Abstract

With rapid progresses in quantum technologies, quantum devices will be possibly networked at a much larger scale in the near future, over which effective analysis and synthesis are very demanding. In this paper, we construct signal flow graphs for linear quantum networks that are more concise than the traditional block diagram representation. Starting from two interconnected linear quantum systems, we present a bidirectional signal flow graph that describes the quantum action and backaction between them. Such signal flow graph can be naturally applied to non-Markovian systems with colored quantum noise inputs, and thus can include more general linear components such as spectral filters and dispersive quantum waveguides. These components can be integrated to build complex feedback networks via interconnections or serial products, where either direct or indirect coherent feedback loops are envisioned as bidirectional flows of quantum signals. Finally, we introduce the Riegle 9;s matrix gain rule to calculate transfer functions between source and sink nodes in a linear quantum network with multiple overlapping feedback loops. The theory provides a basis for synthesizing non-Markovian linear quantum feedback networks in the frequency-domain.