Information Transfer Fidelity in Networks of Spins

Networks of spins, or spintronic networks, are given an Information Transfer Fidelity (ITF) derived from an upper bound on the probability of transmission of the excitation from one spin to another. It is shown that this theoretical bound can be reached asymptotically in time under certain conditions. The process of achieving maximum transfer probability is given a dynamical model, the translation on the torus, and the time to reach the maximum probability is estimated using the simultaneous Diophantine approximation computationally implemented using a variant of the Lenstra-Lenstra-Lovász (LLL) algorithm. The ITF induces a prametric on the network. For a ring with homogeneous couplings, it is shown that this prametric satisfies the triangle inequality, opening up the road to an ITF geometry, which turns out to be completely different from the geometry of the physical arrangement of the spin in the spintronic device. It is shown that transfer fidelities and transfer times can be improved by means of simple controls taking the form of strong localized magnetic fields, opening up the possibility for intelligent design of spintronic networks and dynamic routing of information encoded in such networks. The approach is much more flexible than engineering the couplings to favor some transfers