Network Synthesis of Linear Dynamical Quantum Stochastic Systems

TL;DR

This paper develops a systematic synthesis theory for linear dynamical quantum stochastic systems, enabling the construction and implementation of quantum controllers and circuits from basic quantum optical components.

Contribution

It introduces a method to construct complex quantum systems from simpler oscillators and discusses systematic synthesis in quantum optics.

Findings

Construction of quantum systems from interconnected oscillators

Systematic synthesis approach for quantum optical networks

Illustrative example demonstrating the synthesis process

Abstract

The purpose of this paper is to develop a synthesis theory for linear dynamical quantum stochastic systems that are encountered in linear quantum optics and in phenomenological models of linear quantum circuits. In particular, such a theory will enable the systematic realization of coherent/fully quantum linear stochastic controllers for quantum control, amongst other potential applications. We show how general linear dynamical quantum stochastic systems can be constructed by assembling an appropriate interconnection of one degree of freedom open quantum harmonic oscillators and, in the quantum optics setting, discuss how such a network of oscillators can be approximately synthesized or implemented in a systematic way from some linear and non-linear quantum optical elements. An example is also provided to illustrate the theory.