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arXiv:1102.5713 · Journal of Physics B Atomic Molecular and Optical Physics

Quantum feedback for rapid state preparation in the presence of control imperfections

Joshua Combes, Howard M. Wiseman

Published Jul 25, 2011• 25 citations
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Abstract

Quantum feedback control protocols can improve the operation of quantum devices. Here we examine the performance of a purification protocol when there are imperfections in the controls. The ideal feedback protocol produces an x -eigenstate from a mixed state in the minimum time, and is known as rapid state preparation. The imperfections we examine include time delays in the feedback loop, finite strength feedback, calibration errors and inefficient detection. We analyse these imperfections using the Wiseman–Milburn feedback master equation and related formalism. We find that the protocol is most sensitive to time delays in the feedback loop. For systems with slow dynamics, however, our analysis suggests that inefficient detection would be the bigger problem. We also show how system imperfections, such as dephasing and damping, can be included in a model via the feedback master equation.

DOI
10.1088/0953-4075/44/15/154008

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Quantum feedback control protocols can improve the operation of quantum devices. Here we examine the performance of a purification protocol when there are imperfections in the controls. The ideal feedback protocol produces an x -eigenstate from a mixed state in the minimum time, and is known as rapid state preparation. The imperfections we examine include time delays in the feedback loop, finite strength feedback, calibration errors and inefficient detection. We analyse these imperfections using the Wiseman–Milburn feedback master equation and related formalism. We find that the protocol is most sensitive to time delays in the feedback loop. For systems with slow dynamics, however, our analysis suggests that inefficient detection would be the bigger problem. We also show how system imperfections, such as dephasing and damping, can be included in a model via the feedback master equation.
Feedback control protocols can stabilize and enhance the operation of quantum devices, however, unavoidable delays in the feedback loop adversely affect their performance. We introduce a quantum control methodology, combining open-loop control with quantum filtering, which is not constrained by feedback delays. For the problems studied (rapid purification and rapid measurement) we analytically derive lower bounds on the control performance that are comparable with the best corresponding bounds for feedback protocols.
Quantum control is an essential tool for the operation of quantum technologies such as quantum computers, simulators, and sensors. Although there are sophisticated theoretical tools for developing quantum control protocols, formulating optimal protocols while incorporating experimental conditions remains a challenge. In this paper, motivated by recent advances in realization of real-time feedback control in circuit quantum electrodynamics systems, we study the effect of experimental imperfections on the optimality of qubit purification protocols. Specifically, we find that the optimal control solutions in the presence of detector inefficiency and non-negligible decoherence can be significantly different from the known solutions to idealized dynamical models. In addition, we present a simplified form of the verification theorem to examine the global optimality of a control protocol.
Abstract. This paper reconsiders the properties of a scheme for the rapid purification of the quantum state of a qubit, proposed recently in Jacobs 2003 Phys. Rev. A 67 030301(R). The qubit starts in a completely mixed state, and information is obtained by a continuous measurement. Jacobs ’ rapid purification protocol uses Hamiltonian feedback control to maximise the average purity of the qubit for a given time, with a factor of two increase in the purification rate over the no-feedback protocol. However, by re-examining the latter approach, we show that it mininises the average time taken for a qubit to reach a given purity. In fact, the average time taken for the no-feedback protocol beats that for Jacobs ’ protocol by a factor of two. We discuss how this is compatible with Jacobs ’ result, and the usefulness of the different approaches. Reconsidering Rapid Qubit Purification by Feedback 2 1.
This paper reconsiders the claimed rapidity of a scheme for the purification of the quantum state of a qubit, proposed recently in Jacobs (2003 Phys. Rev. A 67 030301(R)). The qubit starts in a completely mixed state, and information is obtained by a continuous measurement. Jacobs' rapid purification protocol uses Hamiltonian feedback control to maximize the average purity of the qubit for a given time , with a factor of two increase in the purification rate over the no-feedback protocol. However, by re-examining the latter approach, we show that it minimizes the average time taken for a qubit to reach a given purity . In fact, the average time taken for the no-feedback protocol beats that for Jacobs' protocol by a factor of two. We discuss how this is compatible with Jacobs' result and the usefulness of the different approaches.
Feedback control in quantum transport has been predicted to give rise to several interesting effects, among them quantum state stabilization and the realization of a mesoscopic Maxwell's daemon. These results were derived under the assumption that control operations on the system are affected instantaneously after the measurement of electronic jumps through it. In this contribution, I describe how to include a delay between detection and control operation in the master equation theory of feedback-controlled quantum transport. I investigate the consequences of delay for the state stabilization and Maxwell's daemon schemes. Furthermore, I describe how delay can be used as a tool to probe coherent oscillations of electrons within a transport system and how this formalism can be used to model finite detector bandwidth.
We investigate feedback control of linear quantum systems subject to feedback-loop time delays. In particular, we examine the relation between the potentially achievable control performance and the time delays and provide theoretical guidelines for the future experimental setup in two physical systems, which are typical in this research field. The evaluation criterion for the analysis is given by the optimal control performance formula, the derivation of which is from the classical control theoretic results about the input-output delay systems.