  Robust control of quantum systems is an increasingly relevant field of study
amidst the second quantum revolution, but there remains a gap between taming
quantum physics and robust control in its modern analytical form that
culminated in fundamental performance bounds. With certain exceptions such as
quantum optical systems that can be modeled as linear stochastic differential
equations, quantum systems are not amenable to linear, time-invariant,
measurement-based robust control techniques, and thus novel gap-bridging
techniques must be developed. This survey is written for control theorists to
provide a review of the current state of quantum control and outline the
challenges faced in trying to apply modern robust control to quantum systems.
We present issues that arise when applying classical robust control theory to
quantum systems, typical methods used by quantum physicists to explore such
systems and their robustness, as well as a discussion of open problems to be
addressed in the field. We focus on general, practical applications and recent
work to enable control researchers to contribute to advancing this burgeoning
field.
