Competence Center Quantum Computing Rhineland-Palatinate

Quantum chemistry on quantum computers is considered to be one of the first realistic use cases in which an advantage of quantum computers is demonstrated. Especially in the simulation of metals strong electron-electron correlations occur, which are efficiently solved by the entanglement of quantum computers in contrast to conventional methods.

Algorithms such as the Variational Quantum Eigensolver (VQE) and mixed approaches, so-called »shallow-depth circuits« algorithms, which are state of the art, show promising potential on quantum computers. Currently, we are in the intermediate NISQ (Noisy Intermediate Scale Quantum) development stage of hardware technology, with significant progress in the number of available qubits and error rates in recent years. Nevertheless, not all known quantum algorithms can yet be successfully implemented due to the limitations of error rates and decoherence effects. When developing new quantum computing workflows, science often combines robust classical approaches with algorithms on the quantum computer.

Examples of such hybrid quantum/classical approaches are variational algorithms like the VQE for quantum chemistry simulation. Variational algorithms are suitable methods for current hardware with respect to the required gate depth and the error tolerance of the algorithm. The parts that are computationally intensive for classical high-performance computers are solved on the quantum computer, while the other parts of the workflow are calculated on conventional computers.

However, the scaling of these hybrid methods compared to purely classical methods on high performance computers remains the subject of research. We are tackling this exciting topic at the Fraunhofer ITWM.

The current issues of stochastic capital and energy market simulations as well as asset management pose great challenges to computing power, which even conventional high-performance computing (HPC) techniques can only fulfill to a limited extent. The new technology of quantum computing opens up the perspective of solving previously incalculable problems in the near future or creating new simulation approaches.

We develop algorithms for the valuation of financial derivatives, the modelling of energy markets with stochastic variables and for the solution of mixed-integer optimisation problems in the financial and energy industry. The research also includes the investigation of various infrastructures such as gate-based quantum computers, quantum simulators and digital annealers for the high-performance implementation of the developed methods. Digital Annealers use a procedure inspired by quantum annealing. Here a global minimum of a given target function is found by a process that uses quantum fluctuations.

Direct applications can be found in the strategic allocation of assets, energy park management and risk analysis of portfolios on an industrial scale.

In recent years, the improved quality of computed tomography (CT) images has led to a digitalization of the material characterization process for composite materials. Today, commercially available CT devices have a maximum resolution of less than one micron and produce 3D images with up to (4096x4096x4096) voxels. New algorithms based on Fourier transformations are needed for analysis. These Fourier transforms are the most time consuming algorithms in simulation.

Quantum Fourier transformations accelerate the simulation for realistic geometries by a factor of 100 to 1000. This is our starting point. We want to use acceleration and look at the accuracy and errors of quantum Fourier transformations and their applicability to real problems.

Nowadays, image analysis is often slower than data acquisition or can not exploit the data completely. The amount of image data grows faster than the speed of the analysis methods. This is due to:

• new acquisition methods
• higher resolutions
• higher dimensionality
• wider availability of new camera systems

One example is the computed tomography device Gulliver provided to the Civil Engineering of TU Kaiserslautern by the DFG (Deutsche Forschungsgemeinschaft). This globally unique experimental facility will image concrete beams during bending tests. One experiment will generate approximately 2TB image data. Thus quantum computing promising faster processing of larger data sets is very attractive for image processing.

Typical image analysis solutions consist of numerous, multiply linked image transformations. Many filtering and analysis algorithms are either based on or sped up considerably using the discrete Fourier transform.

Replacing it by its quantum counterpart bears therefore particularly high potential for efficiently processing huge image data as provided eg by Gulliver.  Exploiting this potential requires however representing images including discrete connectivities accordingly.

Quantum Machine Learning (QML) is an emerging interdisciplinary research area at the interface of quantum physics and artificial intelligence. The underlying idea is to adapt classical learning algorithms for use on quantum computers in order to combine the advantages of quantum technology with the statistical framework of machine learning. Since quantum physics itself is characterized by an inherently statistical behavior, this synthesis offers the potential to achieve a technological breakthrough also on near-term quantum computers.

We develop QML algorithms in an application-based context and evaluate the practicability and performance of quantum approaches in comparison with classical approaches. For this purpose, we consider regression, classification and data encoding problems motivated by real-world applications, for example in the field of image processing and process engineering. By identifying interesting use cases and making them run on IBM quantum computers, we use QML to advance on the road to quantum readiness.