Quantum computing through the lens of control: A tutorial introduction

Abstract: 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.