S. G. Schirmer, E. Jonckheere, F. C. Langbein. Design of Feedback Control Laws for Information Transfer in Spintronics Networks. IEEE Trans Automatic Control, 63(8):2523-2536, 2018. [DOI:10.1109/TAC.2017.2777187] [arXiv:1607.05294] [PDF]
Optimization results for the information transfer probability from spin 1 to 3 for an XX-ring of 7 spins over spatial biases and time.
Information encoded in networks of stationary, interacting spin-1/2 particles is central for many applications ranging from quantum spintronics to quantum information processing. Without control, however, information transfer through such networks is generally inefficient. Currently available control methods to maximize the transfer fidelities and speeds mainly rely on dynamic control using time-varying fields and often assume instantaneous readout. We present an alternative approach to achieving efficient, high-fidelity transfer of excitations by shaping the energy landscape via the design of time-invariant feedback control laws without recourse to dynamic control. Both instantaneous readout and the more realistic case of finite readout windows are considered. The technique can also be used to freeze information by designing energy landscapes that achieve Anderson localization. Perfect state or super-optimal transfer and localization are enabled by conditions on the eigenstructure of the system and signature properties for the eigenvectors. Given the eigenstructure enabled by super-optimality, it is shown that feedback controllers that achieve perfect state transfer are, surprisingly, also the most robust with regard to uncertainties in the system and control parameters.
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