The quest for a practical quantum advantage or the importance of applications for quantum computing

Quantum computing as emerging technology raises high expectations to accelerate complicated calculations, superseding capabilities of presently available supercomputers and to provide a solution to the ever-increasing challenge of processing big amount of data. Besides theoretical promises, quantum computers have successfully been realized in experimental settings during the past few years, and can now also be accessed commercially. Given this availability of quantum computers, their application potential can be scrutinized. Promised to lead to disruptive changes in addressing and solving problems from the domains of simulation, optimization and machine learning, quantum computers have been researched in context of many application scenarios in industrial and academic setting in the recent years. However, it turns out that currently available quantum computers are still to small in size and limited in quality to fulfill the high hopes set in them at the moment. This review reflects on the current state of the technology coming from the perspective of the application, and indicates the developments required on hardware, software and algorithmic side to eventually make quantum computing beneficial for applications.