Quantum control of a single qubit

Brańczyk, Agata M.; Mendonça, Paulo E. M. F.; Gilchrist, Alexei; Doherty, Andrew C.; Bartlett, Stephen D.

doi:10.1103/physreva.75.012329

Cited by 76 publications

(121 citation statements)

References 38 publications

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“…In this section we present simulations of the continuous-time quantum feedback protocol specified in Eqn. (17), in which these imperfections are now incorporated. We use the full stochastic master equation including finite detector bandwidth that is derived in [42],…”

Section: Experimental Realizationmentioning

confidence: 99%

“…Some quantum information applications that have been proposed to date include, rapid purification of qubits or qubit registers [9][10][11][12][13][14], quantum error correction [15,16], transmission of quantum information through noisy channels [17], adaptive measurement for quantum state discrimination [18][19][20], and several forms of quantum state preparation and stabilization [21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

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Deterministic generation of remote entanglement with active quantum feedback

Martin¹,

Motzoi²,

Li³

et al. 2015

Phys. Rev. A

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We consider the task of deterministically entangling two remote qubits using joint measurement and feedback, but no directly entangling Hamiltonian. In order to formulate the most effective experimentally feasible protocol, we introduce the notion of average sense locally optimal (ASLO) feedback protocols, which do not require real-time quantum state estimation, a difficult component of real-time quantum feedback control. We use this notion of optimality to construct two protocols which can deterministically create maximal entanglement: a semiclassical feedback protocol for low efficiency measurements and a quantum feedback protocol for high efficiency measurements. The latter reduces to direct feedback in the continuous-time limit, whose dynamics can be modeled by a Wiseman-Milburn feedback master equation which yields an analytic solution in the limit of unit measurement efficiency. Our formalism can smoothly interpolate between continuous-time and discrete-time descriptions of feedback dynamics, and we exploit this feature to then derive a superior hybrid protocol for arbitrary non-unit measurement efficiency that switches between quantum and semiclassical protocols. Finally, we show using simulations incorporating experimental imperfections that deterministic entanglement of remote superconducting qubits may be achieved with current technology using the continuous-time feedback protocol alone.

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Section: Experimental Realizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Deterministic generation of remote entanglement with active quantum feedback

Martin¹,

Motzoi²,

Li³

et al. 2015

Phys. Rev. A

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“…The fundamental limit to the precision of the estimate in QPE is set by quantum mechanics [1,2]. Thus one of the key issues in QPE is the development of practical methodologies which allow measurements to approach or exceed the standard quantum limit (SQL) for a given measurement coupling [6,7,8,9,10,11,12]. Because of its wide-ranging technological relevance, the prime example of QPE is estimating an optical phase shift [13,14,15,16,17,18,19,20].…”

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confidence: 99%

Adaptive Optical Phase Estimation Using Time-Symmetric Quantum Smoothing

et al. 2010

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Quantum parameter estimation has many applications, from gravitational wave detection to quantum key distribution. We present the first experimental demonstration of the time-symmetric technique of quantum smoothing. We consider both adaptive and non-adaptive quantum smoothing, and show that both are better than their well-known time-asymmetric counterparts (quantum filtering). For the problem of estimating a stochastically varying phase shift on a coherent beam, our theory predicts that adaptive quantum smoothing (the best scheme) gives an estimate with a mean-square error up to 2 √ 2 times smaller than that from non-adaptive quantum filtering (the standard quantum limit). The experimentally measured improvement is 2.24 ± 0.14.PACS numbers: 42.50. Dv, 42.50.Xa, 03.65.Ta, 06.90.+v Quantum parameter estimation (QPE) is the problem of estimating an unknown classical parameter (or process) which plays a role in the preparation (or dynamics) of a quantum system [1,2], and is central to many fields including gravitational wave interferometry [5], quantum computing [3], and quantum key distribution [4]. The fundamental limit to the precision of the estimate in QPE is set by quantum mechanics [1,2]. Thus one of the key issues in QPE is the development of practical methodologies which allow measurements to approach or exceed the standard quantum limit (SQL) for a given measurement coupling [6,7,8,9,10,11,12]. Because of its wide-ranging technological relevance, the prime example of QPE is estimating an optical phase shift [13,14,15,16,17,18,19,20].Apart from some theoretical papers [19,20], work in this area of QPE has concentrated upon the problem of estimating a fixed, but unknown phase shift, which can be thought of as preparing the quantum state with an average phase equal to this parameter. It was shown theoretically [15] that for this problem adaptive homodyne measurements coupled with an optimal estimation filter can yield an estimate with mean-square error smaller than the standard quantum limit (as set by perfect heterodyne detection). This was demonstrated experimentally in Ref.[16] using very weak coherent states (for which the factor of improvement is at most 2). More recent theory and experiment have shown that interferometric measurements with photon counting can also be improved using adaptive techniques [17,18].A far richer, and in many cases more experimentally relevant, problem of quantum phase estimation arises when the phase evolves dynamically under the influence of an unknown classical stochastic process [19,20]. The general problem of estimating a classical process dynamically coupled to a quantum system under continuous measurement has recently been considered by Tsang [21], who introduced three main categories of quantum estimation: prediction or filtering, smoothing, and retrodiction. Of those, prediction or filtering is a causal estimation technique that can be used in real-time applications [24]. Smoothing and retrodiction are acausal and so cannot be used in real time, but they can be use...

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“…Interestingly, the analysis of the feedback-enacted procedures may be also regarded as stemming from the communication-oriented approach of [19,20], or as a particular instance of a quantum error-correction procedure [21]. In a similar spirit, an interesting discussion on the ensuing trade-off between information gain and disturbance for different measurement strategies in a single-qubit setting can be found in [22]. From a technical point of view, our main results fur-ther demonstrate the usefulness of linear algebraic methods for finite-dimensional quantum control settings, along the lines introduced in [23].…”

Section: Introductionmentioning

confidence: 99%

Single-bit feedback and quantum-dynamical decoupling

Ticozzi

Viola

2006

Phys. Rev. A

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Synthesizing an effective identity evolution in a target system subjected to unwanted unitary or non-unitary dynamics is a fundamental task for both quantum control and quantum information processing applications. Here, we investigate how single-bit, discrete-time feedback capabilities may be exploited to enact or to enhance quantum procedures for effectively suppressing unwanted dynamics in a finite-dimensional open quantum system. An explicit characterization of the joint unitary propagators correctable by a single-bit feedback strategy for arbitrary evolution time is obtained. For a two-dimensional target system, we show how by appropriately combining quantum feedback with dynamical decoupling methods, concatenated feedback-decoupling schemes may be built, which can operate under relaxed control assumptions and can outperform purely closed-loop and open-loop protocols.

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Quantum control of a single qubit

Cited by 76 publications

References 38 publications

Deterministic generation of remote entanglement with active quantum feedback

Deterministic generation of remote entanglement with active quantum feedback

Adaptive Optical Phase Estimation Using Time-Symmetric Quantum Smoothing

Single-bit feedback and quantum-dynamical decoupling

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