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

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

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

Gene Expression Is Not Random: Scaling, Long-Range Cross-Dependence, and Fractal Characteristics of Gene Regulatory Networks

Gene expression is a vital process through which cells react to the environment and express functional behavior. Understanding the dynamics of gene expression could prove crucial in unraveling the physical complexities involved in this process. Specifically, understanding the coherent complex structure of transcriptional dynamics is the goal of numerous computational studies aiming to study and finally control cellular processes. Here, we report the scaling properties of gene expression time series in Escherichia coli and Saccharomyces cerevisiae. Unlike previous studies, which report the fractal and long-range dependency of DNA structure, we investigate the individual gene expression dynamics as well as the cross-dependency between them in the context of gene regulatory network. Our results demonstrate that the gene expression time series display fractal and long-range dependence characteristics. In addition, the dynamics between genes and linked transcription factors in gene regulatory networks are also fractal and long-range cross-correlated. The cross-correlation exponents in gene regulatory networks are not unique. The distribution of the cross-correlation exponents of gene regulatory networks for several types of cells can be interpreted as a measure of the complexity of their functional behavior

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

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

Statistically characterizing robustness and fidelity of quantum controls and quantum control algorithms

Robustness of quantum operations or controls is important to build reliable quantum devices. The robustness-infidelity measure (RIM_p) is introduced to statistically quantify in a single measure the robustness and fidelity of a controller as the p-th order Wasserstein distance between the fidelity distribution of the controller under any uncertainty and an ideal fidelity distribution. The RIM_p is the p-th root of the p-th raw moment of the infidelity distribution. Using a metrization argument, we justify why RIM_1 (the average infidelity) is a good practical robustness measure. Based on the RIM_p, an algorithmic robustness-infidelity measure (ARIM) is developed to quantify the expected robustness and fidelity of controllers found by a control algorithm. The utility of the RIM and ARIM is demonstrated on energy landscape controllers of spin-1/2 networks subject to Hamiltonian uncertainty. The robustness and fidelity of individual controllers as well as the expected robustness and fidelity of controllers found by different popular quantum control algorithms are characterized. For algorithm comparisons, stochastic and non-stochastic optimization objectives are considered. Although high fidelity and robustness are often conflicting objectives, some high-fidelity, robust controllers can usually be found, irrespective of the choice of the quantum control algorithm. However, for noisy or stochastic optimization objectives, adaptive sequential decision-making approaches, such as reinforcement learning, have a cost advantage compared to standard control algorithms and, in contrast, the high infidelities obtained are more consistent with high RIM values for low noise levels

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

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

Dynamic Neural-Based Buffer Management for Queuing Systems with Self-Similar Characteristics

Buffer management in queuing systems plays an important role in addressing the tradeoff between efficiency measured in terms of overall packet loss and fairness measured in terms of individual source packet loss. Complete partitioning (CP) of a buffer with the best fairness characteristic and complete sharing (CS) of a buffer with the best efficiency characteristic are at the opposite ends of the spectrum of buffer management techniques. Dynamic partitioning buffer management techniques aim at addressing the tradeoff between efficiency and fairness. Ease of implementation is the key issue when determining the practicality of a dynamic buffer management technique. In this paper, two novel dynamic buffer management techniques for queuing systems accommodating self-similar traffic patterns are introduced. The techniques take advantage of the adaptive learning power of perceptron neural networks when applied to arriving traffic patterns of queuing systems. Relying on the water-filling approach, our proposed techniques are capable of coping with the tradeoff between packet loss and fairness issues. Computer simulations reveal that both of the proposed techniques enjoy great efficiency and fairness characteristics as well as ease of implementation