Mixed LQG and $H_\infty$ Coherent Feedback Control for Linear Quantum Systems

TL;DR

This paper develops methods for designing mixed LQG and H-infinity coherent feedback controllers for linear quantum systems, demonstrating effectiveness through cavity and DPA examples.

Contribution

It introduces two algorithms, LMI and genetic, for controller design in quantum systems, and establishes a lower bound for LQG control performance.

Findings

LMI and genetic algorithms effectively design controllers for quantum systems.

A lower bound for LQG control is established.

Algorithms are validated on passive and non-passive quantum systems.

Abstract

The purpose of this paper is to study the mixed linear quadratic Gaussian (LQG) and $H_\infty$ optimal control problem for linear quantum stochastic systems, where the controller itself is also a quantum system, often referred to as "coherent feedback controller". A lower bound of the LQG control is proved. Then two different methods, rank constrained linear matrix inequality (LMI) method and genetic algorithm are proposed for controller design. A passive system (cavity) and a non-passive one (degenerate parametric amplifier, DPA) demonstrate the effectiveness of these two proposed algorithms.