Efficient Characterisation and Optimal Control of Open Quantum Systems - Mathematical Foundations and Physical Applications

Since no physical system can ever be completely isolated from its environment, the study of open quantum systems is pivotal to reliably and accurately control complex quantum systems. In practice, reliability of the control field needs to be confirmed via certification of the target evolution while accuracy requires the derivation of high-fidelity control schemes in the presence of decoherence. In the first part of this thesis an algebraic framework is presented that allows to determine the minimal requirements on the unique characterisation of arbitrary unitary gates in open quantum systems, independent on the particular physical implementation of the employed quantum device. To this end, a set of theorems is devised that can be used to assess whether a given set of input states on a quantum channel is sufficient to judge whether a desired unitary gate is realised. This allows to determine the minimal input for such a task, which proves to be, quite remarkably, independent of system size. These results allow to elucidate the fundamental limits regarding certification and tomography of open quantum systems. The combination of these insights with state-of-the-art Monte Carlo process certification techniques permits a significant improvement of the scaling when certifying arbitrary unitary gates. This improvement is not only restricted to quantum information devices where the basic information carrier is the qubit but it also extends to systems where the fundamental informational entities can be of arbitary dimensionality, the so-called qudits. The second part of this thesis concerns the impact of these findings from the point of view of Optimal Control Theory (OCT). OCT for quantum systems utilises concepts from engineering such as feedback and optimisation to engineer constructive and destructive interferences in order to steer a physical process in a desired direction. It turns out that the aforementioned mathematical findings allow to deduce novel optimisation functionals that significantly reduce not only the required memory for numerical control algorithms but also the total CPU time required to obtain a certain fidelity for the optimised process. The thesis concludes by discussing two problems of fundamental interest in quantum information processing from the point of view of optimal control - the preparation of pure states and the implementation of unitary gates in open quantum systems. For both cases specific physical examples are considered: for the former the vibrational cooling of molecules via optical pumping and for the latter a superconducting phase qudit implementation. In particular, it is illustrated how features of the environment can be exploited to reach the desired targets.

Meshing highly regular structures: The case of super carbon nanotubes of arbitrary order

Mesh generation is an important step inmany numerical methods.We present the “HierarchicalGraphMeshing” (HGM)method as a novel approach to mesh generation, based on algebraic graph theory.The HGM method can be used to systematically construct configurations exhibiting multiple hierarchies and complex symmetry characteristics. The hierarchical description of structures provided by the HGM method can be exploited to increase the efficiency of multiscale and multigrid methods. In this paper, the HGMmethod is employed for the systematic construction of super carbon nanotubes of arbitrary order, which present a pertinent example of structurally and geometrically complex, yet highly regular, structures. The HGMalgorithm is computationally efficient and exhibits good scaling characteristics. In particular, it scales linearly for super carbon nanotube structures and is working much faster than geometry-based methods employing neighborhood search algorithms. Its modular character makes it conducive to automatization. For the generation of a mesh, the information about the geometry of the structure in a given configuration is added in a way that relates geometric symmetries to structural symmetries. The intrinsically hierarchic description of the resulting mesh greatly reduces the effort of determining mesh hierarchies for multigrid and multiscale applications and helps to exploit symmetry-related methods in the mechanical analysis of complex structures.

Identifying the factors governing attitude towards the e-Agriservice among dairy farmers in Maharashtra, India

