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arXiv:1609.07946

Uncertainty decomposition of quantum networks in SLH framework

Peyman Azodi, Alireza Khayatian, Peyman Setoodeh, Mohammad Hassan Asemani

Published Sep 26, 2016• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.1609.07946

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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.
Summary 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.
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.
Many emerging quantum technologies demand precise engineering and control over networks consisting of quantum mechanical degrees of freedom connected by propagating electromagnetic fields, or quantum input-output networks. Here we review recent progress in theory and experiment related to such quantum input-output networks, with a focus on the SLH framework, a powerful modeling framework for networked quantum systems that is naturally endowed with properties such as modularity and hierarchy. We begin by explaining the physical approximations required to represent any individual node of a network, e.g. atoms in cavity or a mechanical oscillator, and its coupling to quantum fields by an operator triple (S,L,H). Then we explain how these nodes can be composed into a network with arbitrary connectivity, including coherent feedback channels, using algebraic rules, and how to derive the dynamics of network components and output fields. The second part of the review discusses several extensions to the basic SLH framework that expand its modeling capabilities, and the prospects for modeling integrated implementations of quantum input-output networks. In addition to summarizing major results and recent literature, we discuss the potential applications and limitations of the SLH framework and quantum input-output networks, with the intention of providing context to a reader unfamiliar with the field.
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.
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.