Entanglement Creations and Quantum Gate Implementations of Spin Qubits With Lyapunov Control

In this paper, we propose a scheme for the entanglement creations and the quantum gate implementations of spin qubits via Lyapunov control. We first show that three types of Bell states can be generated in one step with the traditional Lyapunov control. After that, the traditional Lyapunov control is generalized with the design of two Lyapunov functions that characterize the distance between two unitary operators. Thus, the Lyapunov control can be also used in constructing desired unitary operations. The performance of the entanglement creations and the quantum gate implementations are both estimated via numerical simulations. The results show the scheme holds robustness against the errors of the fields and couplings. As the generalization of Lyapunov control can not only be used in spin systems, the scheme may benefit the quantum information processing in different quantum systems.