Adaptive Fidelity-Based Density Tracking for Open Quantum Systems

TL;DR

This paper introduces an adaptive control method for quantum systems that learns in real-time to track desired density matrices without prior system knowledge, ensuring fidelity and robustness through a geometric-preserving PID controller.

Contribution

It develops a novel online learning-based adaptive control framework for quantum density tracking that does not require prior knowledge of system parameters.

Findings

Effective density tracking demonstrated in simulations.

Robustness to measurement noise confirmed.

Preserves quantum state geometry during control.

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.