Tangential Interpolatory Projection for Model Reduction of Linear Quantum Stochastic Systems

TL;DR

This paper introduces a tangential interpolatory projection method for reducing the complexity of linear quantum stochastic systems while preserving their physical realizability and passivity, with proven error bounds and practical examples.

Contribution

It develops a novel model reduction technique that maintains quantum system properties and provides error analysis, applicable to both active and passive systems.

Findings

Preserves physical realizability in reduced models

Provides error bounds for the reduction method

Demonstrates effectiveness through practical examples

Abstract

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.