82 research outputs found
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 -design tools to reveal a crossover region in the space of controllers where objectives usually thought to be conflicting are actually concordant
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 ().
For example, at , 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
Design of Feedback Control Laws for Information Transfer in Spintronics Networks
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. \new{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. \new{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
Sample-efficient Model-based Reinforcement Learning for Quantum Control
We propose a model-based reinforcement learning (RL) approach for noisy
time-dependent gate optimization with improved sample complexity over
model-free RL. Sample complexity is the number of controller interactions with
the physical system. Leveraging an inductive bias, inspired by recent advances
in neural ordinary differential equations (ODEs), we use an auto-differentiable
ODE parametrised by a learnable Hamiltonian ansatz to represent the model
approximating the environment whose time-dependent part, including the control,
is fully known. Control alongside Hamiltonian learning of continuous
time-independent parameters is addressed through interactions with the system.
We demonstrate an order of magnitude advantage in the sample complexity of our
method over standard model-free RL in preparing some standard unitary gates
with closed and open system dynamics, in realistic numerical experiments
incorporating single shot measurements, arbitrary Hilbert space truncations and
uncertainty in Hamiltonian parameters. Also, the learned Hamiltonian can be
leveraged by existing control methods like GRAPE for further gradient-based
optimization with the controllers found by RL as initializations. Our algorithm
that we apply on nitrogen vacancy (NV) centers and transmons in this paper is
well suited for controlling partially characterised one and two qubit systems.Comment: 14+6 pages, 6+4 figures, comments welcome
Sensitivity and robustness of quantum spin-1 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 μ 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
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. 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
Robustness of energy landscape control to dephasing
As shown in previous work, in some cases closed quantum systems exhibit a non-conventional absence of trade-off between 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 nonzero 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
Applying classical control techniques to quantum systems: entanglement versus stability margin and other limitations
Development of robust quantum control has been challenging and there are numerous obstacles to applying classical robust control to quantum system including bilinearity, marginal stability, state preparation errors, nonlinear figures of merit. The requirement of marginal stability, while not satisfied for closed quantum systems, can be satisfied for open quantum systems where Lindbladian behavior leads to non-unitary evolution, and allows for nonzero classical stability margins, but it remains difficult to extract physical insight when classical robust control tools are applied to these systems. We consider a straightforward example of the entanglement between two qubits dissipatively coupled to a lossy cavity and analyze it using the classical stability margin and structured perturbations. We attempt, where possible, to extract physical insight from these analyses. Our aim is to highlight where classical robust control can assist in the analysis of quantum systems and identify areas where more work needs to be done to develop specific methods for quantum robust control
Sample-efficient model-based reinforcement learning for quantum control
We propose a model-based reinforcement learning (RL) approach for noisy time-dependent gate optimization with reduced sample complexity over model-free RL. Sample complexity is defined as the number of controller interactions with the physical system. Leveraging an inductive bias, inspired by recent advances in neural ordinary differential equations (ODEs), we use an autodifferentiable ODE, parametrized by a learnable Hamiltonian ansatz, to represent the model approximating the environment, whose time-dependent part, including the control, is fully known. Control alongside Hamiltonian learning of continuous time-independent parameters is addressed through interactions with the system. We demonstrate an order of magnitude advantage in sample complexity of our method over standard model-free RL in preparing some standard unitary gates with closed and open system dynamics, in realistic computational experiments incorporating single-shot measurements, arbitrary Hilbert space truncations, and uncertainty in Hamiltonian parameters. Also, the learned Hamiltonian can be leveraged by existing control methods like GRAPE (gradient ascent pulse engineering) for further gradient-based optimization with the controllers found by RL as initializations. Our algorithm, which we apply to nitrogen vacancy (NV) centers and transmons, is well suited for controlling partially characterized one- and two-qubit systems
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