The landscape of quantum transitions driven by single-qubit unitary transformations with implications for entanglement

This paper considers the control landscape of quantum transitions in multi-qubit systems driven by unitary transformations with single-qubit interaction terms. The two-qubit case is fully analyzed to reveal the features of the landscape including the nature of the absolute maximum and minimum, the saddle points and the absence of traps. The results permit calculating the Schmidt state starting from an arbitrary two-qubit state following the local gradient flow. The analysis of multi-qubit systems is more challenging, but the generalized Schmidt states may also be located by following the local gradient flow. Finally, we show the relation between the generalized Schmidt states and the entanglement measure based on the Bures distance

К вопросу определения октановых и цетановых чисел расчетным методом

Установлена связь октанового числа моторных топлив с их относительной плотностью и групповым углеводородным составом, а цетанового числа - с относительной плотностью, вязкостью, температурами застывания и вспышки, содержанием серы. Анализом матриц коэффициентов корреляции выбраны аргументы уравнений регрессии. Проверка полученных уравнений дала удовлетворительные результаты

Efficient Algorithms for Optimal Control of Quantum Dynamics: The "Krotov'' Method unencumbered

Efficient algorithms for the discovery of optimal control designs for coherent control of quantum processes are of fundamental importance. One important class of algorithms are sequential update algorithms generally attributed to Krotov. Although widely and often successfully used, the associated theory is often involved and leaves many crucial questions unanswered, from the monotonicity and convergence of the algorithm to discretization effects, leading to the introduction of ad-hoc penalty terms and suboptimal update schemes detrimental to the performance of the algorithm. We present a general framework for sequential update algorithms including specific prescriptions for efficient update rules with inexpensive dynamic search length control, taking into account discretization effects and eliminating the need for ad-hoc penalty terms. The latter, while necessary to regularize the problem in the limit of infinite time resolution, i.e., the continuum limit, are shown to be undesirable and unnecessary in the practically relevant case of finite time resolution. Numerical examples show that the ideas underlying many of these results extend even beyond what can be rigorously proved.Comment: 19 pages, many figure

Detection of vancomycin resistances in enterococci within 3 1/2 Hours

Vancomycin resistant enterococci (VRE) constitute a challenging problem in health care institutions worldwide. Novel methods to rapidly identify resistances are highly required to ensure an early start of tailored therapy and to prevent further spread of the bacteria. Here, a spectroscopy-based rapid test is presented that reveals resistances of enterococci towards vancomycin within 3.5 hours. Without any specific knowledge on the strain, VRE can be recognized with high accuracy in two different enterococci species. By means of dielectrophoresis, bacteria are directly captured from dilute suspensions, making sample preparation very easy. Raman spectroscopic analysis of the trapped bacteria over a time span of two hours in absence and presence of antibiotics reveals characteristic differences in the molecular response of sensitive as well as resistant Enterococcus faecalis and Enterococcus faecium. Furthermore, the spectroscopic fingerprints provide an indication on the mechanisms of induced resistance in VRE

Capturing the essence of grounded theory: the importance of understanding commonalities and variants

This paper aims to capture the essence of grounded theory (GT) by setting out its commonalities and variants and, importantly, the implications of the latter for the implementation of the former, and for the truth claims and the contributions to knowledge that a GT study might make. Firstly, three ontological and epistemological variants of GT are outlined. Secondly, the commonalities of GT are set out as eight core elements of GT methodology that are individually necessary, but only sufficient collectively, to define a GT study. These elements are: an iterative process; theoretical sampling; theoretical sensitivity; codes, memos and concepts; constant comparison; theoretical saturation; fit, work, relevance and modifiability; and substantive theory. Thirdly, the implications of the ontological and epistemological variants of GT for, firstly, the implementation of the core common elements of the methodology and, secondly, the truth claims and contributions to knowledge that might be made, are discussed. Finally, the paper concludes by arguing that published GT studies in sport, exercise and health research have not always explicitly demonstrated a full understand of the commonalities and variants of GT, and that researchers publishing GT studies must take responsibility for doing this

“An ethnographic seduction”: how qualitative research and Agent-based models can benefit each other

We provide a general analytical framework for empirically informed agent-based simulations. This methodology provides present-day agent-based models with a sound and proper insight as to the behavior of social agents — an insight that statistical data often fall short of providing at least at a micro level and for hidden and sensitive populations. In the other direction, simulations can provide qualitative researchers in sociology, anthropology and other fields with valuable tools for: (a) testing the consistency and pushing the boundaries, of specific theoretical frameworks; (b) replicating and generalizing results; (c) providing a platform for cross-disciplinary validation of results

Quantum pattern recognition with liquid-state nuclear magnetic resonance

A novel quantum pattern recognition scheme is presented, which combines the idea of a classic Hopfield neural network with adiabatic quantum computation. Both the input and the memorized patterns are represented by means of the problem Hamiltonian. In contrast to classic neural networks, the algorithm can return a quantum superposition of multiple recognized patterns. A proof of principle for the algorithm for two qubits is provided using a liquid state NMR quantum computer.Comment: updated version, Journal-ref adde

Optimal Control for Generating Quantum Gates in Open Dissipative Systems

Optimal control methods for implementing quantum modules with least amount of relaxative loss are devised to give best approximations to unitary gates under relaxation. The potential gain by optimal control using relaxation parameters against time-optimal control is explored and exemplified in numerical and in algebraic terms: it is the method of choice to govern quantum systems within subspaces of weak relaxation whenever the drift Hamiltonian would otherwise drive the system through fast decaying modes. In a standard model system generalising decoherence-free subspaces to more realistic scenarios, openGRAPE-derived controls realise a CNOT with fidelities beyond 95% instead of at most 15% for a standard Trotter expansion. As additional benefit it requires control fields orders of magnitude lower than the bang-bang decouplings in the latter.Comment: largely expanded version, superseedes v1: 10 pages, 5 figure