Quantum feedback control: how to use verification theorems and viscosity solutions to find optimal protocols |
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Authors: | Kurt Jacobs Alireza Shabani |
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Affiliation: | 1. Department of Physics , University of Massachusetts at Boston , Boston, MA, USA kurt.jacobs@umb.edu kjacobs@cs.umb.edu;3. Department of Electrical Engineering , University of Southern California , Los Angeles, CA, USA |
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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. |
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Keywords: | quantum feedback control verification theorems viscosity solutions |
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