Information and communication technology (ICT) projects have a great potential to revolutionise the information delivery system by bridging the gap between farmers and extension personnel. aAQUA (Almost All Questions Answered) portal was launched by the Developmental Informatics Laboratory (DIL) at Indian Institute of Technology (IIT) Mumbai, Maharashtra, India in 2003 as an information providing system to deliver technology options and tailored information for the problems and queries raised by Indian dairy farmers. To measure the effectiveness of this service the attitudinal dimensions of the users of aAQUA e-Agriservice were investigated using a 22 item scale. A simple random sampling technique was used to select 120 dairy farmers from which data were collected and subjected to factor analysis to identify the underlying constructs in this research. From the attitude items, four components were extracted and named as the pessimistic, utility, technical and efficacy perspective, which influenced the development of varied level of attitudinal inclination towards the e-Agriservice. These components explained 64.40 per cent of variation in the attitude of the users towards the aAQUA e-Agriservice. This study provides a framework for technically efficient service provision that might help to reduce the pessimistic attitude of target population to adopt e-Agriservice in their farming system. The results should also be helpful for researchers, academics, ICT based service providers and policy makers to consider these perspectives while planning and implementing ICT projects.

Hierarchical Object Recognition Using Libraries of Parameterized Model Sub-Parts

This thesis describes the development of a model-based vision system that exploits hierarchies of both object structure and object scale. The focus of the research is to use these hierarchies to achieve robust recognition based on effective organization and indexing schemes for model libraries. The goal of the system is to recognize parameterized instances of non-rigid model objects contained in a large knowledge base despite the presence of noise and occlusion. Robustness is achieved by developing a system that can recognize viewed objects that are scaled or mirror-image instances of the known models or that contain components sub-parts with different relative scaling, rotation, or translation than in models. The approach taken in this thesis is to develop an object shape representation that incorporates a component sub-part hierarchy- to allow for efficient and correct indexing into an automatically generated model library as well as for relative parameterization among sub-parts, and a scale hierarchy- to allow for a general to specific recognition procedure. After analysis of the issues and inherent tradeoffs in the recognition process, a system is implemented using a representation based on significant contour curvature changes and a recognition engine based on geometric constraints of feature properties. Examples of the system's performance are given, followed by an analysis of the results. In conclusion, the system's benefits and limitations are presented.

Fat-Tree Routing for Transit

The Transit network provides high-speed, low-latency, fault-tolerant interconnect for high-performance, multiprocessor computers. The basic connection scheme for Transit uses bidelta style, multistage networks to support up to 256 processors. Scaling to larger machines by simply extending the bidelta network topology will result in a uniform degradation of network latency between all processors. By employing a fat-tree network structure in larger systems, the network provides locality and universality properties which can help minimize the impact of scaling on network latency. This report details the topology and construction issues associated with integrating Transit routing technology into fat-tree interconnect topologies.

Poly-Si₁₋xGex Film Growth for Ni Germanosilicided Metal Gate

Scaling down of the CMOS technology requires thinner gate dielectric to maintain high performance. However, due to the depletion of poly-Si gate, it is difficult to reduce the gate thickness further especially for sub-65 nm CMOS generation. Fully silicidation metal gate (FUSI) is one of the most promising solutions. Furthermore, FUSI metal gate reduces gate-line sheet resistance, prevents boron penetration to channels, and has good process compatibility with high-k gate dielectric. Poly-SiGe gate technology is another solution because of its enhancement of boron activation and compatibility with the conventional CMOS process. Combination of these two technologies for the formation of fully germanosilicided metal gate makes the approach very attractive. In this paper, the deposition of undoped Poly-Si₁₋xGex (0 < x < 30% ) films onto SiO₂ in a low pressure chemical vapor deposition (LPCVD) system is described. Detailed growth conditions and the characterization of the grown films are presented.

