Quantum Robust Optimal Control for Linear Complex Quantum Systems With Uncertainties

Abstract

The aim of this note is to study quantum robust optimal control problem for a class of linear quantum systems with uncertainties. It is shown that such problem can be converted into a mixed linear quadratic Gaussian (LQG) and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H^{\infty }$</tex-math></inline-formula> quantum control problem. A physical model described by complex quantum stochastic differential equations (CQSDEs) is presented for the quantum system with uncertainties. The quantum system described by CQSDEs is called a complex quantum system in terms of annihilation and creation operators [1]. For an uncertain quantum system, we build a connection with a scaled linear system without uncertainty. The desired quantum robust optimal control results are derived based on the connection. We provide one numerical procedure for quantum robust optimal controller synthesis and then provide an example. The resulting controller presents robustness and optimal performance.