUL 12 |
Type of Article | Article |
ISSN | 2469-9950 |
Abstract | 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. |
DOI | 10.1103/PhysRevB.100.014511 |