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This paper is concerned with constructing an optimal controller in thecoherent quantum Linear Quadratic Gaussian problem. A coherent quantumcontroller is itself a quantum system and is required to be physicallyrealizable. The use of coherent control avoids the need for classicalmeasurements, which inherently entail the loss of quantum information. Physicalrealizability corresponds to the equivalence of the controller to an openquantum harmonic oscillator and relates its state-space matrices to theHamiltonian, coupling and scattering operators of the oscillator. TheHamiltonian parameterization of the controller is combined with Frechetdifferentiation of the LQG cost with respect to the state-space matrices toobtain equations for the optimal controller. A quasi-separation principle forthe gain matrices of the quantum controller is established, and a Newton-likeiterative scheme for numerical solution of the equations is outlined.

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