Double Braiding Majoranas for Quantum Computing and Hamiltonian Engineering

We propose and analyze a family of periodic braiding protocols in systems with multiple localized Majorana modes (majoranas) for the purposes of Hamiltonian engineering. The protocols rely on double braids draids which flip the signs of both majoranas, as one is taken all the way around the other. Rapid draiding can be used to dynamically suppress some or all intermajorana couplings. Suppressing all couplings can drastically reduce residual majorana dynamics, producing a more robust computational subspace. Nontrivial topological models can be obtained by selectively applying draids to some of the overlapping (imperfect) majoranas. Remarkably, draids can be implemented without having to physically braid majoranas or performing projective measurements. For instance, we show that draids can be performed by periodically modulating the coupling between a quantum dot and a topological superconducting wire to dynamically suppress the hybridization of majoranas in the quantum wire. In current experimental setups, this could lead to suppression of this coupling by a few orders of magnitude. The robustness of this protocol can be shown to parallel the topological robustness of physically braided majoranas. We propose an architecture that implements draids between distant majorana modes within a quantum register using a setup with multiple quantum dots and also discuss measurement-based ways of implementing the same.