Robust Quantum Control in Closed and Open Systems: Theory and Practice

TL;DR

This paper reviews the current state and challenges of applying modern robust control techniques to quantum systems, highlighting the need for novel methods to bridge the gap between quantum physics and control theory.

Contribution

It provides a comprehensive review of quantum control, discusses the limitations of classical control methods for quantum systems, and outlines open problems for future research.

Findings

Classical robust control techniques often do not directly apply to quantum systems.

Quantum optical systems can sometimes be modeled as linear stochastic differential equations.

Identifies key open problems and challenges in applying robust control to quantum systems.

Abstract

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.