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.

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.

Vegetation changes in a river oasis on the southern rim of the Taklamakan Desert in China between 1956 and 2000

The indigenous vegetation surrounding the river oases on the southern rim of the Taklamakan Desert has drastically diminished due to overexploitation as a source of fodder, timber and fuel for the human population. The change in the spatial extent of landscape forms and vegetation types around the Qira oasis was analyzed by comparing SPOT satellite images from 1998 with aerial photographs from 1956. The analysis was supplemented by field surveys in 1999 and 2000. The study is part of a joint Chinese-European project with the aim of assessing the current state of the foreland vegetation, of gathering information on the regeneration potential and of suggesting procedures for a sustainable management. With 33 mm of annual precipitation, plants can only grow if they have access to groundwater, lakes or rivers. Most of the available water comes into the desert via rivers in the form of seasonal flooding events resulting from snow melt in the Kun Lun Mountains. This water is captured in canal systems and used for irrigation of arable fields. Among the eight herbaceous and woody vegetation types and the type of open sand without any plant life that were mapped in 2000 in the oasis foreland, only the latter, the oasis border between cultivated land and open Populus euphratica forests and Tamarix ramosissima-Phragmites australis riverbed vegetation could be clearly identified on the photographs from 1956. The comparison of the images revealed that the oasis increased in area between 1956 and 2000. Shifting sand was successfully combated near to the oasis borders but increased in extent at the outward border of the foreland vegetation. In contrast to expectations, the area covered with Populus trees was smaller in 1956 than today due to some new forests in the north of the oasis that have grown up since 1977. Subfossil wood and leaf remnants of Populus euphratica that were found in many places in the foreland must have originated from forests destroyed before 1956. In the last 50 years, the main Qira River has shifted its bed significantly northward and developed a new furcation with a large new bed in 1986. The natural river dynamics are not only an important factor in forming the oasis’ landscape but also in providing the only possible regeneration sites for all occurring plant species. The conclusion of the study is that the oasis landscape has changed considerably in the last 50 years due to natural floodings and to vegetation degradation by human overexploitation. The trend towards decreasing width of the indigenous vegetation belt resulting from the advancing desert and the expansion of arable land is particularly alarming because a decrease in its protective function against shifting sand can be expected in the future.

Prevalence of intestinal parasites in small ruminants and their senstivity to treatments with ethnobotanical remedies in Cholistan, Pakistan

