Rapid-state purification protocols for a Cooper pair box

Griffith, Elias J.; Hill, Charles D.; Ralph, Jason F.; Wiseman, Howard Mark; Jacobs, Kurt

doi:10.1103/physrevb.75.014511

Cited by 22 publications

(24 citation statements)

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“…This paper was prompted by the absence of such arguments in the current physics literature (but see [8]). In particular, we have verified the optimality of previously proposed control strategies for two problems of current interest [1,2,3,20,21,22] in nonlinear quantum feedback control.…”

Section: Discussionmentioning

confidence: 81%

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Optimality of Feedback Control Strategies for Qubit Purification

Wiseman

Bouten

2008

Quantum Inf Process

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Recently two papers [K. Jacobs, Phys. Rev. A 67, 030301(R) (2003); H. M. Wiseman and J. F. Ralph, New J. Physics 8, 90 (2006)] have derived control strategies for rapid purification of qubits, optimized with respect to various goals. In the former paper the proof of optimality was not mathematically rigorous, while the latter gave only heuristic arguments for optimality. In this paper we provide rigorous proofs of optimality in all cases, by applying simple concepts from optimal control theory, including Bellman equations and verification theorems.

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Section: Discussionmentioning

confidence: 81%

“…Various strategies with finite controls were investigated numerically for a particular (solid-state) setting in Ref. [21], with no claims of optimality.…”

Section: Discussionmentioning

confidence: 99%

Optimality of Feedback Control Strategies for Qubit Purification

Wiseman

Bouten

2008

Quantum Inf Process

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“…Subsequent studies on rapid purification showed that the proposed protocol was optimal, in that it maximized the average rate of purification, but it did not minimize the time taken to reach a given level of purity [15]. Other work has generalized these results for different optimization conditions [16], N-level systems [17], practical implementation of the controls [18], shared entangled states [19], imperfections [20], inefficient detection [21], and mixed protocols [21,22]. In particular, Li et al demonstrated that when the efficiency of the detector is lower than 50%, there is no predicted speed up in purification rate [21].…”

Section: Introductionmentioning

confidence: 99%

Efficient quantum filtering for quantum feedback control

Rouchon

Ralph

2015

Phys. Rev. A

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We discuss an efficient numerical scheme for the recursive filtering of diffusive quantum stochastic master equations. We show that the resultant quantum trajectory is robust and may be used for feedback based on inefficient measurements. The proposed numerical scheme is amenable to approximation, which can be used to further reduce the computational burden associated with calculating quantum trajectories and may allow real-time quantum filtering. We provide a two-qubit example where feedback control of entanglement may be within the scope of current experimental systems.

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“…Recently it has been shown that it is possible to increase the speed at which a measurement purifies the state of a quantum system by using real-time feedback control as the measurement proceeds [1,2,3,4,5,6,7,8,9]. Specifically, by using feedback to keep the state of the system diagonal in a basis that is unbiased with respect to the measured observable, one can make the system purity increase deterministically at a rate faster than the increase of the average purity by measurement alone [1,2].…”

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confidence: 99%

Rapid Measurement of Quantum Systems Using Feedback Control

2008

Self Cite

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We introduce a feedback control algorithm that increases the speed at which a measurement extracts information about a d-dimensional system by a factor that scales as d 2 . Generalizing this algorithm, we apply it to a register of n qubits and show an improvement O(n). We derive analytical bounds on the benefit provided by the feedback and perform simulations that confirm that this speedup is achieved.PACS numbers: 02.30Yy, Recently it has been shown that it is possible to increase the speed at which a measurement purifies the state of a quantum system by using real-time feedback control as the measurement proceeds [1,2,3,4,5,6,7,8,9]. Specifically, by using feedback to keep the state of the system diagonal in a basis that is unbiased with respect to the measured observable, one can make the system purity increase deterministically at a rate faster than the increase of the average purity by measurement alone [1,2]. Since this protocol requires an unbiased basis, it exploits a purely quantum mechanical effect. However, as a consequence this quantum feedback protocol prevents the observer from obtaining full information about the initial preparation of the system, and is therefore not appropriate for use in applications such as communication channels [10]. It is for this reason that the effect of the protocol is termed rapid-purification and not rapid-measurement.Here we present a new protocol that can be applied to both quantum and classical systems, and that, in contrast to quantum rapid-purification, increases the rate at which the observer gains information about the initial preparation, as well as the rate at which the state is purified. This protocol therefore achieves not merely rapid purification, but also rapid measurement, and can be used in communication channels, state stabilisation, read out and error correction in quantum computers. It is also distinct from the rapid state-discrimination protocol introduced recently in [11], which is only applicable to non-orthogonal states and thus to quantum systems. Our protocol can be applied to all systems with dimension d > 2. Asumming the measured observable scales with d, we show that our protocol increases the speed of a measurement by a factor O(d 2 ) over an unaided measurement on a qudit. This is in contrast to the O(d) speed-up acheived by previous protocols [2]. We generalise our protocol for a register of n qubits, each being measured independently and continuously, and obtain an improvement O(n).The evolution of the state ρ of a system subject to a continuous measurement of an observable X is given by the stochastic master equation (SME) [13,14] whereThe measurement strength, γ, determines the rate at which information is extracted, and thus the rate at which the system is projected onto a single eigenstate of X [12]. We denote the continuous measurement record obtained by the observer as r(t), and dr = √ 4γ X dt + dW . We assume that the measurement strength is much smaller than the strength of the Hamiltonians that can be controlled by feedback, so ...

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Rapid-state purification protocols for a Cooper pair box

Cited by 22 publications

References 21 publications

Optimality of Feedback Control Strategies for Qubit Purification

Optimality of Feedback Control Strategies for Qubit Purification

Efficient quantum filtering for quantum feedback control

Rapid Measurement of Quantum Systems Using Feedback Control

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