  Quantum computing is a fascinating interdisciplinary research field that
promises to revolutionize computing by efficiently solving previously
intractable problems. Recent years have seen tremendous progress on both the
experimental realization of quantum computing devices as well as the
development and implementation of quantum algorithms. Yet, realizing
computational advantages of quantum computers in practice remains a widely open
problem due to numerous fundamental challenges. Interestingly, many of these
challenges are connected to performance, robustness, scalability, optimization,
or feedback, all of which are central concepts in control theory. This paper
provides a tutorial introduction to quantum computing from the perspective of
control theory. We introduce the mathematical framework of quantum algorithms
ranging from basic elements including quantum bits and quantum gates to more
advanced concepts such as variational quantum algorithms and quantum errors.
The tutorial only requires basic knowledge of linear algebra and, in
particular, no prior exposure to quantum physics. Our main goal is to equip
readers with the mathematical basics required to understand and possibly solve
(control-related) problems in quantum computing. In particular, beyond the
tutorial introduction, we provide a list of research challenges in the field of
quantum computing and discuss their connections to control.
