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arXiv:1607.05294 · IEEE Transactions on Automatic Control

Design of Feedback Control Laws for Information Transfer in Spintronics Networks

Sophie G. Schirmer, Edmond A. Jonckheere, Frank C. Langbein

Published Nov 23, 2017• 24 citations

Abstract

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 superoptimal transfer and localization are enabled by conditions on the eigenstructure of the system and signature properties for the eigenvectors. Given the eigenstructure enabled by superoptimality, 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.

DOI: 10.1109/tac.2017.2777187

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Control laws for selective transfer of information encoded in excitations of a quantum network, based on shaping the energy landscape using time-invariant, spatially-varying bias fields, can be successfully designed by using numerical optimization. Such control laws, already departing from classicality by replacing closed-loop asymptotic stability with alternative notions of localization, have the intriguing property that for all practical purposes they achieve the upper bound on the fidelity, yet the (logarithmic) sensitivity of the fidelity to such structured perturbation as spin coupling errors and bias field leakages is nearly vanishing. Here, these differential sensitivity results are extended to large structured variations using μ-design tools to reveal a crossover region in the space of controllers where objectives usually thought to be conflicting are actually concordant.

Propagation of information encoded in spin degrees of freedom through networks of coupled spins enables important applications in spintronics and quantum information processing. We study control of information propagation in networks of spin-1/2 particles with uniform nearest neighbor couplings forming a ring with a single excitation in the network as simple prototype of a router for spin-based information. Specifically optimizing spatially distributed potentials, which remain constant during information transfer, simplifies the implementation of the routing scheme. However, the limited degrees of freedom makes finding a control that maximizes the transfer probability in a short time difficult. We show that the structure of the eigenvalues and eigenvectors must fulfill a specific condition to be able to maximize the transfer fidelity, and demonstrate that a specific choice among the many potential structures that fulfill this condition significantly improves the solutions found by optimal control.

This data set contains energy landscape controllers for information propagation in networks of spin-1/2 particles (qubits) with a ring topology and uniform nearest neighbor couplings of XXZ type. The controllers are optimized to maximize the fidelity of excitation transfer between nodes of ring in the single excitation subspace. The network can be regarded as simple prototype of a router for spin-based information. The dataset contains controllers for rings ranging in size from 3 to 20 spins with excitation transfer from node 1 to nodes 2, 3, ... ceil(N/2) considered. Controllers optimized for both instantaneous readout and time-windowed (finite bandwidth) readout are included.

This data set contains energy landscape controllers for information propagation in networks of spin-1/2 particles (qubits) with a ring topology and uniform nearest neighbor couplings of XXZ type. The controllers are optimized to maximize the fidelity of excitation transfer between nodes of ring in the single excitation subspace. The network can be regarded as simple prototype of a router for spin-based information. The dataset contains controllers for rings ranging in size from 3 to 20 spins with excitation transfer from node 1 to nodes 2, 3, ... ceil(N/2) considered. Controllers optimized for both instantaneous readout and time-windowed (finite bandwidth) readout are included.

Abstract The design and analysis of controllers to regulate excitation transport in quantum spin rings presents challenges in the application of classical feedback control techniques to synthesize effective control and generates results in contradiction to the expectations of classical control theory. This paper examines the robustness of controllers designed to optimize the fidelity of an excitation transfer to uncertainty in system and control parameters. We use the logarithmic sensitivity of the fidelity error as the robustness measure, drawing on the classical control analog of the sensitivity of the tracking error. Our analysis shows that quantum systems optimized for coherent transport demonstrate significantly different correlation between error and the log-sensitivity depending on whether the controller is optimized for readout at an exact time T or over a time-window T ± Δ /2.

Quantum spin networks form a generic system to describe a range of quantum devices for quantum information processing and sensing applications. Understanding how to con- trol them is essential to achieve devices with practical function- alities. Energy landscape shaping is a novel control paradigm to achieve selective transfer of excitations in a spin network with surprisingly strong robustness towards uncertainties in the Hamiltonians. Here we study the effect of decoherence, specifically generic pure dephasing, on the robustness of these controllers. Results indicate that while the effectiveness of the controllers is reduced by decoherence, certain controllers remain sufficiently effective, indicating potential to find highly effective controllers without exact knowledge of the decoherence processes.