Quantum Noises, Physical Realizability and Coherent Quantum Feedback Control

Arbitrary linear time invariant systems can be implemented as quantum systems if additional quantum noises are permitted in the implementation. We give several results concerning how many additional quantum noise channels are necessary to implement state space realizations and transfer functions as quantum systems. We also give algorithms to do so. We demonstrate the utility of these results with an algorithm for obtaining a suboptimal solution to a coherent quantum LQG control problem.This work was supported by the Australian Research Council and the Air Force Office of Scientific Research (Grants FA2386-09-1-4089 and FA2386-12-1-4075

Notes on Coherent Feedback Control for Linear Quantum Systems

This paper considers some formulations and possible approaches to the coherent LQG and $H^\infty$ quantum control problems. Some new results for these problems are presented in the case of annihilation operator only quantum systems showing that in this case, the optimal controllers are trivial controllers.Comment: A preliminary version is to appear in the proceedings of the 2013 Australian Control COnferenc

On the generalization of linear least mean squares estimation to quantum systems with non-commutative outputs

The purpose of this paper is to study the problem of generalizing the Belavkin-Kalman filter to the case where the classical measurement signal is replaced by a fully quantum non-commutative output signal. We formulate a least mean squares estimation problem that involves a non-commutative system as the filter processing the non-commutative output signal. We solve this estimation problem within the framework of non-commutative probability. Also, we find the necessary and sufficient conditions which make these non-commutative estimators physically realizable. These conditions are restrictive in practice.Comment: 31 page

Coherent-Classical Estimation for Quantum Linear Systems

This paper introduces a problem of coherent-classical estimation for a class of linear quantum systems. In this problem, the estimator is a mixed quantum-classical system which produces a classical estimate of a system variable. The coherent-classical estimator may also involve coherent feedback. An example involving optical squeezers is given to illustrate the efficacy of this idea.Comment: A version of this paper will appear in the Proceedings of the 2013 Australian Control Conferenc

Direct and Indirect Couplings in Coherent Feedback Control of Linear Quantum Systems

The purpose of this paper is to study and design direct and indirect couplings for use in coherent feedback control of a class of linear quantum stochastic systems. A general physical model for a nominal linear quantum system coupled directly and indirectly to external systems is presented. Fundamental properties of stability, dissipation, passivity, and gain for this class of linear quantum models are presented and characterized using complex Lyapunov equations and linear matrix inequalities (LMIs). Coherent $H^\infty$ and LQG synthesis methods are extended to accommodate direct couplings using multistep optimization. Examples are given to illustrate the results.Comment: 33 pages, 7 figures; accepted for publication in IEEE Transactions on Automatic Control, October 201

Coherent controllers for optical-feedback cooling of quantum oscillators

We study the cooling performance of optical-feedback controllers for open optical and mechanical resonators in the Linear Quadratic Gaussian setting of stochastic control theory. We utilize analysis and numerical optimization of closed-loop models based on quantum stochastic differential equations to show that coherent control schemes, where we embed the resonator in an interferometer to achieve all-optical feedback, can outperform optimal measurement-based feedback control schemes in the quantum regime of low steady-state excitation number. These performance gains are attributed to the coherent controller's ability to simultaneously process both quadratures of an optical probe field without measurement or loss of fidelity, and may guide the design of coherent feedback schemes for more general problems of robust nonlinear and robust control.Comment: 15 pages, 20 figures. Submitted to Physical Review X. Follow-up paper to arXiv:1206.082