Tangential Interpolatory Projection for Model Reduction of Linear Quantum Stochastic Systems
For researchers in quantum optics and quantum control, this provides a physically-constrained model reduction technique that preserves quantum mechanical properties, though the approach is incremental over classical interpolatory projection methods.
This paper develops a model reduction method for linear quantum stochastic systems that matches input-output responses at selected frequencies while preserving physical realizability. The method achieves error bounds and is demonstrated on active and passive quantum systems.
This paper presents a model reduction method for the class of linear quantum stochastic systems often encountered in quantum optics and their related fields. The approach is proposed on the basis of an interpolatory projection ensuring that specific input-output responses of the original and the reduced-order systems are matched at multiple selected points (or frequencies). Importantly, the physical realizability property of the original quantum system imposed by the law of quantum mechanics is preserved under our tangential interpolatory projection. An error bound is established for the proposed model reduction method and an avenue to select interpolation points is proposed. A passivity preserving model reduction method is also presented. Examples of both active and passive systems are provided to illustrate the merits of our proposed approach.