Computer Integrated Business: Theoretische und empirische Analyse der bisherigen Ansätze und zukünftigen Perspektiven

Die Arbeit stellt einen strukturellen Rahmen zur Einordnung sowohl bisheriger als auch zukünftiger organisationstheoretischer und DV-technologischer Entwicklungen zur Umsetzung eines Computer Integrated Business (CIB) bereit. Dazu analysiert sie bisherige Ansätze und zukünftige Perspektiven eines CIB mittels theoretischer und empirischer Bearbeitungsverfahren. Die Notwendigkeit zur Unternehmensintegration ergibt sich aus dem betriebswirtschaftlichen Konzept der Arbeitsteilung, über die das Phänomen der Economies of Scale erschlossen wird. Die Arbeitsteilung wurde zum Gestaltungskonzept in den Fabriken der industriellen Revolution. Komplexe Arbeitsgänge wurden in spezialisierte Teilaufgaben zerlegt und nach Möglichkeit auf maschinelle bzw. technologische Potentiale übertragen. Die Zielsetzung lag zunächst in der Automatisierung des Materialflusses, während der Informationsfluss noch lange Zeit im Hintergrund stand. Mittlerweile ermöglichen leistungsfähige DV-Systeme auch die Automatisierung des Informationsflusses und damit die DV-gestützte Integration des Unternehmens, die den Kern des CIB-Konzeptes darstellt. Das CIB-Konzept wurde Ende der achtziger Jahre am Fraunhofer-Institut für Arbeitswirtschaft und Organisation als Erweiterung des Computer Integrated Manufacturing (CIM) für Industrieunternehmen von Bullinger geprägt, jedoch in seiner Zielsetzung als Modell zur Totalintegration von Unternehmen danach nicht maßgeblich weiterentwickelt. Vielmehr wurden in der Folgezeit überwiegend Teilintegrationslösungen diskutiert, wie z. B. Konzepte zur Integration der Fertigung oder zur Unterstützung der Teamarbeit. Der Aspekt der umfassenden, unternehmensinternen Integration rückte Mitte der neunziger Jahre durch die an Popularität gewinnende Internet-Technologie an den Rand der wissenschaftlichen Diskussion. Erst nach dem Zusammenbruch der ersten Internet-Euphorie und der anschließenden wirtschaftlichen Rezession gewann das Integrationsthema am Anfang dieses Jahrzehnts mit Hinblick auf dadurch mögliche Kostenvorteile wieder an Bedeutung. Die Diskussion wurde jedoch mit starkem technologischem Fokus geführt (z. B. zum Thema Enterprise Application Integration) und Aspekte der Unternehmensorganisation wurden bestenfalls grob, jedoch nicht im Detail diskutiert. Die vorliegende Arbeit bearbeitet die CIB-Thematik umfassend sowohl aus unternehmensorganisatorischer als auch DV-technologischer Sicht und bewegt sich deshalb interdisziplinär zwischen den Wissenschaftsbereichen der Betriebswirtschaft und der Informatik. Die Untersuchung wird vor dem Hintergrund einer sozio-technologischen Unternehmensorganisation geführt, in der DV-technologische Potentiale neben humanen Potentialen zur Erreichung der Unternehmensziele eingesetzt werden. DV-technologische Potentiale übernehmen darin einerseits Integrationsaufgaben und werden andererseits aber selbst zum Integrationsziel. Die Herausforderung für die Unternehmensführung besteht in der Konfiguration des CIB und im Finden eines Gleichgewichts zwischen Arbeitsteilung und Integration auf der einen sowie humanen und technologischen Potentialen auf der anderen Seite, letztendlich aber auch in der Automatisierung der Integration. Die Automatisierung der Integration stellt mit Hinblick auf die durch Umweltveränderungen bedingte Konfigurationsanpassung ein bisher konzeptionell nur ansatzweise gelöstes Problem dar. Der technologischen Integrationsarchitektur sowie den verwendeten Methoden des Prozessdesigns und der Software-Entwicklung kommt bei der Lösung dieses Problems eine hohe Bedeutung zu. Über sie bestimmt sich die Anpassungsfähigkeit und geschwindigkeit des CIB. Es kann vermutet werden, dass eine Lösung jedoch erst erreicht wird, wenn sich die Unternehmensorganisation vom Konzept der zentralen Koordination abwendet und stattdessen an dezentralen Koordinationsmechanismen unter Verwendung ultrastabiler Anpassungsprogramme orientiert, wie sie z. B. in der Biologie bei Insektenkulturen untersucht wurden.

A computer-algebraic approach to the study of the symmetry properties of molecules and clusters

This thesis work is dedicated to use the computer-algebraic approach for dealing with the group symmetries and studying the symmetry properties of molecules and clusters. The Maple package Bethe, created to extract and manipulate the group-theoretical data and to simplify some of the symmetry applications, is introduced. First of all the advantages of using Bethe to generate the group theoretical data are demonstrated. In the current version, the data of 72 frequently applied point groups can be used, together with the data for all of the corresponding double groups. The emphasize of this work is placed to the applications of this package in physics of molecules and clusters. Apart from the analysis of the spectral activity of molecules with point-group symmetry, it is demonstrated how Bethe can be used to understand the field splitting in crystals or to construct the corresponding wave functions. Several examples are worked out to display (some of) the present features of the Bethe program. While we cannot show all the details explicitly, these examples certainly demonstrate the great potential in applying computer algebraic techniques to study the symmetry properties of molecules and clusters. A special attention is placed in this thesis work on the flexibility of the Bethe package, which makes it possible to implement another applications of symmetry. This implementation is very reasonable, because some of the most complicated steps of the possible future applications are already realized within the Bethe. For instance, the vibrational coordinates in terms of the internal displacement vectors for the Wilson's method and the same coordinates in terms of cartesian displacement vectors as well as the Clebsch-Gordan coefficients for the Jahn-Teller problem are generated in the present version of the program. For the Jahn-Teller problem, moreover, use of the computer-algebraic tool seems to be even inevitable, because this problem demands an analytical access to the adiabatic potential and, therefore, can not be realized by the numerical algorithm. However, the ability of the Bethe package is not exhausted by applications, mentioned in this thesis work. There are various directions in which the Bethe program could be developed in the future. Apart from (i) studying of the magnetic properties of materials and (ii) optical transitions, interest can be pointed out for (iii) the vibronic spectroscopy, and many others. Implementation of these applications into the package can make Bethe a much more powerful tool.

