Coherent quantum filtering for physically realizable linear quantum plants

Vladimirov, Igor G.; Petersen, Ian R.

doi:10.23919/ecc.2013.6669506

Cited by 32 publications

(73 citation statements)

References 20 publications

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“…QUANTUM STOCHASTIC SYSTEMS Although some results have been obtained in [2], [26] regarding least mean squares estimators for quantum systems with non-commutative output signals, the physical realizability conditions turns out to be an obstacle for finding the analytic solution. Furthermore, due to the Heisenberg uncertainty principle, there is a fundamental limit for the mean squared estimation error.…”

Section: Cmt Coherent Observers For Linearmentioning

confidence: 97%

Covariance matrix tracking coherent observers for linear quantum stochastic systems

Zhang

Hush

James

2015

2015 American Control Conference (ACC)

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It is becoming apparent that coherent feedback control of quantum systems has significant advantages over measurement-based control, but not much progress has been made on coherent estimators. In our previous work, a class of coherent quantum observers was developed, which tracks linear quantum stochastic systems in the sense of mean values. However, in the majority of quantum technologies, apart from mean value quantities, correlations and variances are critical elements because they are connected with energy and entanglement. Therefore, in this paper, we create a covariance matrix tracking (CMT) coherent observer that enables the asymptotic tracking of both the mean and covariance matrix of a quantum system. The existence of CMT observers is analyzed, and a sufficient and necessary condition is provided to ensure the physical realization of CMT observers to be consistent with the laws of quantum mechanics. The performance of a CMT vs. mean tracking coherent observer is compared in an illustrated example, and we demonstrate for the first time coherent tracking of entanglement. These results shed light on observer-based coherent control design.

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Section: Cmt Coherent Observers For Linearmentioning

confidence: 97%

Covariance matrix tracking coherent observers for linear quantum stochastic systems

Zhang

Hush

James

2015

2015 American Control Conference (ACC)

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“…Different approaches to design coherent quantum observers are discussed in [2,18,19]. However, as with the quantum control problems mentioned above, the main difficulties come from the fact that a coherent quantum observer should satisfy physical realizability constraints.…”

Section: Introductionmentioning

confidence: 99%

Design of coherent quantum observers for linear quantum systems

Vuglar¹,

Amini²

2014

New J. Phys.

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Quantum versions of control problems are often more difficult than their classical counterparts because of the additional constraints imposed by quantum dynamics. For example, the quantum LQG and quantum ∞ H optimal control problems remain open. To make further progress, new, systematic and tractable methods need to be developed. This paper gives three algorithms for designing coherent quantum observers, i.e., quantum systems that are connected to a quantum plant and their outputs provide information about the internal state of the plant. Importantly, coherent quantum observers avoid measurements of the plant outputs. We compare our coherent quantum observers with a classical (measurement-based) observer by way of an example involving an optical cavity with thermal and vacuum noises as inputs.

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“…This allows the matrix c to be assigned any value by an appropriate choice of b, which plays a part in the stabilization issue mentioned above. Although (26) simplifies the algebraic manipulations, it is the rank properties of the matrices D, d that are most important.…”

Section: Quantum Controllermentioning

confidence: 99%

“…which parameterizes PR quantum controllers (3) through (24), (25), with the controller noise feedthrough matrix d ∈ R p 2 ×m 2 being fixed and satisfying (26). Accordingly, the minimization in (27) is carried out over the set…”

Section: Coherent Quantum Lqg Control Problemmentioning

confidence: 99%

“…Despite the previous results, the CQLQG control problem does not lend itself to an "elegant" solution (for example, in the form of decoupled Riccati equations as in the classical case [10]) and remains a subject of research. Since the main difficulties are caused by the coupling of the equations due to the PR constraints, a conversion of the CQLQG control problem to an unconstrained problem by using Lagrange multipliers was considered in [26] for a related coherent quantum filtering problem which is a simplified feedback-free version of the CQLQG control problem.…”

Section: Introductionmentioning

confidence: 99%

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A gradient descent approach to optimal coherent quantum LQG controller design

Sichani

Vladimirov

Petersen

2015

2015 American Control Conference (ACC)

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This paper is concerned with the Coherent Quantum Linear Quadratic Gaussian (CQLQG) control problem of finding a stabilizing measurement-free quantum controller for a quantum plant so as to minimize an infinite-horizon mean square performance index for the fully quantum closed-loop system. In comparison with the observation-actuation structure of classical controllers, the coherent quantum feedback is less invasive to the quantum dynamics and quantum information. Both the plant and the controller are open quantum systems whose dynamic variables satisfy the canonical commutation relations (CCRs) of a quantum harmonic oscillator and are governed by linear quantum stochastic differential equations (QSDEs). In order to correspond to such oscillators, these QSDEs must satisfy physical realizability (PR) conditions, which are organised as quadratic constraints on the controller matrices and reflect the preservation of CCRs in time. The CQLQG problem is a constrained optimization problem for the steady-state quantum covariance matrix of the plant-controller system satisfying an algebraic Lyapunov equation. We propose a gradient descent algorithm equipped with adaptive stepsize selection for the numerical solution of the problem. The algorithm finds a local minimum of the LQG cost over the parameters of the Hamiltonian and coupling operators of a stabilizing PR quantum controller, thus taking the PR constraints into account. A convergence analysis of the proposed algorithm is presented. A numerical example of a locally optimal CQLQG controller design is provided to demonstrate the algorithm performance.

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Coherent quantum filtering for physically realizable linear quantum plants

Cited by 32 publications

References 20 publications

Covariance matrix tracking coherent observers for linear quantum stochastic systems

Covariance matrix tracking coherent observers for linear quantum stochastic systems

Design of coherent quantum observers for linear quantum systems

A gradient descent approach to optimal coherent quantum LQG controller design

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