An architecture for "draiding" majoranas for quantum computing*

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 suppresses some or all inter-majorana couplings, improving putative quantum memories, and realizing topological models. 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 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 quantum register using a setup with multiple quantum dots.