A Quasi-separation Principle and Newton-like Scheme for Coherent Quantum LQG Control

TL;DR

This paper develops a new approach for designing optimal coherent quantum controllers in LQG problems, leveraging a quasi-separation principle and a Newton-like iterative scheme to ensure physical realizability and optimality.

Contribution

It introduces a quasi-separation principle for quantum controller gain matrices and a Newton-like method for solving the associated optimal control equations.

Findings

Established a quasi-separation principle for quantum controllers.

Proposed a Newton-like iterative scheme for controller optimization.

Ensured physical realizability of controllers through Hamiltonian parameterization.

Abstract

This paper is concerned with constructing an optimal controller in the coherent quantum Linear Quadratic Gaussian problem. A coherent quantum controller is itself a quantum system and is required to be physically realizable. The use of coherent control avoids the need for classical measurements, which inherently entail the loss of quantum information. Physical realizability corresponds to the equivalence of the controller to an open quantum harmonic oscillator and relates its state-space matrices to the Hamiltonian, coupling and scattering operators of the oscillator. The Hamiltonian parameterization of the controller is combined with Frechet differentiation of the LQG cost with respect to the state-space matrices to obtain equations for the optimal controller. A quasi-separation principle for the gain matrices of the quantum controller is established, and a Newton-like iterative scheme for numerical solution of the equations is outlined.