On some open questions in bilinear quantum control

TL;DR

This paper introduces key issues in controlling infinite-dimensional quantum systems governed by bilinear Schrödinger equations, highlighting recent developments, examples, and open questions in the field.

Contribution

It provides an overview of modern control challenges in infinite-dimensional quantum systems and presents well-studied examples as test cases for future research.

Findings

Survey of recent advances in quantum control

Presentation of four well-studied quantum systems

Identification of open theoretical and practical questions

Abstract

The aim of this paper is to provide a short introduction to modern issues in the control of infinite dimensional closed quantum systems, driven by the bilinear Schr\"odinger equation. The first part is a quick presentation of some of the numerous recent developments in the fields. This short summary is intended to demonstrate the variety of tools and approaches used by various teams in the last decade. In a second part, we present four examples of bilinear closed quantum systems. These examples were extensively studied and may be used as a convenient and efficient test bench for new conjectures. Finally, we list some open questions, both of theoretical and practical interest.