Open and closed spin chains as multiprocessor wires: optimal engineering and reachability

Abstract: We consider the perfect transfer of a state between arbitrary nodes of one-dimensional spin-1/2 chain with optimally engineered couplings. Motivated by the fact that such a system could be used as a data bus for connecting multiple quantum processors, we derive two necessary and sufficient conditions that have to be met in order to perfectly transfer a state between any two nodes and we employ them to examine both open and closed geometries. Analytical calculations and numerical optimizations are performed for both cases in order to determine the reachability of certain target states and to provide optimal values for the couplings which ensure perfect fidelity. An important finding is that even-sized closed chains allow for perfect transfer between any pair of sites and therefore are a promising platform for the implementation of data bus protocols.