Abstract
For high-dimensional closed quantum systems, this paper proposes a novel quantum Lyapunov control scheme based on the particle swarm optimization algorithm and achieves a high-probability population transfer of the system to a non-isolated target eigenstate in the LaSalle invariant set under usual smooth Lyapunov control laws. Via a quadratic Lyapunov function with unknown parameters, a control law with the unknown parameters is designed; based on the LaSalle invariance principle and the energy-level connectivity graph, the stability of the system is analyzed; by using the particle swarm optimization algorithm, a set of optimal parameters is obtained to achieve the control goal. In particular, we propose a path planning method based on the energy-level connectivity graph to determine the initial values of the unknown parameters, which is such that the optimization algorithm can efficiently and conveniently find a set of optimal solutions of the unknown parameters. Numerical simulation experiments on a five-level quantum system and a three-qubit system demonstrate that the proposed Lyapunov control scheme based on the particle swarm optimization algorithm has a good control effect.
Highlights
Since Tarn, Rabitz and Ong et al started studying quantum control theory in 1980s [1]–[3], research on quantum control theory has made great progress and breakthroughs and quantum control has been successfully applied in quantum optics, atomic physics, quantum chemistry, quantum computing, and quantum communication [4]–[8], e.g., the preparation and manipulation of pure states that act as information carriers in the process of quantum computing, the manipulation of single atoms in the field of atomic physics, the preparation of compressed coherent states in the field of quantum optics, and the preparation and manipulation of entangled states in quantum communication
This paper has solved the problem of high-probability population transfer of high-dimensional closed quantum systems under Lyapunov control to a non-isolated target eigenstate in the largest invariant set by using the particle swarm optimization algorithm
We have designed a control law via a Lyapunov function with unknown parameters and proposed a path planning method based on the energy-level connectivity graph to determine the inequality relationship satisfied by those unknown parameters
Summary
Since Tarn, Rabitz and Ong et al started studying quantum control theory in 1980s [1]–[3], research on quantum control theory has made great progress and breakthroughs and quantum control has been successfully applied in quantum optics, atomic physics, quantum chemistry, quantum computing, and quantum communication [4]–[8], e.g., the preparation and manipulation of pure states that act as information carriers in the process of quantum computing, the manipulation of single atoms in the field of atomic physics, the preparation of compressed coherent states in the field of quantum optics, and the preparation and manipulation of entangled states in quantum communication. For high-dimensional quantum systems, [30] proposed a multilayer Lyapunov control scheme based on the energy-level connectivity graph by analyzing the frequency selectivity characteristic of the Lyapunov control law and achieved a layer-by-layer high-probability population transfer to the target eigenstate. 1) We propose a novel quantum Lyapunov control scheme based on particle swarm optimization for high-dimensional closed quantum systems by combining Lyapunov control and optimization calculation and efficiently solve the problem of high-probability population transfer of the system to a non-isolated target eigenstate in the LaSalle invariant set.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
