Robust Stability of Uncertain Quantum Input-Output Networks

TL;DR

This paper develops a systematic approach to analyze the stability and robustness of uncertain quantum input-output networks using uncertainty decomposition, small-gain theorem, and Lyapunov methods, including LMI-based criteria.

Contribution

It introduces a general uncertainty framework in the SLH formalism and derives new sufficient conditions for robust stability using two distinct methods.

Findings

Provides generalized small-gain theorem for quantum networks

Reformulates stability analysis as LMI feasibility problem

Offers systematic tools for robustness assessment in quantum networks

Abstract

This paper presents a systematic method to analyze stability and robustness of uncertain Quantum Input-Output Networks (QIONs). A general form of uncertainty is introduced into quantum networks in the SLH formalism. Results of this paper are built up on the notion of uncertainty decomposition wherein the quantum network is decomposed into nominal (certain) and uncertain sub-networks in cascade connection. Sufficient conditions for robust stability are derived using two different methods. In the first approach, a generalized small-gain theorem is presented and in the second approach, robust stability is analyzed within the framework of Lyapunov theory. In the second method, the robust stability problem is reformulated as feasibility of a Linear Matrix Inequality (LMI), which can be examined using the well-established systematic methods in the literature.