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arXiv:2604.06574

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

Guofeng Zhang, Ian R. Petersen

quant-pheess.SYSubmitted Apr 8, 2026• Announced Apr 9, 2026• 0 citations
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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.

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The purpose of this paper is to study the mixed linear quadratic Gaussian (LQG) and H∞ optimal control problem for linear quantum stochastic systems, where the controller itself is also a quantum system, often referred to as ‘coherent feedback controller’. A lower bound of the LQG control is proved. Then two different methods, rank-constrained linear matrix inequality method and genetic algorithm are for controller design. A passive system (cavity) and a non-passive one (degenerate parametric amplifier) demonstrate the effectiveness of these two proposed algorithms.