H2 Model Reduction for Completely Passive Linear Quantum Systems

Passive linear quantum systems are widely encountered in quantum optics due to their inherent stability and energy‐dissipation characteristics. With the increasing deployment of such systems, the dimensions of passive linear quantum networks can grow rapidly, thereby increasing the computational burden of feedback control and estimation. Hence, model reduction methods should be developed to construct lower‐order models while preserving physical realizability, a constraint absent from classical model reduction. This article proposes an ‐norm‐based model reduction approach for completely passive linear quantum systems, which yields a physically realizable reduced‐order model that closely approximates the original system dynamics. This is achieved by explicitly incorporating the physical realizability conditions that preserve the quantum nature of the reduced system into the model reduction problem. Unlike classical model reduction settings, these physical realizability conditions introduce nonlinear constraints into the optimization problem. To handle these constraints, an observability‐Gramian‐based optimization formulation is developed. By converting the nonlinear equality constraints into inequality constraints, we enable an alternating direction method of multiplier (ADMM)‐iterative LMI (ILMI) algorithm framework to be constructed for solving the model reduction optimization problem. In contrast to existing methods that primarily provide a posteriori criteria for evaluating approximation performance, the proposed approach directly incorporates the error into the construction of the reduced‐order model. Two numerical examples, involving a three‐oscillator series‐connected system and a large‐scale chain‐connected quantum system, consistently demonstrate that the proposed method preserves the dominant input–output characteristics of the original systems.