arXiv:1609.07947

Robustly Stable Uncertain Linear Stochastic Quantum Systems: Definition and Analysis

Peyman Azodi, Alireza Khayatian, Peyman Setoodeh

Published Sep 26, 2016• 1 citation

Abstract

This paper presents a systematic method to analyze the robustness of uncertain linear stochastic quantum systems . Uncertainties are studied in the optical realization, where all the corresponding parameters are affected. First, robustly stable LSQSs are defined and then, by the use of the uncertainty decomposition algorithm, robust stability of the LSQSs is analyzed within two different approaches. In the first approach, a sufficient small-gain-like theorem is presented and in the second approach, another sufficient condition for robust stability based on Lyapunov theory is presented. The robust stability analysis is validated via a case study.

Related papers

Uncertainty decomposition of uncertain linear stochastic quantum networks

Peyman Azodi, Alireza Khayatian, Mohammad Hassan Asemani

This paper presents a systematic method to analyze uncertain linear stochastic quantum systems (LSQS), when uncertainties are defined in optical realization. A decomposition theorem is stated which separates the nominal and uncertain parts of a general uncertain LSQS, in cascaded connection. This decomposition is further extended to state space realization of LSQS. An illustrative example clarifies the effectiveness of the proposed robust stability analysis.

Sep 26, 20160 citations

3 Robust Stability of Quantum Systems with Nonlinear Dynamic Uncertainties

Ian R. Petersen

This paper considers the problem of robust stability for a class of uncertain nonlinear quantum systems subject to unknown perturbations in the system Hamiltonian. The nominal system is a linear quantum system defined by a linear vector of coupling operators and a quadratic Hamiltonian. This paper extends previous results on the robust stability of nonlinear quantum systems to allow for quantum systems with dynamic uncertainties. These dynamic uncertainties are required to satisfy a certain quantum stochastic integral quadratic constraint. The robust stability condition is given in terms of a strict bounded real condition. This result is applied to the robust stability analysis of an optical parametric amplifier.

Aug 16, 20167 citations

Robust stability of quantum systems with nonlinear dynamic uncertainties

Ian R. Petersen

arXiv:1309.0576IEEE Conference on Decision and Control (CDC)Dec 1, 20136 citations

Uncertainty decomposition of quantum networks in SLH framework

Peyman Azodi, Alireza Khayatian, Peyman Setoodeh +1 more

This paper presents a systematic method to decompose uncertain linear quantum input-output networks into uncertain and nominal subnetworks, when uncertainties are defined in SLH representation. To this aim, two decomposition theorems are stated, which show how an uncertain quantum network can be decomposed into nominal and uncertain subnetworks in cascaded connection and how uncertainties can be translated from SLH parameters into state-space parameters. As a potential application of the proposed decomposition scheme, robust stability analysis of uncertain quantum networks is briefly introduced. The proposed uncertainty decomposition theorems take account of uncertainties in all three parameters of a quantum network and bridge the gap between SLH modeling and state-space robust analysis theory for linear quantum networks.

arXiv:1609.07946Sep 26, 20160 citations

Coherent robust H∞control of uncertain linear quantum stochastic systems

Chengdi Xiang, Ian R. Petersen, Daoyi Dong

This paper considers a class of uncertain linear quantum systems subject to uncertain perturbations in the system Hamiltonian. We present a method to design a coherent robust H∞controller so that the closed loop system is robustly stable and achieves a prescribed level of disturbance attenuation with all the admissible uncertainties.

IEEE Conference on Decision and Control (CDC)Dec 1, 20154 citations

Robust stability analysis of an optical parametric amplifier quantum system

Ian R. Petersen

This paper considers the problem of robust stability for a class of uncertain nonlinear quantum systems subject to unknown perturbations in the system Hamiltonian. The case of a nominal linear quantum system is considered with non-quadratic perturbations to the system Hamiltonian. The paper extends recent results on the robust stability of nonlinear quantum systems to allow for non-quadratic perturbations to the Hamiltonian which depend on multiple parameters. A robust stability condition is given in terms of a strict bounded real condition. This result is then applied to the robust stability analysis of a nonlinear quantum system which is a model of an optical parametric amplifier.

arXiv:1303.6025Asian Control Conference (ASCC)Jun 1, 20136 citations