Coherent H^(∞)Control for Linear Quantum Systems With Uncertainties in the Interaction Hamiltonian

This work conducts robust H^(∞)analysis for a class of quantum systems subject to perturbations in the interaction Hamiltonian.A necessary and sufficient condition for the robustly strict bounded real property of this type of uncertain quantum system is proposed.This paper focuses on the study of coherent robust H^(∞)controller design for quantum systems with uncertainties in the interaction Hamiltonian.The desired controller is connected with the uncertain quantum system through direct and indirect couplings.A necessary and sufficient condition is provided to build a connection between the robust H^(∞)control problem and the scaled H^(∞)control problem.A numerical procedure is provided to obtain coefficients of a coherent controller.An example is presented to illustrate the controller design method.

Generalized control of quantum systems in the frame of vector treatment

For the state control problem in finite-dimensional quantum systems with any initial state and a goal eigenstate, this paper studies the design method of control laws via the Lyapunov technology and in the vector frame, which ensures the convergence of any initial state toward the goal state. The stability of the closed-loop system in the goal eigenstate is analyzed and proven via the invariance principle. The simulation experiment on a spin-1/2 system shows the effectiveness of the designed control laws.

Feedback stabilization of N-dimensional stochastic quantum systems based on bang-bang control

For an N-dimensional quantum system under the influence of continuous measurement, this paper presents a switching control scheme where the control law is of bang-bang type and achieves asymptotic preparation of an arbitrarily given eigenstate of a non-degenerate and degenerate measurement operator, respectively. In the switching control strategy, we divide the state space into two parts： a set containing a target state, and its complementary set. By analyzing the stability of the stochastic system model under consideration, we design a constant control law and give some conditions that the control Hamiltonian satisfies so that the system trajectories in the complementary set converge to the set which contains the target state. Further, for the case of a non-degenerate measurement operator, we show that the system trajectories in the set containing the target state will automatically converge to the target state via quantum continuous measurement theory; while for the case of a degenerate measurement operator, the corresponding system trajectories will also converge to the target state via the construction of the control Hamiltonians. The convergence of the whole closed-loop systems under the cases of a non-degenerate and a degenerate measurement operator is strictly proved. The effectiveness of the proposed switching control scheme is verified by the simulation experiments on a finite-dimensional angular momentum system and a two-qubit system.