Analyzing shapes as compositions of distances

We propose to analyze shapes as “compositions” of distances in Aitchison geometry as an alternate and complementary tool to classical shape analysis, especially when size is non-informative. Shapes are typically described by the location of user-chosen landmarks. However the shape – considered as invariant under scaling, translation, mirroring and rotation – does not uniquely define the location of landmarks. A simple approach is to use distances of landmarks instead of the locations of landmarks them self. Distances are positive numbers defined up to joint scaling, a mathematical structure quite similar to compositions. The shape fixes only ratios of distances. Perturbations correspond to relative changes of the size of subshapes and of aspect ratios. The power transform increases the expression of the shape by increasing distance ratios. In analogy to the subcompositional consistency, results should not depend too much on the choice of distances, because different subsets of the pairwise distances of landmarks uniquely define the shape. Various compositional analysis tools can be applied to sets of distances directly or after minor modifications concerning the singularity of the covariance matrix and yield results with direct interpretations in terms of shape changes. The remaining problem is that not all sets of distances correspond to a valid shape. Nevertheless interpolated or predicted shapes can be backtransformated by multidimensional scaling (when all pairwise distances are used) or free geodetic adjustment (when sufficiently many distances are used)

Searching for consensus in ahp-group decision making. A bayesian perspective

This paper sets out to identify the initial positions of the different decision makers who intervene in a group decision making process with a reduced number of actors, and to establish possible consensus paths between these actors. As a methodological support, it employs one of the most widely-known multicriteria decision techniques, namely, the Analytic Hierarchy Process (AHP). Assuming that the judgements elicited by the decision makers follow the so-called multiplicative model (Crawford and Williams, 1985; Altuzarra et al., 1997; Laininen and Hämäläinen, 2003) with log-normal errors and unknown variance, a Bayesian approach is used in the estimation of the relative priorities of the alternatives being compared. These priorities, estimated by way of the median of the posterior distribution and normalised in a distributive manner (priorities add up to one), are a clear example of compositional data that will be used in the search for consensus between the actors involved in the resolution of the problem through the use of Multidimensional Scaling tools

Group preference structures in AHP–group decision making

This paper presents a procedure that allows us to determine the preference structures (PS) associated to each of the different groups of actors that can be identified in a group decision making problem with a large number of individuals. To that end, it makes use of the Analytic Hierarchy Process (AHP) (Saaty, 1980) as the technique to solve discrete multicriteria decision making problems. This technique permits the resolution of multicriteria, multienvironment and multiactor problems in which subjective aspects and uncertainty have been incorporated into the model, constructing ratio scales corresponding to the priorities relative to the elements being compared, normalised in a distributive manner (wi = 1). On the basis of the individuals’ priorities we identify different clusters for the decision makers and, for each of these, the associated preference structure using, to that end, tools analogous to those of Multidimensional Scaling. The resulting PS will be employed to extract knowledge for the subsequent negotiation processes and, should it be necessary, to determine the relative importance of the alternatives being compared using anyone of the existing procedures

Comparing methods for dimensionality reduction when data are density functions

Functional Data Analysis (FDA) deals with samples where a whole function is observed for each individual. A particular case of FDA is when the observed functions are density functions, that are also an example of infinite dimensional compositional data. In this work we compare several methods for dimensionality reduction for this particular type of data: functional principal components analysis (PCA) with or without a previous data transformation and multidimensional scaling (MDS) for diferent inter-densities distances, one of them taking into account the compositional nature of density functions. The difeerent methods are applied to both artificial and real data (households income distributions)

Dynamic graphics of parametrically linked multivariate methods used in compositional data analysis

Many multivariate methods that are apparently distinct can be linked by introducing one or more parameters in their definition. Methods that can be linked in this way are correspondence analysis, unweighted or weighted logratio analysis (the latter also known as "spectral mapping"), nonsymmetric correspondence analysis, principal component analysis (with and without logarithmic transformation of the data) and multidimensional scaling. In this presentation I will show how several of these methods, which are frequently used in compositional data analysis, may be linked through parametrizations such as power transformations, linear transformations and convex linear combinations. Since the methods of interest here all lead to visual maps of data, a "movie" can be made where where the linking parameter is allowed to vary in small steps: the results are recalculated "frame by frame" and one can see the smooth change from one method to another. Several of these "movies" will be shown, giving a deeper insight into the similarities and differences between these methods