Livestock production contributes substantially to the livelihoods of poor rural farmers in Pakistan; strengthening pastoral communities plays an imperative role in the country’s thrive for poverty alleviation. Intestinal helminths constitute a major threat for pastoral livestock keepers in the whole country because chronic infestation leads to distinct losses in livestock productivity, particularly the growth of young animals. Synthetic anthelmintics have long been considered the only effective way of controlling this problem but high prices, side effects and chemical residues/toxicity problems, or development of resistance, lead to their very limited use in many pastoral systems. Additionally, poor pastoralists in remote areas of Pakistan hardly have access to appropriate anthelmintic drugs, which are also relatively expensive due to the long routes of transportation. The search for new and more sustainable ways of supporting livestock keepers in remote areas has given rise to studies of ethno-botanicals or traditional plant-based remedies to be used in livestock health care. Plant-based remedies are cheap or free of cost, environmentally safe and generally create no problem of drug resistance; they thus might substitute allopathic drugs. Furthermore, these remedies are easily available in remote areas and simple to prepare and/or administer. Cholistan desert is a quite poor region of Pakistan and the majority of its inhabitants are practicing a nomadic life. The region’s total livestock population (1.29 million heads) is almost twice that of the human population. Livestock husbandry is the primordial occupation of the communities and traditionally wealth assessment was based on the number of animals, especially goats and sheep, owned by an individual. Fortunately, about 60% of this desert region is richly endowed with highly adapted grasses, shrubs and trees. This natural flora has a rich heritage of scientifically unexplored botanical pharmacopoeia. Against this background, the present research project that was conducted under the umbrella of the International Center for Development and Decent Work at Kassel University, focused on a development aspect: in the Cholistan desert region it was firstly examined how pastoralists manage their livestock, which major health problems they face for the different animal species, and which of the naturally occurring plants they use for the treatment of animal diseases (Chapter 2). For this purpose, a baseline survey was carried out across five locations in Cholistan, using a structured questionnaire to collect data from 100 livestock farmers (LF) and 20 local healers (LH). Most of LF and LH were illiterate (66%; 70%). On average, LH had larger herds (109 animals) than LF (85 animals) and were more experienced in livestock husbandry and management. On average LF spent about 163 Euro per year on the treatment of their livestock, with a huge variability in expenditures. Eighty-six traditional remedies based on 64 plants belonging to 43 families were used. Capparaceae was the botanical family with the largest number of species used (4), followed by Chenopodiaceae, Poaceae, Solanaceae and Zygophyllaceae (3). The plants Capparis decidua (n=55 mentions), Salsola foetida (n=52), Suaeda fruticosa (n=46), Haloxylon salicornicum (n=42) and Haloxylon recurvum (n=39) were said to be most effective against the infestations with gastrointestinal parasites. Aerial parts (43%), leaves (26%), fruits (9%), seeds and seed oils (9%) were the plant parts frequently used for preparation of remedies, while flowers, roots, bulbs and pods were less frequently used (<5%). Common preparations were decoction, jaggery and ball drench; oral drug administration was very common. There was some variation in the doses used for different animal species depending on age, size and physical condition of the animal and severity of the disease. In a second step the regionally most prevalent gastrointestinal parasites of sheep and goats were determined (Chapter 3) in 500 animals per species randomly chosen from pastoral herds across the previously studied five localities. Standard parasitological techniques were applied to identify the parasites in faecal samples manually collected at the rectum. Overall helminth prevalence was 78.1% across the 1000 animals; pure nematode infestations were most prevalent (37.5%), followed by pure trematode (7.9%), pure cestode (2.6%) and pure protozoa infestations (0.8%). Mixed infestations with nematodes and trematodes occurred in 6.4% of all animals, mixed nematode-cestode infestations in 3.8%, and all three groups were found in 19.1% of the sheep and goats. In goats more males (81.1%) than females (77.0%) were infested, the opposite was found in sheep (73.6% males, 79.5% females). Parasites were especially prevalent in suckling goats (85.2%) and sheep (88.5%) and to a lesser extent in young (goats 80.6%, sheep 79.3%) and adult animals (goats 72.8%, sheep 73.8%). Haemonchus contortus, Trichuris ovis and Paramphistomum cervi were the most prevalent helminths. In a third step the in vitro anthelmintic activity of C. decidua, S. foetida, S. fruticosa, H. salicornicum and H. recurvum (Chapter 2) was investigated against adult worms of H. contortus, T. ovis and P. cervi (Chapter 3) via adult motility assay (Chapter 4). Various concentrations ranging from 7.8 to 500 mg dry matter/ml of three types of extracts of each plant, i.e. aqueous, methanol, and aqueous-methanol (30:70), were used at different time intervals to access their anthelmintic activity. Levamisol (0.55 mg/ml) and oxyclozanide (30 mg/ml) served as positive and phosphate-buffered saline as negative control. All extracts exhibited minimum and maximum activity at 2 h and 12 h after parasite exposure; the 500 mg/ml extract concentrations were most effective. Plant species (P<0.05), extract type (P<0.01), parasite species (P<0.01), extract concentration (P<0.01), time of exposure (P<0.01) and their interactions (P<0.01) had significant effects on the number of immobile/dead helminths. From the comparison of LC50 values it appeared that the aqueous extract of C. decidua was more potent against H. contortus and T. ovis, while the aqueous extract of S. foetida was effective against P. cervi. The methanol extracts of H. recurvum were most potent against all three types of parasites, and its aqueous-methanol extract was also very effective against T. ovis and P. cervi. Based on these result it is concluded that the aqueous extract of C. decidua, as well as the methanol and aqueous-methanol extract of H. recurvum have the potential to be developed into plant-based drugs for treatment against H. contortus, T. ovis and P. cervi infestations. Further studies are now needed to investigate the in vivo anthelmintic activity of these plants and plant extracts, respectively, in order to develop effective, cheap and locally available anthelmintics for pastoralists in Cholistan and neighboring desert regions. This will allow developing tangible recommendations for plant-based anthelminthic treatment of sheep and goat herds, and by this enable pastoralists to maintain healthy and productive flocks at low costs and probably even manufacture herbal drugs for marketing on a regional scale.

Optimization-Based Robotic Manipulation for Safe Interaction with Human Operators

This thesis investigates a method for human-robot interaction (HRI) in order to uphold productivity of industrial robots like minimization of the shortest operation time, while ensuring human safety like collision avoidance. For solving such problems an online motion planning approach for robotic manipulators with HRI has been proposed. The approach is based on model predictive control (MPC) with embedded mixed integer programming. The planning strategies of the robotic manipulators mainly considered in the thesis are directly performed in the workspace for easy obstacle representation. The non-convex optimization problem is approximated by a mixed-integer program (MIP). It is further effectively reformulated such that the number of binary variables and the number of feasible integer solutions are drastically decreased. Safety-relevant regions, which are potentially occupied by the human operators, can be generated online by a proposed method based on hidden Markov models. In contrast to previous approaches, which derive predictions based on probability density functions in the form of single points, such as most likely or expected human positions, the proposed method computes safety-relevant subsets of the workspace as a region which is possibly occupied by the human at future instances of time. The method is further enhanced by combining reachability analysis to increase the prediction accuracy. These safety-relevant regions can subsequently serve as safety constraints when the motion is planned by optimization. This way one arrives at motion plans that are safe, i.e. plans that avoid collision with a probability not less than a predefined threshold. The developed methods have been successfully applied to a developed demonstrator, where an industrial robot works in the same space as a human operator. The task of the industrial robot is to drive its end-effector according to a nominal sequence of grippingmotion-releasing operations while no collision with a human arm occurs.

