Characterization and Control of Quantum Spin Chains and Rings

Information flow in quantum spin networks is considered. Two types of control -- temporal bang-bang switching control and control by varying spatial degrees of freedom -- are explored and shown to be effective in speeding up information transfer and increasing transfer fidelities. The control is model-based and therefore relies on accurate knowledge of the system parameters. An efficient protocol for simultaneous identification of the coupling strength and the exact number of spins in a chain is presented.Comment: to appear in ISCCSP 201

Robustness of Energy Landscape Controllers for Spin Rings under Coherent Excitation Transport

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. In this paper, we examine 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 measure of robustness, drawing on the classical control analog of the sensitivity of the tracking error. In our analysis we demonstrate 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 about T.Comment: 10 pages, 4 figures, 2 table

Quantum kinetic exciton-LO-phonon interaction in CdSe

Oscillations with a period of ∼150 fs are observed in the four-wave mixing (FWM) signal of bulk CdSe and interpreted in terms of non-Markovian exciton–LO-phonon scattering. The experiments show evidence of phonon quantum kinetics in semiconductors of strong polar coupling strength and high exciton binding energy. By comparison of the spectral and temporal response of the FWM signal in bulk CdSe and CdSe quantum dots, we demonstrate the influence of continuum states on the interference of electron-hole pair polarizations coupled via an LO phonon

Structured Singular Value Analysis for Spintronics Network Information Transfer Control

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 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 $\mu$-design tools to reveal a crossover region in the space of controllers where objectives usually thought to be conflicting are actually concordant

Sensitivity and Robustness of Quantum Spin-1/2 Rings to Parameter Uncertainty

Selective transfer of information between spin-1/2 particles arranged in a ring is achieved by optimizing the transfer fidelity over a readout time window via shaping, externally applied, static bias fields. Such static control fields have properties that clash with the expectations of classical control theory. Previous work has shown that there are cases in which the logarithmic differential sensitivity of the transfer fidelity to uncertainty in coupling strength or spillage of the bias field to adjacent spins is minimized by controllers that produce the best fidelity. Here we expand upon these examples and examine cases of both classical and non-classical behavior of logarithmic sensitivity to parameter uncertainty and robustness as measured by the p function for quantum systems. In particular we examine these properties in an 11-spin ring with a single uncertainty in coupling strength or a single bias spillage

Spin recovery in the 25nm gate length InGaAs field effect transistore

We augmented an ensemble Monte-Carlo semiconductor device simulator [3] to incorporate electron spin degrees of freedom using a Bloch equation model to investigate the feasibility of spintronic devices. Results are presented for the steady state polarization and polarization decay due to scattering and spin orbit coupling for a III-V MOSFET device as a function of gate voltages, injection polarization and strain

Robustness of Energy Landscape Control to Dephasing

As shown in previous work, in some cases closed quantum systems exhibit a non-conventional trade-off in performance and robustness in the sense that controllers with the highest fidelity can also provide the best robustness to parameter uncertainty. As the dephasing induced by the interaction of the system with the environment guides the evolution to a more classically mixed state, it is worth investigating what effect the introduction of dephasing has on the relationship between performance and robustness. In this paper we analyze the robustness of the fidelity error, as measured by the logarithmic sensitivity function, to dephasing processes. We show that introduction of dephasing as a perturbation to the nominal unitary dynamics requires a modification of the log-sensitivity formulation used to measure robustness about an uncertain parameter with non-zero nominal value used in previous work. We consider controllers optimized for a number of target objectives ranging from fidelity under coherent evolution to fidelity under dephasing dynamics to determine the extent to which optimizing for a specific regime has desirable effects in terms of robustness. Our analysis is based on two independent computations of the log-sensitivity: a statistical Monte Carlo approach and an analytic calculation. We show that despite the different log sensitivity calculations employed in this study, both demonstrate that the log-sensitivity of the fidelity error to dephasing results in a conventional trade-off between performance and robustness.Comment: 11 pages, four figures, and three table

Robust Control Performance for Open Quantum Systems

The robustness of quantum control in the presence of uncertainties is important for practical applications but their quantum nature poses many challenges for traditional robust control. In addition to uncertainties in the system and control Hamiltonians and initial state preparation, there is uncertainty about interactions with the environment leading to decoherence. This paper investigates the robust performance of control schemes for open quantum systems subject to such uncertainties. A general formalism is developed, where performance is measured based on the transmission of a dynamic perturbation or initial state preparation error to a final density operator error. This formulation makes it possible to apply tools from classical robust control, especially structured singular value analysis, to assess robust performance of controlled, open quantum systems. However, there are additional difficulties that must be overcome, especially at low frequency ($s\approx0$). For example, at $s=0$, the Bloch equations for the density operator are singular, and this causes lack of continuity of the structured singular value. We address this issue by analyzing the dynamics on invariant subspaces and defining a pseudo-inverse that enables us to formulate a specialized version of the matrix inversion lemma. The concepts are demonstrated with an example of two qubits in a leaky cavity under laser driving fields and spontaneous emission. In addition, a new performance index is introduced for this system. Instead of the tracking or transfer fidelity error, performance is measured by the steady-steady entanglement generated, which is quantified by a non-linear function of the system state called concurrence. Simulations show that there is no conflict between this performance index, its log-sensitivity and stability margin under decoherence, unlike for conventional control problems [...].Comment: 12 pages, 5 figures, 2 table

Time optimal information transfer in spintronics networks

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 rings of $\tfrac{1}{2}$-spins with uniform nearest neighbour couplings forming a ring with a single excitation in the network as simple prototype of a router for spin-based information. Specifically optimising 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 maximises the transfer probability in a short time difficult. The structure of the eigenvalues and eigenvectors must fulfill a specific condition to be able to maximise the transfer fidelity. While there are many potential structures that fulfill this condition, we choose a specific one, which in turn significantly improves the solutions found by optimal control

Information transfer in spintronics networks under worst case uncertain parameter errors

novel quantum landscape optimization with respect to bias field control inputs is developed with the goal of achieving optimal transfer fidelity subject to robustness against bias field, spin couplings and other uncertainties. This objective is achieved by minimization of a convex combination of fidelity error and worst-case perturbation of fidelity error under directional perturbation of uncertain parameters. The novelty is that the end-point perturbations of the parameters are points of a random uniform sampling of the sphere centered at the nominal values of the parameters. This reveals that the previously developed perfect state transfer with zero sensitivity solution keeps high fidelity and robustness under large rather than differential perturbations