Model-free, Learning-based Control of LGKS Quantum System

Abstract: This paper presents a model-free, learning-based adaptive controller for the density tracking problem in a two-level Lindblad-Gorini-Kossakowski-Sudarshan (LGKS) quantum system. The adaptive controller is based on the continuous-time retrospective cost adaptive control. To preserve the geometric properties of the quantum system, an adaptive PID controller driven and optimized by Ulhmann's fidelity is used. The proposed controller is validated in simulation for a low and a high-entropy density-tracking problem.