Framework for Learning and Control in the Classical and Quantum Domains

Control and learning are key to technological advancement, both in the classical and quantum domains, yet their interrelationship is insufficiently clear in the literature, especially between classical and quantum definitions of control and learning. We construct a framework that formally relates learning and control, both classical and quantum, to each other, with this formalism showing how learning can aid control. Furthermore, our framework helps to identify interesting unsolved problems in the nexus of classical and quantum control and learning and help in choosing tools to solve problems. As a use case, we cast the well-studied problem of adaptive quantum-enhanced interferometric-phase estimation as a supervised learning problem for devising feasible control policies. Our unification of these fields relies on diagrammatically representing the state of knowledge, which elegantly summarizes existing knowledge and exposes knowledge gaps.