Quantum Feedback Control: How to use Verification Theorems and Viscosity Solutions to Find Optimal Protocols

TL;DR

This paper introduces a simplified approach to quantum feedback control, demonstrating how verification theorems and viscosity solutions can be used to identify and compute optimal control protocols in quantum systems.

Contribution

It provides an accessible explanation of verification theorems and viscosity solutions for quantum feedback control, along with a practical example of their application.

Findings

Verification theorems can efficiently verify optimality of protocols.

Viscosity solutions enable numerical computation of optimal control protocols.

The methods are illustrated with a relevant quantum control example.

Abstract

While feedback control has many applications in quantum systems, finding optimal control protocols for this task is generally challenging. So-called "verification theorems" and "viscosity solutions" provide two useful tools for this purpose: together they give a simple method to check whether any given protocol is optimal, and provide a numerical method for finding optimal protocols. While treatments of verification theorems usually use sophisticated mathematical language, this is not necessary. In this article we give a simple introduction to feedback control in quantum systems, and then describe verification theorems and viscosity solutions in simple language. We also illustrate their use with a concrete example of current interest.