Coherent feedback $H^\infty$ control of quantum linear systems
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911574544875520 |
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| author | Zhang, Guofeng Petersen, Ian R. |
| author_facet | Zhang, Guofeng Petersen, Ian R. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_06574 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Coherent feedback $H^\infty$ control of quantum linear systems Zhang, Guofeng Petersen, Ian R. Quantum Physics Systems and Control 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. |
| title | Coherent feedback $H^\infty$ control of quantum linear systems |
| topic | Quantum Physics Systems and Control |
| url | https://arxiv.org/abs/2604.06574 |