Recent achievements in quantum control have resulted in advanced techniques for designing controllers for applications in quantum communication, computing, and sensing. However, the susceptibility of such systems to noise and uncertainties necessitates robust controllers that perform effectively under these conditions to realize the full potential of quantum devices. The time-domain log-sensitivity and a recently introduced robustness infidelity measure (RIM) are two means to quantify controller robustness in quantum systems. The former can be found analytically, while the latter requires Monte-Carlo sampling. In this letter, the correlation between the log-sensitivity and the RIM for evaluating the robustness of single excitation transfer fidelity in spin chains and rings in the presence of dephasing is investigated. We show that the expected differential sensitivity of the error agrees with the differential sensitivity of the RIM, where the expectation is over the error probability distribution. Statistical analysis also demonstrates that the log-sensitivity and the RIM are linked via the differential sensitivity, and that the differential sensitivity and RIM are highly concordant. This unification of two means (one analytic and one via sampling) to assess controller robustness in a variety of realistic scenarios provides a first step in unifying various tools to model and assess robustness of quantum controllers.

A 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.

In this paper, we explore a new approach to optimization of cost or utility functions defined over a surface, a manifold, or its simplicial decomposition. In the era of Big Data, heterogeneous signal samples sometimes embed with less distortion in a lower dimensional space if the embedding space is a manifold rather than the traditional Euclidean space. If a utility function is defined over the data and if there is a need to identify significant events defined by extreme values of the utility function, we are faced with the problem of identifying the extreme minima/maxima points of the cost/utility function defined over the manifold or its triangulation. The fundamental idea developed here is to observe that at the extreme points the graph of the utility function has extreme curvature. Accordingly, the celebrated Ricci/Yamabe flow for uniformization of the curvature of the graph will show significant "curvature transport" in the vicinity of the extreme values, hence allowing their rapid identification, obviating the classical sorting. The novel theoretical contribution is to accelerate the process by compounding the Laplace operator.

Realizing the SETO 2030 mission of reducing solar energy costs to 3-5 c/kWh will require innovative enabling research on effective, cost-efficient integration of local PV within distribution systems. However, the intermittent and variable nature of PVs compels operators to impose conservative hosting capacity constraints. Given the extremely high variability of (intermittent and unpredictable) solar energy generation, relaxing the capacity constraints (which are currently around 15%) and achieving 100% or greater integration of renewables will require a fundamental transformation of the power grid via the utilization of exponentially larger amounts of AMI enabled fine-grained data. To address the challenges in increasing the penetration of renewable energy based DERs, this project envisions an Enhanced System Layer (ESL) at the distribution network level that is reliable, cost-effective and scalable to millions of Distributed Energy Resources (DERs)/devices. This includes developing: 1) Transformative and highly scalable machine learning based predictive analytics tools that plug into distribution system planning and provide real-time situational awareness at the distribution level for short and long-term operational planning. The tools will be built using novel data-driven energy models of millions of active nodes with AMI, 2) Adaptive stochastic analysis and optimization algorithms for real-time grid operations, 3) Dynamic Scenario Analysis using parallel Cloudenabled implementations with < 1 minute computational cycle times.

Rapid proliferation of renewables in power grids requires novel solutions to address the challenges arising due to the intermittent nature of renewable generation. Energy storage has emerged as the most promising technology to ensure reliable grid operations by providing supply demand matching services with low ramp up times. In this work, we explore the use of Mobile Energy Storage Systems (MESS) to lower the cost of operations of a grid consisting of multiple micro-grids. We develop a novel algorithm which jointly maximizes the reduction in cost achieved by assigning MESS to micro-grids while minimizing the cost of relocation of MESS between different micro-grids. Finally, we evaluate our approach using simulations on real world datasets.