Research On Hamiltonian Identification For Quantum Systems Via Learning Control

With the rapid development of science and technology,quantum information technology,as a technology of the future,has attracted much attention because of its powerful information processing ability.Quantum control is a new discipline formed by the theory of cybernetics and quantum mechanics.It mainly studies the dynamics evolution of quantum system and its regulation mechanism from the viewpoint of cybernetics and system theory.With the development of quantum information technology such as quantum communication and quantum computing,the development of quantum control discipline is becoming more and more necessary to provide theoretical and technical support.The study of quantum control theory will provide important theoretical support for the development of quantum communication and quantum computation to practical applications.In quantum control problems,parameter identification of quantum system Hamiltonian is a core task,Hamiltonian parameter identification is of great significance for the state evolution and control of quantum systems.In this paper,we adopt a method based on sample learning control(Sampling-based Learning Control,SLC)and gradient flow algorithm to identify the Hamiltonian parameters of quantum systems.First of all,the parameters given a guess and guess according to the design by SLC to get the optimal control strategy,active control of the system from a known initial state to a target state easily identified by quantum measurement,if the optimal control strategy for system to be identified,with higher fidelity to the target state control the speculation,accord with the real values of the parameters,otherwise the speculation does not conform to the true value of the parameter.In order to ensure the reliability and accuracy of parameter identification,a cross validation method is used to determine the required estimated Hamiltonian parameter values in the interval,and a two point search method is used to refine the interval and identify the final Hamiltonian parameters with a certain precision.In numerical simulation,we apply the proposed method to Hamiltonian parameter identification for typical quantum systems,including:identification the parameter of the two-level quantum system Hamiltonian and the three-level system Hamiltonian.The experimental results demonstrate the effectiveness of the proposed method for identification of Hamiltonian parameters based on quantum ensemble classification.