Quantum feedback control: how to use verification theorems and viscosity solutions to find optimal protocols
Kurt Jacobs, Alireza Shabani · Contemporary Physics · 2008
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.