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.

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.

Understanding Recreational Services of Urban Riverfront Space for Planning Purposes

In the process of urbanization, natural and semi-natural landscapes are increasingly cherished as open space and recreational resource. Urban rivers are part of this kind of resource and thus play an important role in managing urban resilience and health. Employing the example of Tianjin, this doctoral dissertation research aims at learning to understand how to plan and design for the interface zones between urban water courses and for the land areas adjacent to such water courses. This research also aims at learning how to link waterfront space with other urban space in order to make a recreational space system for the benefit of people. Five questions of this dissertation are: 1) what is the role of rivers in spatial and open space planning? 2) What are the human needs regarding outdoor open space? 3) How do river and water front spatial structures affect people's recreational activities? 4) How to define the recreational service of urban river and waterfront open space? 5) How might answering these question change planning and design of urban open space? Quantitative and qualitative empirical approaches were combined in this study for which literature review and theoretical explorations provide the basis. Empirical investigations were conducted in the city of Tianjin. The quantitative approach includes conducting 267 quantitative interviews, and the qualitative approach includes carrying out field observations and mappings. GIS served to support analysis and visualization of empirical information that was generated through this study. By responding to the five research questions, findings and lessons include the following: 1) In the course of time rivers have gained importance in all levels and scales of spatial planning and decision making. Regarding the development of ecological networks, mainly at national scale, rivers are considered significant linear elements. Regarding regional and comprehensive development, river basins and watersheds are often considered as the structural link for strategic ecological, economic, social and recreational planning. For purposes of urban planning, particularly regarding recreational services in cities, the distribution of urban open spaces often follows the structure of river systems. 2) For the purpose of classifying human recreational needs that relate to outdoor open space Maslow's hierarchy of human needs serves as theoretical basis. The classes include geographical, safety, physiological, social and aesthetic need. These classes serve as references while analyzing river and waterfront open space and other kinds of open space. 3) Regarding the question how river and waterfront spatial structures might affect people's recreational activities, eight different landscape units were identified and compared in the case study area. Considering the thermal conditions of Tianjin, one of these landscape units was identified as affording the optimal spatial arrangement which mostly meets recreational needs. The size and the shape of open space, and the plants present in an open space have been observed as being most relevant regarding recreational activities. 4) Regarding the recreational service of urban river and waterfront open space the results of this research suggest that the recreational service is felt less intensively as the distances between water 183 front and open space user’s places of residence are increasing. As a method for estimating this ‘Service Distance Effect’ the following formula may be used: Y = a*ebx. In this equation Y means the ‘Service Distance’ between homes and open space, and X means the percentage of the people who live within this service distance. Coefficient "a" represents the distance of the residential area nearest to the water front. The coefficient "b" is a comprehensive capability index that refers to the size of the available and suitable recreational area. 5) Answers found to the questions above have implications for the planning and design of urban open space. The results from the quantitative study of recreational services of waterfront open space were applied to the assessment of river-based open space systems. It is recommended that such assessments might be done employing the network analysis function available with any GIS. In addition, several practical planning and designing suggestions are made that would help remedy any insufficient base for satisfying recreational needs. The understanding of recreational need is considered helpful for the proposing planning and designing ideas and for the changing of urban landscapes. In the course of time Tianjin's urban water system has shrunk considerably. At the same time rivers and water courses have shaped Tianjin's urban structure in noticeable ways. In the process of urbanization water has become increasingly important to the citizens and their everyday recreations. Much needs to be changed in order to improve recreational opportunities and to better provide for a livable city, most importantly when considering the increasing number of old people. Suggestions made that are based on results of this study, might be implemented in Tianjin. They are 1) to promote the quality of the waterfront open space and to make all linear waterfront area accessible recreational spaces. Then, 2), it is advisable to advocate the concept of green streets and to combine green streets with river open space in order to form an everyday recreational network. And 3) any sound urban everyday recreational service made cannot rely on only urban rivers; the whole urban structure needs to be improved, including adding small open space and optimize the form of urban communities, finally producing a multi-functional urban recreational network.

1st Kassel Student Workshop on Security in Distributed Systems

With this document, we provide a compilation of in-depth discussions on some of the most current security issues in distributed systems. The six contributions have been collected and presented at the 1st Kassel Student Workshop on Security in Distributed Systems (KaSWoSDS’08). We are pleased to present a collection of papers not only shedding light on the theoretical aspects of their topics, but also being accompanied with elaborate practical examples. In Chapter 1, Stephan Opfer discusses Viruses, one of the oldest threats to system security. For years there has been an arms race between virus producers and anti-virus software providers, with no end in sight. Stefan Triller demonstrates how malicious code can be injected in a target process using a buffer overflow in Chapter 2. Websites usually store their data and user information in data bases. Like buffer overflows, the possibilities of performing SQL injection attacks targeting such data bases are left open by unwary programmers. Stephan Scheuermann gives us a deeper insight into the mechanisms behind such attacks in Chapter 3. Cross-site scripting (XSS) is a method to insert malicious code into websites viewed by other users. Michael Blumenstein explains this issue in Chapter 4. Code can be injected in other websites via XSS attacks in order to spy out data of internet users, spoofing subsumes all methods that directly involve taking on a false identity. In Chapter 5, Till Amma shows us different ways how this can be done and how it is prevented. Last but not least, cryptographic methods are used to encode confidential data in a way that even if it got in the wrong hands, the culprits cannot decode it. Over the centuries, many different ciphers have been developed, applied, and finally broken. Ilhan Glogic sketches this history in Chapter 6.

