In the single-shot X-ray structure analysis, X-ray scattering patterns of individual nanoparticles are recorded in each laser shot. In doing so, the particles are destroyed as a result of the energy deposition during the scattering process by hydrodynamic expansion or Coloumbexplosion. For this reason, the use of ultrashort pulses with pulse lengths in the femtosecond range is the key to single-shot analysis of individual nanoparticles. There is the possibility of structure elucidation of supramolecular systems such as proteins, which often can not be crystallized, or the single-shot analysis of extremely fragile systems which are only accessible in the gas phase. For example, snapshots of statistical growth processes of nanostructures in the gas phase or the morphology of rotating suprafluid droplets become visible for the first time.
Currently, the repetition rate in the X-ray scattering images increases steadily and is already penetrating several kHz and in future probably MHz, so that an individual evaluation of single scattering images, which have interesting symmetries, is no longer practicable. From this, we can derive directly the necessity of fast, automated and, if necessary, self-learning selection and reconstruction methods.

While in the 20th century structure elucidation by means of scattering methods was essentially limited to crystalline solids, whereas non-crystalline matter has come into the focus of structural research in recent decades. On the one hand, this is due to the technical relevance of amorphous materials such as polymers, gels, colloidal suspensions and liquid crystals, on the other hand due to the availability of highly brilliant and coherent radiation sources for short-wave light. Synchronous third-and fourth-generation synchrotron sources provide coherent X-ray access to structural short-range ordering and local symmetry in noncrystalline matter. Such amorphous structures often occur in soft condensed matter, which is understood to mean systems with weak interactions, which on the one hand can easily avoid external constraints and thus can be manipulated by external fields, on the other hand characterized by strong fluctuations. The properties of such systems are therefore essentially determined by dynamic processes, which are accessible with time-resolved methods or quasi-elastic scattering methods in the time domain.

At present, such a large amount of data is produced with a time resolution in the range of milliseconds that a systematic evaluation of the data is only possible to a very limited extent. That is why the experimental possibilities of third and fourth generation synchronization radiation sources with much higher time resolution require new strategies for the automated evaluation of very large amounts of data. Artificial intelligence methods such as neural network based machine learning are a promising approach to extract information on the structure and dynamics of complex systems from large datasets.

In modern quantum optics and quantum information processing, it is necessary to fully characterize the quantum state of correlated systems consisting of several subsystems or modes. For this purpose, statistical measurement data must be recorded in a high-dimensional parameter space and used to reconstruct the quantum state, taking into account physical constraints.
However, the complexity of quantum computers and quantum simulators scales exponentially with the number of available quantum systems. Similarly, the measurement effort scales for a rigorous quantum state reconstruction, so that traditional methods fail even with very few correlated quantum systems. Recent developments, such as Integrated photonic waveguide structures capable of interferometrically stable generation and manipulation of complex multimode states require novel approaches to effectively reconstruct high-dimensional quantum states based on limited measurement data. On the one hand, it has been shown that artifacts in tomographic medical imaging techniques can be effectively suppressed in neural network reconstruction. This approach can be directly applied to quantum state tomography. On the other hand, the usable information in the initial state is partly present in smaller subsystems in a certain form of representation, such as the photonic density matrix. The determination of the optimal tomographic projections in the measurement for the statistically most significant reconstruction of reconfigurable subsystems already fails with low complexity, such that for scalability also novel approaches are required, which influence the tomographic parameters of the ongoing measurement during the reconstruction. The approaches are comparable to the dynamic analysis problems and control questions that are addressed in WP2.
For the tasks described here, which can also be characterized as inverse problems, explicit methods are either inaccessible or not feasible in time. At this point, the potential of machine learning should come into play.