Tangential interpolatory projection for model reduction of completely passive linear quantum stochastic systems

This paper presents a tangential interpolatory projection model reduction method for the class of completely passive linear quantum stochastic systems, often encountered in quantum optics and related fields. We show that the important physical realizability property of the full-order system is preserved through the interpolatory projection approximation. Sufficient conditions that guarantee asymptotic stability and minimality of the reduced-order approximation are established. We also present an optimization based routine for selection of interpolation points and propose a heuristic approach to select tangent directions, the key elements of the interpolatory projection method for multiple-input multiple-output systems. An example is presented to illustrate the utility of our proposed approach.