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Understanding the quantum control landscape (QCL) is important for designing effective quantum control strategies. In this study, we analyze the QCL for a single two-level quantum system (qubit) using various control strategies. We employ Principal Component Analysis (PCA), to visualize and analyze the QCL for higher dimensional control parameters. Our results indicate that dimensionality reduction techniques such as PCA, can play an important role in understanding the complex nature of quantum control in higher dimensions. Evaluations of traditional control techniques and machine learning algorithms reveal that Genetic Algorithms (GA) outperform Stochastic Gradient Descent (SGD), while Q-learning (QL) shows great promise compared to Deep Q-Networks (DQN) and Proximal Policy Optimization (PPO). Additionally, our experiments highlight the importance of reward function design in DQN and PPO demonstrating that using immediate reward results in improved performance rather than delayed rewards for systems with short time steps. A study of solution space complexity was conducted by using Cluster Density Index (CDI) as a key metric for analyzing the density of optimal solutions in the landscape. The CDI reflects cluster quality and helps determine whether a given algorithm generates regions of high fidelity or not. Our results provide insights into effective quantum control strategies, emphasizing the significance of parameter selection and algorithm optimization.

Quantum control is a necessary tool for a variety of modern quantum technologies as it allows to optimally manipulate quantum systems for various tasks. Traps are points of local but not global optimum of the objective functional for a given quantum control problem. In a more general sense, traps are critical points of the objective functional which are hard to escape by local search algorithms. Here a review of some results of the analysis of possibility of having traps in landscapes of coherently controlled closed quantum systems is given. In one-qubit case, there are no traps. For special multilevel quantum systems, higher-order traps may appear.

Quantum systems with dynamical symmetries have conserved quantities that are preserved under coherent control. Therefore, such systems cannot be completely controlled by means of only coherent control. In particular, for such systems, the maximum transition probability between some pairs of states over all coherent controls can be less than one. However, incoherent control can break this dynamical symmetry and increase the maximum attainable transition probability. The simplest example of such a situation occurs in a three-level quantum system with dynamical symmetry, for which the maximum probability of transition between the ground and intermediate states using only coherent control is 1/2, whereas it is about 0.687 using coherent control assisted by incoherent control implemented through the non-selective measurement of the ground state, as was previously analytically computed. In this work, we study and completely characterize all critical points of the kinematic quantum control landscape for this measurement-assisted transition probability, which is considered as a function of the kinematic control parameters (Euler angles). The measurement-driven control used in this work is different from both quantum feedback and Zeno-type control. We show that all critical points are global maxima, global minima, saddle points or second-order traps. For comparison, we study the transition probability between the ground and highest excited states, as well as the case when both these transition probabilities are assisted by incoherent control implemented through the measurement of the intermediate state.

Optimally shaped femtosecond laser pulses can often be effectively identified in adaptive feedback quantum control experiments, but elucidating the underlying control mechanism can be a difficult task requiring significant additional analysis. We introduce landscape Hessian analysis (LHA) as a practical experimental tool to aid in elucidating control mechanism insights. This technique is applied to the dissociative ionization of CH2BrI using shaped fs laser pulses for optimization of the absolute yields of ionic fragments as well as their ratios for the competing processes of breaking the C-Br and C-I bonds. The experimental results suggest that these nominally complex problems can be reduced to a low-dimensional control space with insights into the control mechanisms. While the optimal yield for some fragments is dominated by a non-resonant intensity-driven process, the optimal generation of other fragments maa difficult task requiring significant additionaly be explained by a non-resonant process coupled to few level resonant dynamics. Theoretical analysis and modeling is consistent with the experimental observations.

Numerical and experimental realizations of quantum control are closely connected to the properties of the mapping from the control to the unitary propagator (Rabitz et al. in Science 303(5666):1998–2001, 2004 ). For bilinear quantum control problems, no general results are available to fully determine when this mapping is singular or not. In this paper we give sufficient conditions, in terms of elements of the evolution semigroup, for a trajectory to be non-singular. We identify two lists of “way-points” that, when reached, ensure the non-singularity of the control trajectory. It is found that under appropriate hypotheses one of those lists does not depend on the values of the coupling operator matrix.

A common goal in the sciences is optimization of an objective function by selecting control variables such that a desired outcome is achieved. This scenario can be expressed in terms of a control landscape of an objective considered as a function of the control variables. At the most basic level, it is known that the vast majority of quantum control landscapes possess no traps, whose presence would hinder reaching the objective. This paper reviews and extends the quantum control landscape assessment, presenting evidence that the same highly favourable landscape features exist in many other domains of science. The implications of this broader evidence are discussed. Specifically, control landscape examples from quantum mechanics, chemistry and evolutionary biology are presented. Despite the obvious differences, commonalities between these areas are highlighted within a unified mathematical framework. This mathematical framework is driven by the wide-ranging experimental evidence on the ease of finding optimal controls (in terms of the required algorithmic search effort beyond the laboratory set-up overhead). The full scope and implications of this observed common control behaviour pose an open question for assessment in further work. This article is part of the themed issue ‘Horizons of cybernetical physics’.

