Experimentally realizable control fields in quantum Lyapunov control

TL;DR

This paper investigates the robustness and practicality of quantum Lyapunov control by analyzing time-delay effects, exploring pulse train and bang-bang control methods, and assessing convergence efficiency in high-dimensional systems.

Contribution

It demonstrates that quantum Lyapunov control is robust against time delays, feasible with pulse or bang-bang signals, and effective for complex quantum systems.

Findings

Lyapunov control is robust against time delay.

Pulse train and bang-bang signals can replace continuous control fields.

Convergence time indicates high efficiency in high-dimensional systems.

Abstract

As a hybrid of techniques from open-loop and feedback control, Lyapunov control has the advantage that it is free from the measurement-induced decoherence but it includes the system's instantaneous message in the control loop. Often, the Lyapunov control is confronted with time delay in the control fields and difficulty in practical implementations of the control. In this paper, we study the effect of time-delay on the Lyapunov control, and explore the possibility of replacing the control field with a pulse train or a bang-bang signal. The efficiency of the Lyapunov control is also presented through examining the convergence time of the controlled system. These results suggest that the Lyapunov control is robust gainst time delay, easy to realize and effective for high-dimensional quantum systems.