Modeling and Control of Quantum Systems: An Introduction

TL;DR

This paper provides a comprehensive introduction to the modeling and control of quantum systems, highlighting theoretical foundations, control approaches, and unique quantum features affecting feedback design.

Contribution

It offers a self-contained overview of quantum control theory, including models, controllability, stability, and tailored control design methods for quantum systems.

Findings

Quantum systems require specialized control tools due to their probabilistic nature.

Controllability and stability results are summarized for both closed and open quantum systems.

A survey of control design methods guides future research in quantum control.

Abstract

The scope of this work is to provide a self-contained introduction to a selection of basic theoretical aspects in the modeling and control of quantum mechanical systems, as well as a brief survey on the main approaches to control synthesis. While part of the existing theory, especially in the open-loop setting, stems directly from classical control theory (most notably geometric control and optimal control), a number of tools specifically tailored for quantum systems have been developed since the 1980s, in order to take into account their distinctive features: the probabilistic nature of atomic-scale physical systems, the effect of dissipation and the irreversible character of the measurements have all proved to be critical in feedback-design problems. The relevant dynamical models for both closed and open quantum systems are presented, along with the main results on their controllability and stability. A brief review of several currently available control design methods is meant to provide the interested reader with a roadmap for further studies.