Changes of traditional farming systems and their effects on land degradation and socio-economic conditions in the Inle Lake region, Myanmar

At many locations in Myanmar, ongoing changes in land use have negative environmental impacts and threaten natural ecosystems at local, regional and national scales. In particular, the watershed area of Inle Lake in eastern Myanmar is strongly affected by the environmental effects of deforestation and soil erosion caused by agricultural intensification and expansion of agricultural land, which are exacerbated by the increasing population pressure and the growing number of tourists. This thesis, therefore, focuses on land use changes in traditional farming systems and their effects on socio-economic and biophysical factors to improve our understanding of sustainable natural resource management of this wetland ecosystem. The main objectives of this research were to: (1) assess the noticeable land transformations in space and time, (2) identify the typical farming systems as well as the divergent livelihood strategies, and finally, (3) estimate soil erosion risk in the different agro-ecological zones surrounding the Inle Lake watershed area. GIS and remote sensing techniques allowed to identify the dynamic land use and land cover changes (LUCC) during the past 40 years based on historical Corona images (1968) and Landsat images (1989, 2000 and 2009). In this study, 12 land cover classes were identified and a supervised classification was used for the Landsat datasets, whereas a visual interpretation approach was conducted for the Corona images. Within the past 40 years, the main landscape transformation processes were deforestation (- 49%), urbanization (+ 203%), agricultural expansion (+ 34%) with a notably increase of floating gardens (+ 390%), land abandonment (+ 167%), and marshlands losses in wetland area (- 83%) and water bodies (- 16%). The main driving forces of LUCC appeared to be high population growth, urbanization and settlements, a lack of sustainable land use and environmental management policies, wide-spread rural poverty, an open market economy and changes in market prices and access. To identify the diverse livelihood strategies in the Inle Lake watershed area and the diversity of income generating activities, household surveys were conducted (total: 301 households) using a stratified random sampling design in three different agro-ecological zones: floating gardens (FG), lowland cultivation (LL) and upland cultivation (UP). A cluster and discriminant analysis revealed that livelihood strategies and socio-economic situations of local communities differed significantly in the different zones. For all three zones, different livelihood strategies were identified which differed mainly in the amount of on-farm and off-farm income, and the level of income diversification. The gross margin for each household from agricultural production in the floating garden, lowland and upland cultivation was US$ 2108, 892 and 619 ha-1 respectively. Among the typical farming systems in these zones, tomato (Lycopersicon esculentum L.) plantation in the floating gardens yielded the highest net benefits, but caused negative environmental impacts given the overuse of inorganic fertilizers and pesticides. The Revised Universal Soil Loss Equation (RUSLE) and spatial analysis within GIS were applied to estimate soil erosion risk in the different agricultural zones and for the main cropping systems of the study region. The results revealed that the average soil losses in year 1989, 2000 and 2009 amounted to 20, 10 and 26 t ha-1, respectively and barren land along the steep slopes had the highest soil erosion risk with 85% of the total soil losses in the study area. Yearly fluctuations were mainly caused by changes in the amount of annual precipitation and the dynamics of LUCC such as deforestation and agriculture extension with inappropriate land use and unsustainable cropping systems. Among the typical cropping systems, upland rainfed rice (Oryza sativa L.) cultivation had the highest rate of soil erosion (20 t ha-1yr-1) followed by sebesten (Cordia dichotoma) and turmeric (Curcuma longa) plantation in the UP zone. This study indicated that the hotspot region of soil erosion risk were upland mountain areas, especially in the western part of the Inle lake. Soil conservation practices are thus urgently needed to control soil erosion and lake sedimentation and to conserve the wetland ecosystem. Most farmers have not yet implemented soil conservation measures to reduce soil erosion impacts such as land degradation, sedimentation and water pollution in Inle Lake, which is partly due to the low economic development and poverty in the region. Key challenges of agriculture in the hilly landscapes can be summarized as follows: fostering the sustainable land use of farming systems for the maintenance of ecosystem services and functions while improving the social and economic well-being of the population, integrated natural resources management policies and increasing the diversification of income opportunities to reduce pressure on forest and natural resources.