Convergent control strategy of state in open quantum systems

Christian Arenz

Shuang Cong, Fei Yang

A control strategy of quantum states of open quantum system based on Lyapunov method is proposed. On the basis of choosing the average of observable operators as a Lyapunov function, the control laws are designed in interaction picture. We analyze the largest invariant set of the controlled system via Barbalat's Lemma. Based on some assumptions of Hamiltonians, we propose a sufficient condition of the observable operator to guarantee the convergence of the open quantum system, and proof that the proposed strategy can make any pure target state in decoherence-free subspace be globally asymptotic stable under the sufficient condition. Also, we provide a method to construct the observable operator via Schmidt orthogonalization. Numerical experiments on a three-level system validate the effectiveness of the proposed control strategy.

Fei Yang

A convergent state control strategy of open quantum system based on Lyapunov method is proposed for the target state being a pure state in decoherence-free subspaces. Based on the assumptions of all the transition frequencies being different and all the levels being directly coupled,a sufficient condition is proposed for the observation operator to make that the largest invariant set only contains target state.On the basis of choosing the average of observable operators as a Lyapunov function,the control laws are designed in interaction picture and the largest invariant set of the controlled system is analyzed via Barbalat's Lemma. It is shown that any pure target state in decoherence-free subspace is globally asymptotic stable under the sufficient condition given,and the system controlled could be transferred to target state from arbitrary initial state.Also,a method is provided to construct the observation operator via Schmidt orthogonalization.Numerical experiments on a three-level system verify the validity of the proposed control strategy.

Alexander Nikolaevich Pechen, HERSCHEL A. RABITZ

Daniel A. Lidar, Paolo Zanardi A, Lorenzo Campos Venuti

Shahid Qamar, Shuang Cong, Bilal Riaz

In this paper, a Lyapunov-based feedback control (LFC) is proposed for the state transfer of a two-level stochastic quantum system. The quantum state is described in the Cartesian coordinate system. An exponential function is selected as the Lyapunov function to ensure the stability of the system. The Lyapunov-based feedback control strategy is designed according to the stochastic Lyapunov stability theorem. Numerical simulations results show that the proposed LFC strategy has the ability to transfer the stochastic system from any initial mixed state to the desired eigenstate, and the LFC has high convergence rate and high state transfer fidelity.