Fast quantum transfer mediated by topological domain walls

In recent years, the number of proposed quantum protocols which use the protected end states of topological insulators has increased steadily. One of the challenges that most of these protocols face is the exponential scaling of their duration with transfer distance. This increases the number of errors and makes the protocols impractical for long-range transmission of information.

We propose a simple way to eliminate this exponential dependence: the use of topological domain walls as quantum amplifiers, which can exponentially enhance the effective hopping amplitude between the two end states, making the protocols much faster and more robust against all kinds of noise.

We apply this principle to the simplest topological insulator, the SSH chain, in which domain walls are induced by changing the hopping amplitude dimerization. This makes these systems as easy to build as their single-domain counterparts, and could thus be realized in the variety of platforms in which the SSH chain has been implemented, like photonic lattices, cold atom systems or, most recently, silicon-donor semiconducting quantum dots.

Finally, we also studied the previously unexplored domain walls in a flat-band topological model, the Creutz ladder, which has been recently implemented in ultracold atoms. Its domain walls can hold two topological states, one of which can be used as a quantum memory while the other transfers information through the wall. This allows for arbitrarily complex transfer operations between topological states.