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Chinese Control Conference (CCC)

A unified trajectory tracking control for of N-dimensional closed quantum systems

Yu-Qiu Zhou, Shuang Cong, Fangfang Meng

Published Jul 25, 2022• 0 citations
Publisher

Abstract

A Lyapunov-based unified control method for quantum state trajectory tracking control is proposed in this paper. By inducing the error between the controlled state and the target state as error state, the trajectory tracking control problem of the quantum system is transformed into the regular control problem of systematic error state. Through an interaction picture transformation, the spin effect is eliminated. The unified control method is designed in the trajectory tracking control for the quantum system which can also solve the problems caused by the non-ideal quantum systems, where the free Hamiltonian of the system is not strongly regular and (or) not commutes with the target state, and (or) the control Hamiltonian is not fully connected. The unified trajectory tracking control proposed can drive the system from an arbitrary initial state to an arbitrary target state and achieve the purpose of tracking. The numerical simulation experiments and results analyses are given.

DOI
10.23919/ccc55666.2022.9901580

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A Lyapunov-based approach of trajectory tracking in Liouville equation for quantum systems is proposed. By selecting density matrix of controlled system as the system state, and defining the error between controlled state and target one as an error state, the paper regards this error as a new controlled state of system. In such a way the quantum state trajectory tracking problem is changed into the state regulation problem by driving the error state to zero. The control law is designed according to the Lyapunov stability theorem, which can be applied to track different kinds of quantum states including pure state, superposition state and mixed-state. Finally, numerical simulation experiments and results analysis are given.
A control method for trajectory tracking in non-Markovian open quantum systems is proposed in this paper. By inducing the error between the controlled state and the target state as the error state, the trajectory tracking problem of the quantum system is divided into two steps, which the regulation control of the error state and the keeping control of the error state. With the help of Lyapunov stability theorem, the tracking control law is designed to enable the non-Markovian open quantum system to track the evolutionary target quantum system over time. The control parameters are adjusted by simulation experiments, and the numerical simulation experiments are carried out. The tracking control of the quantum system when the initial states of the controlled system and the initial states of the target system are superposition states is implemented in simulation experiments. The experimental results demonstrate the feasibility of the proposed control method and the analysis is given.
A Lyapunov-based unified control method for closed quantum systems is proposed, which can transfer the state of closed quantum system from any initial state to any desired target state. In particular, the proposed control method can work under the conditions that free Hamiltonian of the non-ideal quantum system is not strongly regular, and (or) the Hamiltonian is not fully connected. The simulation experiments of the state transition control between different states of three, four and five qubit systems are carried out to verify that the proposed control method is suitable for all kinds of non-ideal quantum systems and the advantages of Lyapunov-based unified control method. The design process of the proposed method, the calculation process of each parameter in each experiment and the analysis of each experimental result are given in detail.
For quantum state trajectory tracking of density matrix in Liouville equation of quantum systems, with the help of concept in quantum system control, one can apply unitary transformation both to controlled system and free-evolutionary target system such as to change the time-variant and non-stationary target system into a stationary state. Therefore, the quantum state trajectory tracking problem becomes a steering one. State steering control law of the system transformed is designed by means of the Lyapunov stability theorem. Finally, numerical simulation experiments are given for a five-level energy quantum system. The comparison analysis of original system’s trajectory tracking with other method illustrates the advantage in control time of the method proposed.
Abstract An online estimated state feedback control for trajectory tracking in stochastic open quantum systems is proposed in this paper, which is based on the Lyapunov‐based control method. By inducing the error between the controlled state, and the target state as the error state, the trajectory tracking problem of the quantum system is transformed into the error state transition control problem. The quantum state online estimation method QST‐OADM is applied to estimate the state of the error state system online, and the tracking control laws are designed by using the quantum Lyapunov stability theorem for driving the stochastic open quantum system from an arbitrary initial state to an arbitrary trajectory. The numerical simulation experiments and results analyses are given.
Based on model reference adaptive control theory, we design a control law for a given closed quantum system model by means of the Lyapunov stability theorem by choosing a time-varying objective function as the reference model. Meanwhile, the problems of singularities and a very large value of the control fields during the tracking are solved by using an adaptive tracking algorithm. The simulation experiments realize the tracking task from the arbitrary initial states to the time-varying objective function. Under the effect of control law, the state of control system can track from the arbitrary initial state to the state of objective system. Simulation results demonstrate the ability of the control method proposed to adaptively adjust the control laws and real-time track dynamic target system.