Optimal Lyapunov quantum control on two-level systems: convergence and extended techniques

TL;DR

This paper investigates how control field strength affects the efficiency of Lyapunov quantum control in two-level systems and proposes an extended technique combining free evolution and external control to improve control fidelity and guarantee convergence.

Contribution

It introduces an extended control technique that combines free evolution with external control, ensuring convergence and improved fidelity in Lyapunov quantum control of two-level systems.

Findings

Strong control fields can reduce control fidelity.

The extended technique guarantees convergence to the target state.

Analytical design of control laws for exact state steering.

Abstract

Taking a two-level system as an example, we show that a strong control field may enhance the efficiency of optimal Lyapunov quantum control in [Hou et al., Phys. Rev. A \textbf{86}, 022321 (2012)] but could decrease its control fidelity. A relationship between the strength of the control field and the control fidelity is established. An extended technique, which combines free evolution and external control, is proposed to improve the control fidelity. We analytically demonstrate that the extended technique can be used to design a control law for steering a two-level system exactly to the target state. In such a way, the convergence of the extended optimal Lyapunov quantum control can be guaranteed.