Adaptive Fidelity-Based Density Tracking for Open Quantum Systems

Abstract

This paper presents an online learning-based adaptive control framework for density-matrix tracking in a two-level Lindblad-Gorini-Kossakowski-Sudarshan (LGKS) quantum system, in which the feedback control law does not require prior knowledge of the system Hamiltonian or dissipative operators. The adaptive controller is based on a continuous-time formulation of retrospective cost adaptive control (RCAC). To preserve the geometric structure of the quantum-state evolution, an adaptive PID controller driven by Uhlmann's fidelity is employed. The proposed approach is validated in numerical simulations for both low-entropy and high-entropy density-tracking tasks, and robustness to measurement noise in the feedback path is investigated.