Heisenberg picture approach to the stability of quantum Markov systems

Pan, Yu; Amini, Hadis; Zhang, Miao; Gough, John E.; Ugrinovskii, Valery; James, M. R.

doi:10.1063/1.4884300

Cited by 35 publications

(37 citation statements)

References 46 publications

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“…Physicists, mathematicians and engineers have been making joint efforts to control a diversity of systems operating in the quantum regime [5], [9], [11], [21], [23], [25]. Quantum feedback control has become particularly topical [7], [20], [28], [30], as using information gained from a system enables more stable operation of a control protocol [13], [24]. To control a quantum system via feedback, in general we have two options: measurementbased feedback and coherent feedback.…”

Section: Introductionmentioning

confidence: 98%

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: Introductionmentioning

confidence: 98%

Covariance matrix tracking coherent observers for linear quantum stochastic systems

Zhang

Hush

James

2015

2015 American Control Conference (ACC)

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“…The last two decades have witnessed rapid growth in quantum technologies, and control of quantum systems is the main focus of quantum engineering [5], [24], [31]. Quantum feedback control involves interconnecting different systems such that the composite system can achieve desired performance specifications.…”

Section: Introductionmentioning

confidence: 99%

Direct and indirect couplings in the interconnection of open two level quantum systems

Zhang

James

2015

2015 IEEE Conference on Control Applications (CCA)

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Recently, the influences and applications of indirect and direct couplings in coherent feedback control of linear quantum stochastic systems have been investigated. However, bilinear quantum stochastic systems escape the realm of the current known results. Furthermore, as fast tunable coupling of a set of two level quantum systems (qubits) with high coherence plays a vital role in quantum computing operations, in this paper we study direct and indirect couplings in the interconnection of qubits. A physical model described by bilinear quantum stochastic differential equations is presented, and physical realizability conditions (necessary and sufficient algebraic constraints) are provided to guarantee these bilinear quantum stochastic differential equations to correspond to the dynamics of directly or indirectly coupled open two level systems. These results shed light on network synthesis of bilinear quantum stochastic systems and coherent control of multiple qubits.

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“…The covariance matrix of the observer described by Eqs. (12) tracks that of the plant described by Eqs. (10) asymptotically, i.e.,…”

Section: Cmt Coherent Observers For Open Harmonic Oscillatorsmentioning

confidence: 99%

“…It is worth mentioning that B o can be 0 if no additional noise is needed to ensure the physical realizability of an observer described by Eqs. (12) .…”

Section: Cmt Coherent Observers For Open Harmonic Oscillatorsmentioning

confidence: 99%

“…Physicists, mathematicians and engineers have been working in unison to control a number of diverse systems in the quantum regime [1][2][3][4][5][6][7][8]. Quantum control involving feedback has become particularly topical [9][10][11][12], as using information gained from a system can lead to more stable operation of a control protocol [13,14]. Quantum feedback can be split into two paradigms: measurement-based and coherent feedback.…”

Section: Introductionmentioning

confidence: 99%

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Coherently tracking the covariance matrix of an open quantum system

2015

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Coherent feedback control of quantum systems has demonstrable advantages over measurementbased control, but so far there has been little work done on coherent estimators and more specifically coherent observers. Coherent observers are input the coherent output of a specified quantum plant, and are designed such that some subset of the observer and plant's expectation values converge in the asymptotic limit. We previously developed a class of mean tracking (MT) observers for open harmonic oscillators that only converged in mean position and momentum; Here we develop a class of covariance matrix tracking (CMT) coherent observers that track both the mean and covariance matrix of a quantum plant. We derive necessary and sufficient conditions for the existence of a CMT observer, and find there are more restrictions on a CMT observer than there are on a MT observer. We give examples where we demonstrate how to design a CMT observer and show it can be used to track properties like the entanglement of a plant. As the CMT observer provides more quantum information than a MT observer, we expect it will have greater application in future coherent feedback schemes mediated by coherent observers. Investigation of coherent quantum estimators and observers is important in the ongoing discussion of quantum measurement; As they provide estimation of a system's quantum state without explicit use of the measurement postulate in their derivation.

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Heisenberg picture approach to the stability of quantum Markov systems

Cited by 35 publications

References 46 publications

Covariance matrix tracking coherent observers for linear quantum stochastic systems

Covariance matrix tracking coherent observers for linear quantum stochastic systems

Direct and indirect couplings in the interconnection of open two level quantum systems

Coherently tracking the covariance matrix of an open quantum system

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