A system to reduce the effect of CCDs saturation

Colour image segmentation based on the hue component presents some problems due to the physical process of image formation. One of that problems is colour clipping, which appear when at least one of the sensor components is saturated. We have designed a system, that works for a trained set of colours, to recover the chromatic information of those pixels on which colour has been clipped. The chromatic correction method is based on the fact that hue and saturation are invariant to the uniform scaling of the three RGB components. The proposed method has been validated by means of a specific colour image processing board that has allowed its execution in real time. We show experimental results of the application of our method

TU Graz: Course: 707.000 Web Science and Web Technology: Lecture 6: Network Evolution and Process

In this class, we will discuss the nature of network evolution and some selected network processes. We will discuss graph generation algorithms that generate networks with different interesting characteristics. Optional : The Structure and Function of Complex Networks (chapter 8), M.E.J. Newman, SIAM Review 45 167--256 (2003); Optional: Emergence of Scaling in Random Networks, A.L. Barabasi and R. Albert, Science 286, 509 (1999)

Mortalidad por trauma cardiaco penetrante en un hospital de Bogotá, Colombia : análisis de factores asociados

Objetivó: Caracterizar los pacientes con heridas cardiacas penetrantes grado II a VI, describir las características del trauma, tratamiento quirúrgico, evolución clínica e identificar los factores asociados a un desenlace. Metodología: Se diseñó un estudio de asociación en 308 pacientes que ingresaron a cirugía con diagnóstico de herida penetrante de corazón entre enero de 1999 y octubre de 2009. Se excluyeron 68 casos. La serie analizada incluyó 240 pacientes con heridas cardiacas. Se analizaron variables demográficas, clínicas, quirúrgicas y de evolución, tabulados en EXCEL® y analizados en SPSS 20®. Resultados: El promedio de edad fue 27.8 años, principalmente hombres (96%), lesiones por arma cortopunzante 93% y un 7% por proyectil arma de fuego. El estado hemodinámico al ingreso (según Ivatury) fue normal 44%; Shock profundo 34%; Agónicos 18% y 3% fatales. El 67% (n=161) presentaron taponamiento cardiaco. Los grados de lesión cardiaca según la clasificación OIS-AAST fueron: grado II 33%, grado III 13%, grado IV 29%, grado V 22% y grado VI 3%. La ventana pericárdica fue el método diagnóstico confirmatorio de lesión en 63% y las incisiones de abordaje quirúrgico fueron la esternotomía 63% y la toracotomía anterolateral 35%. La mortalidad fue 15% (n=36). Las diferencias en mortalidad entre el estado hemodinámico al inicio de cirugía, mecanismo de lesión y grado de herida, demostraron ser estadísticamente significativas (valor de p<0.001). Conclusiones: El estado hemodinámico y las heridas por arma de fuego son factores asociados a mortalidad. La ventana pericárdica subxifoidea favorece la preferencia y buenos resultados de la esternotomía como vía de abordaje quirúrgico.

Actitudes hacia la discapacidad : la influencia de variables individuales y contextuales

Este trabajo constituye una revisión de la influencia de las variables individuales y contextuales sobre las actitudes hacia la discapacidad. Para alcanzar este objetivo, se describió el concepto de discapacidad desde una perspectiva social, en donde se concibió la discapacidad como un aspecto relacional en vez de una característica individual. Por otra parte se describieron las actitudes hacia la discapacidad, los tipos y sus consecuencias, teniendo en cuenta las percepciones, creencias, emociones, información sobre discapacidad y variables sociodemográficas las cuales tienen un papel significativo en la formación y mantenimiento de las actitudes hacia la discapacidad. Adicionalmente se presentaron algunas de las estrategias de intervención que tiene como propósito mejorar las actitudes, aspecto que puede ayudar o contribuir a la aceptación de las personas con discapacidad. Finalmente, el presente trabajo muestra la necesidad de continuar el estudio de las actitudes hacia la discapacidad, y el mejorar las intervenciones basadas en los hallazgos presentados.