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Chinese Physics Letters

Robust Set Stabilization and Its Instances for Open Quantum Systems

Ming Zhang, Zairong Xi, Tzyh‐Jong Tarn

Published Sep 1, 2018• 3 citations
Publisher

Abstract

We propose and discuss a novel concept of robust set stabilization by permissible controls; this concept is helpful when dealing with both a priori information of model parameters and different permissible controls including quantum measurements.Both controllability and stabilization can be regarded as the special case of the novel concept.An instance is presented for a kind of uncertain open quantum systems to further justify this generalized concept.It is underlined that a new type of hybrid control based on periodically perturbed projective measurements can be the permissible control of uncertain open quantum systems when perturbed projective measurements are available.The sufficient conditions are given for the robust set stabilization of uncertain quantum open systems by the hybrid control, and the design of the hybrid control is reduced to selecting the period of measurements.

DOI
10.1088/0256-307x/35/9/090301

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We propose and discuss a novel concept of robust set stabilization by permissible controls; this concept is helpful when dealing with both a priori information of model parameters and different permissible controls including quantum measurements.Both controllability and stabilization can be regarded as the special case of the novel concept.An instance is presented for a kind of uncertain open quantum systems to further justify this generalized concept.It is underlined that a new type of hybrid control based on periodically perturbed projective measurements can be the permissible control of uncertain open quantum systems when perturbed projective measurements are available.The sufficient conditions are given for the robust set stabilization of uncertain quantum open systems by the hybrid control, and the design of the hybrid control is reduced to selecting the period of measurements.
This paper considers the problem of robust stability for a class of uncertain quantum systems subject to unknown perturbations in the system Hamiltonian. Some general stability results are given for different classes of perturbations to the system Hamiltonian. Then, the special case of a nominal linear quantum system is considered with either quadratic or non-quadratic perturbations to the system Hamiltonian. In this case, robust stability conditions are given in terms of strict bounded real conditions.
We exploit how to overcome phase damping decoherence when the phase damping parameters are uncertain. It is shown that the “relaxed” control goal may be achieved by combing simple open-loop coherent control with periodic projective measurements. Both the sufficient conditions and constructive design procedures are presented. The control design is reduced to selecting the period of projective measurements and fidelity-truncated time based on two lower-bound functions for both probability and fidelity performance. When both probability and fidelity performances are specified, the stabilization time is further maximized by searching the “optimal” period of projective measurements. It is also exemplified that larger uncertainties may lead to shorter stabilization time for the given performance level.
We investigate the impact of undesired Markovian couplings to external systems on the stabilization towards pure states or subspaces of continuously monitored quantum systems under open-loop and feedback control protocols. In particular, we provide sufficient conditions on perturbations to maintain stability of the target and demonstrate the boundedness in mean of the solutions of perturbed systems under open-loop protocols. Effect on the stability of feedback protocols is also analyzed. This work is a step toward a comprehensive robustness analysis of measurement-based control of quantum systems with respect to model perturbations.
This paper considers a Popov type approach to the problem of robust stability for a class of uncertain linear quantum systems subject to unknown perturbations in the system Hamiltonian. A general stability result is given for a general class of perturbations to the system Hamiltonian. Then, the special case of a nominal linear quantum system is considered with quadratic perturbations to the system Hamiltonian. In this case, a robust stability condition is given in terms of a frequency domain condition which is of the same form as the standard Popov stability condition.
This paper considers a Popov type approach to the problem of robust stability for a class of uncertain linear quantum systems subject to unknown perturbations in the system Hamiltonian. A general stability result is given for a general class of perturbations to the system Hamiltonian. Then, the special case of a nominal linear quantum system is considered with quadratic perturbations to the system Hamiltonian. In this case, a robust stability condition is given in terms of a frequency domain condition which is of the same form as the standard Popov stability condition.