Sliding Mode Control of Two-Level Quantum Systems

This paper proposes a robust control method based on sliding mode design for two-level quantum systems with bounded uncertainties. An eigenstate of the two-level quantum system is identified as a sliding mode. The objective is to design a control law to steer the system's state into the sliding mode domain and then maintain it in that domain when bounded uncertainties exist in the system Hamiltonian. We propose a controller design method using the Lyapunov methodology and periodic projective measurements. In particular, we give conditions for designing such a control law, which can guarantee the desired robustness in the presence of the uncertainties. The sliding mode control method has potential applications to quantum information processing with uncertainties.Comment: 29 pages, 4 figures, accepted by Automatic

Effects of uncertainties and errors on Lyapunov control

Lyapunov control (open-loop) is often confronted with uncertainties and errors in practical applications. In this paper, we analyze the robustness of Lyapunov control against the uncertainties and errors in quantum control systems. The analysis is carried out through examinations of uncertainties and errors, calculations of the control fidelity under influences of the certainties and errors, as well as discussions on the caused effects. Two examples, a closed control system and an open control system, are presented to illustrate the general formulism.Comment: 4 pages, 5 figure

Ground-state Stabilization of Open Quantum Systems by Dissipation

Control by dissipation, or environment engineering, constitutes an important methodology within quantum coherent control which was proposed to improve the robustness and scalability of quantum control systems. The system-environment coupling, often considered to be detrimental to quantum coherence, also provides the means to steer the system to desired states. This paper aims to develop the theory for engineering of the dissipation, based on a ground-state Lyapunov stability analysis of open quantum systems via a Heisenberg-picture approach. Algebraic conditions concerning the ground-state stability and scalability of quantum systems are obtained. In particular, Lyapunov stability conditions expressed as operator inequalities allow a purely algebraic treatment of the environment engineering problem, which facilitates the integration of quantum components into a large-scale quantum system and draws an explicit connection to the classical theory of vector Lyapunov functions and decomposition-aggregation methods for control of complex systems. The implications of the results in relation to dissipative quantum computing and state engineering are also discussed in this paper.Comment: 18 pages, to appear in Automatic

Lyapunov Control on Quantum Open System in Decoherence-free Subspaces

A scheme to drive and manipulate a finite-dimensional quantum system in the decoherence-free subspaces(DFS) by Lyapunov control is proposed. Control fields are established by Lyapunov function. This proposal can drive the open quantum system into the DFS and manipulate it to any desired eigenstate of the free Hamiltonian. An example which consists of a four-level system with three long-lived states driven by two lasers is presented to exemplify the scheme. We have performed numerical simulations for the dynamics of the four-level system, which show that the scheme works good.Comment: 5 pages, 6 figure