Parameterization of Stabilizing Linear Coherent Quantum Controllers

TL;DR

This paper extends classical control parameterization techniques to linear coherent quantum controllers, enabling stabilization and control design for quantum harmonic oscillators using frequency domain methods.

Contribution

It introduces a Youla-Kučera parameterization for quantum controllers, addressing stabilization and control problems in the quantum domain with a new frequency domain approach.

Findings

Parameterization of stabilizing quantum controllers in the frequency domain

Formulation of quantum weighted H2 and H-infinity control problems

Proposed gradient descent scheme for quantum H2 control

Abstract

This paper is concerned with application of the classical Youla-Ku\v{c}era parameterization to finding a set of linear coherent quantum controllers that stabilize a linear quantum plant. The plant and controller are assumed to represent open quantum harmonic oscillators modelled by linear quantum stochastic differential equations. The interconnections between the plant and the controller are assumed to be established through quantum bosonic fields. In this framework, conditions for the stabilization of a given linear quantum plant via linear coherent quantum feedback are addressed using a stable factorization approach. The class of stabilizing quantum controllers is parameterized in the frequency domain. Also, this approach is used in order to formulate coherent quantum weighted $H_2$ and $H_\infty$ control problems for linear quantum systems in the frequency domain. Finally, a projected gradient descent scheme is proposed to solve the coherent quantum weighted $H_2$ control problem.