Characteristics Analysis and State Transfer for Non-Markovian Open Quantum Systems

Abstract

The weak-coupled two-level open quantum system described by non-Markovian Time-convolution-less master equation is investigated in this paper. The cut-off frequency c ω , coupling constant α and transition frequency 0 ω , which impact on the system's decay rate ( ) t β , coherence factor C and purity p , are investigated. The appropriate parameters used in system simulation experiments are determined by comparing analysis results of different values of parameters for the effects of system performance. The control laws used to transfer the system states are designed on the basis of the Lyapunov stability theorem. Numerical simulation experiments are implemented under the MATLAB environment. The features of the free evolution trajectory of the non-Markovian systems and the states transfer from a pure state to a desired pure state under the action of the proposed control laws are studied, respectively. By comparing the experimental results, the effectiveness of the proposed quantum Lyapunov control method applied to the state transfer in non-Markovian open quantum systems is verified. Meanwhile, the influences of different control parameters and cut-off frequencies on the system performance are analyzed.

Lyapunov-based control for the operator preparation in Markovian open quantum systems

“…According to (14) and (16), the convergence speed of the first item in V is identical with V dis , while the convergence speed of the second item is twice as much as V dis , thereby the total convergence speed of V is faster than that of V dis .…”

“…Meanwhile, the Lyapunov control method is also appropriate for the timevarying systems and nonlinear systems, and the designed control laws can ensure the stability of control systems, which is a simple and effective method to design control laws. For quantum systems, quantum Lyapunov methods have been studied to the problem of state transfer [14]- [17], state tracking [18], and so on. In this paper well employ this method to the operator preparation of a two level Markovian open quantum system.…”

State Transfer via On-Line State Estimation and Lyapunov-Based Feedback Control for a N-Qubit System

“…Most studies of quantum control are concerned with transferring the state of the system to a desired final state [9,10]. Quantum Lyapunov control (QLC) has been widely studied to control quantum systems for state preparation [11,12], trajectory tracking [13,14] and state transfer [15][16][17] with different Lyapunov functions [18,19]. In QLC, the control laws are designed by keeping the first-order time derivative of a selected Lyapunov function less than zero.…”

Implementation of Controlled‐NOT Gate by Lyapunov Control

“…Interestingly, Lyapunov control has attracted much attention recently . As a powerful quantum control technique, it has the advantages of simplicity and flexibility in designing control fields.…”