Bandtail states in disordered semiconductor materials result in losses in open-circuit voltage ( V oc ) and inhibit carrier transport in photovoltaics. For colloidal quantum dot (CQD) films that promise low-cost, large-area, air-stable photovoltaics, bandtails are determined by CQD synthetic polydispersity and inhomogeneous aggregation during the ligand-exchange process. Here we introduce a new method for the synthesis of solution-phase ligand-exchanged CQD inks that enable a flat energy landscape and an advantageously high packing density. In the solid state, these materials exhibit a sharper bandtail and reduced energy funnelling compared with the previous best CQD thin films for photovoltaics. Consequently, we demonstrate solar cells with higher V oc and more efficient charge injection into the electron acceptor, allowing the use of a closer-to-optimum bandgap to absorb more light. These enable the fabrication of CQD solar cells made via a solution-phase ligand exchange, with a certified power conversion efficiency of 11.28%. The devices are stable when stored in air, unencapsulated, for over 1,000 h. An improved ligand-exchange process allows the realization of solution-deposited films of quantum dots with reduced energetic disorder and, as a result, solar cells with improved open-circuit voltage, charge-carrier transport and stability.

Robust quantum control is crucial for realizing practical quantum technologies. Energy landscape shaping offers an alternative to conventional dynamic control, providing theoretically enhanced robustness and simplifying implementation for certain applications. This work demonstrates the feasibility of robust energy landscape control in a practical implementation with ultracold atoms. We leverage a digital mirror device (DMD) to shape optical potentials, creating complex energy landscapes. To achieve a desired objective, such as efficient quantum state transfer, we formulate a novel hybrid optimization approach that effectively handles both continuous (laser power) and discrete (DMD pixel activation) control parameters. This approach combines constrained quasi-Newton methods with surrogate models for efficient exploration of the vast parameter space. Furthermore, we introduce a framework for analyzing the robustness of the resulting control schemes against experimental uncertainties. By modeling uncertainties as structured perturbations, we systematically assess controller performance and identify robust solutions. We apply these techniques to maximize spin transfer in a chain of trapped atoms, achieving high-fidelity control while maintaining robustness. Our findings provide insights into the experimental viability of controlled spin transfer in cold atom systems. More broadly, the presented optimization and robustness analysis methods apply to a wide range of quantum control problems, offering a toolkit for designing and evaluating robust controllers in complex experimental settings.

As the prevalence of diseases caused by microbial pathogens like bacteria and viruses continues, early detection becomes paramount to curb their spread. Conventional methods for detecting waterborne pathogens, such as the Most Probable Number (MPN) technique, are often complex and time-consuming. This study presents an innovative approach, utilizing gelatin-derived Nano Carbon Quantum Dots (NCQDs) to quantify bacteria in wastewater. NCQDs were synthesized hydrothermal and characterized using FTIR and fluorescence spectroscopy. The fluorescence intensity of NCQDs, upon interaction with bacterial cells, demonstrated a direct correlation with bacterial count, confirmed by a polynomial regression model. Comparative analysis with traditional MPN methods showed a mean error of less than 5%.Consequently, this novel NCQD-based fluorescence technique offers a rapid, cost-effective alternative for water quality assessment, promising notable enhancements in pathogen detection efficiency.Further validation with additional samples is advised to substantiate these findings. The study’s novelty lies in its inventive synthesis approach, utilizing NCQDs for water quality evaluation, formulating a correlation model, and verifyingthe method’s efficacy with real wastewater samples. This study leads to an advancement in water quality assessment and pathogen detection. Graphical Abstract

Coastal wetland communities provide valuable ecosystem services such as erosion prevention, soil accretion, and essential habitat for coastal wildlife, but are some of the most vulnerable to the threats of climate change. This work investigates the combined effects of two climate stressors, elevated temperature (ambient, + 1.7 °C, + 3.4 °C, and 5.1 °C) and elevated CO 2 ( e CO 2 ), on leaf physiological traits of dominant salt marsh plant species. The research took place at the Salt Marsh Accretion Response to Temperature eXperiment (SMARTX) at the Smithsonian Environmental Research Center, which includes two plant communities: a C 3 sedge community and a C 4 grass community. Here we present data collected over five years on rates of stomatal conductance (g s ), quantum efficiency of PSII photochemistry ( F v / F m ), and rates of electron transport (ETR max ). We found that both warming and e CO 2 caused declines in all traits, but the warming effects were greater for the C 3 sedge. This species showed a strong negative stomatal response to warming in 2017 and 2018 (28% and 17% reduction, respectively in + 5.1 °C). However, in later years the negative response to warming was dampened to < 7%, indicating that S. americanus was able to partially acclimate to the warming over time. In 2022, we found that sedges growing in the combined + 5.1 °C e CO 2 plots exhibited more significant declines in g s , F v /F m , and ETR max than in either treatment individually. These results are important for predicting future trends in growth of wetland species, which serve as a large carbon sink that may help mitigate the effects of climate change.