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Updated: May 17, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Robust stability of uncertain linear quantum systems.

Ian R Petersen¹, Valery Ugrinovskii, Matthew R James

¹School of Engineering and Information Technology, University of New South Wales at the Australian Defence Force Academy, Canberra, Australian Capital Territory, Australia. i.r.petersen@gmail.com

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences

|October 24, 2012

Summary

This summary is machine-generated.

This study addresses robust stability in uncertain linear quantum systems with Hamiltonian perturbations. A strict bounded real condition is established for stability analysis, ensuring system reliability despite uncertainties.

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Last Updated: May 17, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Area of Science:

Quantum physics
Control theory
System stability

Background:

Linear quantum systems are fundamental in quantum mechanics and quantum information.
Understanding system stability under perturbations is crucial for reliable quantum technologies.
Uncertainties in the system Hamiltonian can arise from environmental interactions or imperfect control.

Purpose of the Study:

To investigate the robust stability of uncertain linear quantum systems.
To develop a stability condition that accounts for unknown perturbations in the system Hamiltonian.
To analyze the impact of quadratic perturbations on system stability.

Main Methods:

Formulation of the robust stability problem for linear quantum systems.
Analysis of quadratic perturbations to the system Hamiltonian.
Derivation of a stability condition based on the bounded real lemma.

Main Results:

A novel robust stability condition is derived for the considered class of systems.
The condition is shown to be both necessary and sufficient under certain assumptions.
The results provide a mathematical framework for designing stable quantum systems.

Conclusions:

The strict bounded real condition is effective for ensuring robust stability in uncertain linear quantum systems.
This work contributes to the theoretical foundations of quantum system control and design.
Future research can explore extensions to nonlinear quantum systems or different types of perturbations.