Coherent feedback $H^\infty$ control of quantum linear systems

Quantum Physics [Submitted on 8 Apr 2026] Coherent feedback H^\infty control of quantum linear systems Guofeng Zhang, Ian R. Petersen 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: 13 pages, 3 figures. Comments are welcome! 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 Submission history From: Guofeng Zhang [view email] [v1] Wed, 8 Apr 2026 01:38:12 UTC (158 KB) Access Paper: view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 Change to browse by: cs cs.SY eess eess.SY References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)