In image processing, the amount of data to be processed grows rapidly, in particular when dealing with images of more than two dimensions or time series of images. Thus, efficient processing is a challenge, as data sizes may push even supercomputers to their limits. Quantum image processing promises to encode images with logarithmically less qubits than classical pixels in the image. In theory, this is a huge progress, but so far not many experiments have been conducted in practice, in particular on real backends. Often, the precise conversion of classical data to quantum states, the exact implementation, and the interpretation of the measurements in the classical context are challenging. We investigate these practical questions in this paper. In particular, we study the feasibility of the flexible representation of quantum images (FRQI). Furthermore, we check experimentally the limit in the current noisy intermediate-scale quantum era, i.e., up to which image size an image can be encoded, both on simulators and on real backends. Finally, we propose a method for simplifying the circuits needed for the FRQI. With our alteration, the number of gates can be reduced, especially the one of the error-prone controlled-NOT gates. As a consequence, the size of manageable images increases.

Edges are image locations where the gray value intensity changes suddenly. They are among the most important features to understand and segment an image. Edge detection is a standard task in digital image processing, solved, for example, using filtering techniques. However, the amount of data to be processed grows rapidly and pushes even supercomputers to their limits. Quantum computing promises exponentially lower memory usage in terms of the number of qubits compared to the number of classical bits. In this paper, we propose a hybrid method for quantum edge detection based on the idea of a quantum artificial neuron. Our method can be practically implemented on quantum computers, especially on those of the current noisy intermediate-scale quantum era. We compare six variants of the method to reduce the number of circuits and thus the time required for the quantum edge detection. Taking advantage of the scalability of our method, we can practically detect edges in images considerably larger than reached before.

Training a deep learning network requires choosing its weights such that the output minimizes a given loss function. In practice, stochastic gradient descent is frequently used for solving the optimization problem. Several variants of this approach have been suggested in the literature. We study the impact of the choice of the optimization method on the outcome of the learning process at the example of two image processing applications from quite different fields. The first one is artistic style transfer, where the content of one image is combined with the style of another one. The second application is a real world classification task from industry, namely detecting defects in images of air filters. In both cases, clear differences between the results of the individual optimization methods are observed.

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