Coherent feedback $H^\infty$ control of quantum linear systems
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Quantum Physics arXiv:2604.06574 (quant-ph) [Submitted on 8 Apr 2026] Title:Coherent feedback $H^\infty$ control of quantum linear systems Authors:Guofeng Zhang, Ian R. Petersen View a PDF of the paper titled Coherent feedback $H^\infty$ control of quantum linear systems, by Guofeng Zhang and Ian R. Petersen View PDF Abstract:The purpose of this paper is to investigate the coherent feedback $H^\infty$ control problem for linear quantum systems. A key contribution is a simplified design methodology that guarantees closed-loop stability and a prescribed level of disturbance attenuation. It is shown that for general linear quantum systems, a physically realizable quantum controller can be obtained by solving at most four Lyapunov equations. In the passive case, a necessary and sufficient condition is provided in terms of two uncoupled pairs of Lyapunov equations. These results represent a significant simplification over the standard approach, which requires solving two coupled algebraic Riccati equations. The effectiveness of the proposed method is demonstrated through two typical quantum optical devices: an empty optical cavity and a degenerate parametric amplifier. These results provide a computationally efficient procedure for the robust and optimal control of quantum optical and optomechanical systems. Comments: Subjects: Quantum Physics (quant-ph); Systems and Control (eess.SY) Cite as: arXiv:2604.06574 [quant-ph] (or arXiv:2604.06574v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.06574 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Guofeng Zhang [view email] [v1] Wed, 8 Apr 2026 01:38:12 UTC (158 KB) Full-text links: Access Paper: View a PDF of the paper titled Coherent feedback $H^\infty$ control of quantum linear systems, by Guofeng Zhang and Ian R. PetersenView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-04 Change to browse by: cs cs.SY eess eess.SY References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)