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.

Knowledge Building in Landscape Architecture

The objective of this study was to develop an internet-based seminar framework applicable for landscape architecture education. This process was accompanied by various aims. The basic expectation was to keep the main characteristics of landscape architecture education also in the online format. On top of that, four further objectives were anticipated: (1) training of competences for virtual team work, (2) fostering intercultural competence, (3) creation of equal opportunities for education through internet-based open access and (4) synergy effects and learning processes across institutional boundaries. This work started with the hypothesis that these four expected advantages would compensate for additional organisational efforts caused by the online delivery of the seminars and thus lead to a sustainable integration of this new learning mode into landscape architecture curricula. This rationale was followed by a presentation of four areas of knowledge to which the seminar development was directly related (1) landscape architecture as a subject and its pedagogy, (2) general learning theories, (3) developments in the ICT sector and (4) wider societal driving forces such as global citizenship and the increase of open educational resources. The research design took the shape of a pedagogical action research cycle. This approach was constructive: The author herself is teaching international landscape architecture students so that the model could directly be applied in practice. Seven online seminars were implemented in the period from 2008 to 2013 and this experience represents the core of this study. The seminars were conducted with varying themes while its pedagogy, organisation and the technological tools remained widely identical. The research design is further based on three levels of observation: (1) the seminar design on the basis of theory and methods from the learning sciences, in particular educational constructivism, (2) the seminar evaluation and (3) the evaluation of the seminars’ long term impact. The seminar model itself basically consists of four elements: (1) the taxonomy of learning objectives, (2) ICT tools and their application and pedagogy, (3) process models and (4) the case study framework. The seminar framework was followed by the presentation of the evaluation findings. The major findings of this study can be summed up as follows: Implementing online seminars across educational and national boundaries was possible both in term of organisation and technology. In particular, a high level of cultural diversity among the seminar participants has definitively been achieved. However, there were also obvious obstacles. These were primarily competing study commitments and incompatible schedules among the students attending from different academic programmes, partly even in different time zones. Both factors had negative impact on the individual and working group performances. With respect to the technical framework it can be concluded that the majority of the participants were able to use the tools either directly without any problem or after overcoming some smaller problems. Also the seminar wiki was intensively used for completing the seminar assignments. However, too less truly collaborative text production was observed which could be improved by changing the requirements for the collaborative task. Two different process models have been applied for guiding the collaboration of the small groups and both were in general successful. However, it needs to be said that even if the students were able to follow the collaborative task and to co-construct and compare case studies, most of them were not able to synthesize the knowledge they had compiled. This means that the area of consideration often remained on the level of the case and further reflections, generalisations and critique were largely missing. This shows that the seminar model needs to find better ways for triggering knowledge building and critical reflection. It was also suggested to have a more differentiated group building strategy in future seminars. A comparison of pre- and post seminar concept maps showed that an increase of factual and conceptual knowledge on the individual level was widely recognizable. Also the evaluation of the case studies (the major seminar output) revealed that the students have undergone developments of both the factual and the conceptual knowledge domain. Also their self-assessment with respect to individual learning development showed that the highest consensus was achieved in the field of subject-specific knowledge. The participants were much more doubtful with regard to the progress of generic competences such as analysis, communication and organisation. However, 50% of the participants confirmed that they perceived individual development on all competence areas the survey had asked for. Have the additional four targets been met? Concerning the competences for working in a virtual team it can be concluded that the vast majority was able to use the internet-based tools and to work with them in a target-oriented way. However, there were obvious differences regarding the intensity and activity of participation, both because of external and personal factors. A very positive aspect is the achievement of a high cultural diversity supporting the participants’ intercultural competence. Learning from group members was obviously a success factor for the working groups. Regarding the possibilities for better accessibility of educational opportunities it became clear that a significant number of participants were not able to go abroad during their studies because of financial or personal reasons. They confirmed that the online seminar was to some extent a compensation for not having been abroad for studying. Inter-institutional learning and synergy was achieved in so far that many teachers from different countries contributed with individual lectures. However, those teachers hardly ever followed more than one session. Therefore, the learning effect remained largely within the seminar learning group. Looking back at the research design it can be said that the pedagogical action research cycle was an appropriate and valuable approach allowing for strong interaction between theory and practice. However, some more external evaluation from peers in particular regarding the participants’ products would have been valuable.