Framework for Learning and Control in the Classical and Quantum Domains

TL;DR

This paper develops a unified framework linking classical and quantum control and learning, clarifying their interrelationship and aiding in the identification of open problems and the design of control policies.

Contribution

It introduces a formal framework that relates classical and quantum learning and control, using diagrammatic representations to expose knowledge gaps and guide problem-solving.

Findings

Unified diagrammatic framework for classical and quantum control and learning

Application to quantum-enhanced interferometric-phase estimation as a supervised learning problem

Identification of key open problems in classical-quantum control and learning

Abstract

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.