Adaptive Fidelity-Based Density Tracking for Open Quantum Systems

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.

💡 Research Summary

The manuscript introduces a novel, model‑free adaptive control scheme for tracking the density matrix of an open quantum system governed by the Lindblad‑Gorini‑Kossakowski‑Sudarshan (LGKS) master equation. The authors focus on a two‑level (qubit) system and aim to drive the system’s state ρ(t) to a desired target state ρ_d without any prior knowledge of the free Hamiltonian H₀, the control Hamiltonian H₁, or the dissipative jump operators L_i.

Key to the approach is the use of Uhlmann‑Jozsa fidelity F(ρ,ρ_d) as a scalar performance metric. The tracking error is defined as e(t)=1−F(ρ(t),ρ_d), which lies in