Entanglement analysis of atomic processes and quantum registers

During recent years, quantum information processing and the study of N−qubit quantum systems have attracted a lot of interest, both in theory and experiment. Apart from the promise of performing efficient quantum information protocols, such as quantum key distribution, teleportation or quantum computation, however, these investigations also revealed a great deal of difficulties which still need to be resolved in practise. Quantum information protocols rely on the application of unitary and non–unitary quantum operations that act on a given set of quantum mechanical two-state systems (qubits) to form (entangled) states, in which the information is encoded. The overall system of qubits is often referred to as a quantum register. Today the entanglement in a quantum register is known as the key resource for many protocols of quantum computation and quantum information theory. However, despite the successful demonstration of several protocols, such as teleportation or quantum key distribution, there are still many open questions of how entanglement affects the efficiency of quantum algorithms or how it can be protected against noisy environments. To facilitate the simulation of such N−qubit quantum systems and the analysis of their entanglement properties, we have developed the Feynman program. The program package provides all necessary tools in order to define and to deal with quantum registers, quantum gates and quantum operations. Using an interactive and easily extendible design within the framework of the computer algebra system Maple, the Feynman program is a powerful toolbox not only for teaching the basic and more advanced concepts of quantum information but also for studying their physical realization in the future. To this end, the Feynman program implements a selection of algebraic separability criteria for bipartite and multipartite mixed states as well as the most frequently used entanglement measures from the literature. Additionally, the program supports the work with quantum operations and their associated (Jamiolkowski) dual states. Based on the implementation of several popular decoherence models, we provide tools especially for the quantitative analysis of quantum operations. As an application of the developed tools we further present two case studies in which the entanglement of two atomic processes is investigated. In particular, we have studied the change of the electron-ion spin entanglement in atomic photoionization and the photon-photon polarization entanglement in the two-photon decay of hydrogen. The results show that both processes are, in principle, suitable for the creation and control of entanglement. Apart from process-specific parameters like initial atom polarization, it is mainly the process geometry which offers a simple and effective instrument to adjust the final state entanglement. Finally, for the case of the two-photon decay of hydrogenlike systems, we study the difference between nonlocal quantum correlations, as given by the violation of the Bell inequality and the concurrence as a true entanglement measure.

An introduction to ordinary differential equations by computer algebra-systems

We report on an elementary course in ordinary differential equations (odes) for students in engineering sciences. The course is also intended to become a self-study package for odes and is is based on several interactive computer lessons using REDUCE and MATHEMATICA . The aim of the course is not to do Computer Algebra (CA) by example or to use it for doing classroom examples. The aim ist to teach and to learn mathematics by using CA-systems.

Optimizing Robust Quantum Gates in Open Quantum Systems

We are currently at the cusp of a revolution in quantum technology that relies not just on the passive use of quantum effects, but on their active control. At the forefront of this revolution is the implementation of a quantum computer. Encoding information in quantum states as “qubits” allows to use entanglement and quantum superposition to perform calculations that are infeasible on classical computers. The fundamental challenge in the realization of quantum computers is to avoid decoherence – the loss of quantum properties – due to unwanted interaction with the environment. This thesis addresses the problem of implementing entangling two-qubit quantum gates that are robust with respect to both decoherence and classical noise. It covers three aspects: the use of efficient numerical tools for the simulation and optimal control of open and closed quantum systems, the role of advanced optimization functionals in facilitating robustness, and the application of these techniques to two of the leading implementations of quantum computation, trapped atoms and superconducting circuits. After a review of the theoretical and numerical foundations, the central part of the thesis starts with the idea of using ensemble optimization to achieve robustness with respect to both classical fluctuations in the system parameters, and decoherence. For the example of a controlled phasegate implemented with trapped Rydberg atoms, this approach is demonstrated to yield a gate that is at least one order of magnitude more robust than the best known analytic scheme. Moreover this robustness is maintained even for gate durations significantly shorter than those obtained in the analytic scheme. Superconducting circuits are a particularly promising architecture for the implementation of a quantum computer. Their flexibility is demonstrated by performing optimizations for both diagonal and non-diagonal quantum gates. In order to achieve robustness with respect to decoherence, it is essential to implement quantum gates in the shortest possible amount of time. This may be facilitated by using an optimization functional that targets an arbitrary perfect entangler, based on a geometric theory of two-qubit gates. For the example of superconducting qubits, it is shown that this approach leads to significantly shorter gate durations, higher fidelities, and faster convergence than the optimization towards specific two-qubit gates. Performing optimization in Liouville space in order to properly take into account decoherence poses significant numerical challenges, as the dimension scales quadratically compared to Hilbert space. However, it can be shown that for a unitary target, the optimization only requires propagation of at most three states, instead of a full basis of Liouville space. Both for the example of trapped Rydberg atoms, and for superconducting qubits, the successful optimization of quantum gates is demonstrated, at a significantly reduced numerical cost than was previously thought possible. Together, the results of this thesis point towards a comprehensive framework for the optimization of robust quantum gates, paving the way for the future realization of quantum computers.