Using the effects of quantum mechanics for computing challenges has been an often discussed topic for decades. The frequent successes and early products in this area, which we have seen in recent years, indicate that we are currently entering a new era of computing. This paradigm shift will also impact the work of robotic scientists and the applications of robotics. New possibilities as well as new approaches to known problems will enable the creation of even more powerful and intelligent robots that make use of quantum computing cloud services or co-processors. In this position paper, we discuss potential application areas and also point out open research topics in quantum computing for robotics. We go into detail on the impact of quantum computing in artificial intelligence and machine learning, sensing and perception, kinematics as well as system diagnosis. For each topic we point out where quantum computing could be applied based on results from current research.