Quantum Lyapunov Control Based on the Average Value of an Imaginary Mechanical Quantity

TL;DR

This paper proposes a quantum Lyapunov control method based on the average value of an imaginary mechanical quantity, ensuring convergence to a target state in degenerate systems, validated through numerical simulations.

Contribution

It introduces a control law for multi-Hamiltonian quantum systems to achieve convergence to a target state in degenerate cases, extending existing single-control methods.

Findings

Proved convergence of the control system to the target state.

Designed control laws for multi-Hamiltonian systems.

Validated effectiveness through numerical simulations on a three-level system.

Abstract

The convergence of closed quantum systems in the degenerate cases to the desired target state by using the quantum Lyapunov control based on the average value of an imaginary mechanical quantity is studied. On the basis of the existing methods which can only ensure the single-control Hamiltonian systems converge toward a set, we design the control laws to make the multi-control Hamiltonian systems converge to the desired target state. The convergence of the control system is proved, and the convergence to the desired target state is analyzed. How to make these conditions of convergence to the target state to be satisfied is proved or analyzed. Finally, numerical simulations for a three level system in the degenrate case transfering form an initial eigenstate to a target superposition state are studied to verify the effectiveness of the proposed control method.