Robust Stability of Quantum Systems with Nonlinear Dynamic Uncertainties

TL;DR

This paper establishes conditions for the robust stability of uncertain nonlinear quantum systems with dynamic uncertainties, extending previous results and applying them to optical parametric amplifiers.

Contribution

It introduces a new stability criterion for quantum systems with dynamic uncertainties satisfying a quantum stochastic integral quadratic constraint.

Findings

Derived a strict bounded real condition for stability

Extended previous stability results to systems with dynamic uncertainties

Applied the stability condition to an optical parametric amplifier

Abstract

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.