State-Constrained Optimal Control for Coherence Preservation in Multi-Level Open Quantum Systems

TL;DR

This paper develops a control framework for maintaining quantum coherence in multi-level quantum systems modeled by Lindblad equations, addressing dissipation effects with state constraints.

Contribution

It introduces a novel optimal control method incorporating state constraints for coherence preservation in open quantum systems modeled by Lindblad dynamics.

Findings

Effective coherence preservation demonstrated in controlled qutrit systems.

Control strategies account for irreversible decay processes.

Insights into maintaining quantum coherence under dissipation.

Abstract

This paper addresses the optimal control of quantum coherence in multi-level systems, modeled by the Lindblad master equation, which captures both unitary evolution and environmental dissipation. We develop an energy minimization framework to control the evolution of a qutrit (three-level) quantum system while preserving coherence between states. The control problem is formulated using Pontryagin's Minimum Principle in the form of Gamkrelidze, incorporating state constraints to ensure coherence remains within desired bounds. Our approach accounts for Markovian decoherence, demonstrating that the Lindblad operator is non-unital, which reflects the irreversible decay processes inherent in the system. The results provide insights into effectively maintaining quantum coherence in the presence of dissipation.