The SLH framework for modeling quantum input-output networks

TL;DR

The paper reviews the SLH framework for modeling quantum input-output networks, emphasizing its modularity, composition rules, and recent extensions, to advance understanding and design of complex quantum systems.

Contribution

It provides a comprehensive overview of the SLH framework, including recent extensions and applications to integrated quantum networks, highlighting its modeling capabilities and limitations.

Findings

SLH framework enables modular modeling of quantum networks.

Algebraic rules allow arbitrary network composition.

Extensions expand the framework's applicability to complex systems.

Abstract

Many emerging quantum technologies demand precise engineering and control over networks consisting of quantum mechanical degrees of freedom connected by propagating electromagnetic fields, or quantum input-output networks. Here we review recent progress in theory and experiment related to such quantum input-output networks, with a focus on the SLH framework, a powerful modeling framework for networked quantum systems that is naturally endowed with properties such as modularity and hierarchy. We begin by explaining the physical approximations required to represent any individual node of a network, eg. atoms in cavity or a mechanical oscillator, and its coupling to quantum fields by an operator triple $(S,L,H)$. Then we explain how these nodes can be composed into a network with arbitrary connectivity, including coherent feedback channels, using algebraic rules, and how to derive the dynamics of network components and output fields. The second part of the review discusses several extensions to the basic SLH framework that expand its modeling capabilities, and the prospects for modeling integrated implementations of quantum input-output networks. In addition to summarizing major results and recent literature, we discuss the potential applications and limitations of the SLH framework and quantum input-output networks, with the intention of providing context to a reader unfamiliar with the field.