arXiv:quant-ph/0105018 · IEEE Conference on Decision and Control (CDC)

Robust control in the quantum domain

Andrew C. Doherty, J. Doyle, Hideo Mabuchi, Kurt A. Jacobs, Salman Habib

Published Nov 11, 2002• 18 citations

Abstract

Progress in quantum physics has made it possible to perform experiments in which individual quantum systems are monitored and manipulated in real time. The advent of such new technical capabilities provides strong motivation for the development of theoretical and experimental methodologies for quantum feedback control. The availability of such methods would enable radically new approaches to experimental physics in the quantum realm. Likewise, the investigation of quantum feedback control will introduce crucial new considerations to control theory, such as the uniquely quantum phenomena of entanglement and measurement back-action. The extension of established analysis techniques from control theory into the quantum domain may also provide new insight into the dynamics of complex quantum systems. We anticipate that the successful formulation of an input-output approach to the analysis and reduction of large quantum systems could have very general applications in nonequilibrium quantum statistical mechanics and in the nascent field of quantum information theory.

DOI: 10.1109/cdc.2000.912895

Related papers

ROBUST CONTROL IN THE QUANTUM DOMAIN-ENTANGLEMENT, FEEDBACK AND MEASUREMENT BACKACTION

Andrew C. Doherty, Doyle, J.

Recent progress in quantum physics has made it possible to perform experiments in which individual quantum systems are monitored and manipulated in real time.The advent of such new technical capabiMies provides strong motivation for the development of theoretical and experimental methodologies for quantum feedback control.The availability of such methods would enable radically new approachesto experimentalphysics in the quantum realm.Likewise, the investigationof quantumfeedback control will introduce crucialnew considerationsto control theory, such as the uniquely quantum phenomena of entanglement and measurement backaction.The extension of established ana2ysistectilques from control theory into the quantum domain may also provide new insight into the dynamics of complex quantum systems.We anticipate that the successful formulation of an input-output approach to the analysis and reduction of large quantum systems could have very general applications in non-equilibrium quantum statistical mechanics and in the nascent field quantum information theory...

Sep 1, 20000 citations

Experiments in real-time quantum feedback

Hideo Mabuchi

Recent advances in quantum optics and atomic physics have enabled experimenters to begin exploring realtime feedback in quantum settings. In addition to the practical significance of such work for fields like nanotechnology and quantum information processing, research on quantum feedback probes the fundamental physics of conditional evolution for observed systems. Feedback in quantum settings is generally complicated by the intricacies of 'wave-function collapse' and measurement back-action, so that the proper design of quantum feedback controllers will require accurate quantitative models for the measurement process.

IEEE Conference on Decision and Control (CDC)Aug 27, 20034 citations

Quantum Measurement and Feedback Control in Quantum Systems

Ishaan Khan

Quantum systems exhibit unique behaviors governed by principles distinct from classical physics, notably in the realms of measurement and control. This paper explores the fundamental concepts and applications of quantum measurement and feedback control in quantum systems. Measurement in quantum mechanics disrupts the state of a system due to the inherent probabilistic nature of quantum states. This disruption, often described by the collapse of the wave function, presents challenges and opportunities for understanding and manipulating quantum states. Quantum measurement theory addresses how observations affect quantum states and the role of measurement devices in this process. Feedback control mechanisms offer a pathway to mitigate the disruptive effects of measurement and harness them for coherent quantum operations. By continuously monitoring and adjusting quantum systems based on measurement outcomes, feedback control enables stabilization, state preparation, and enhanced coherence times. Examples include quantum error correction, quantum state tomography, and real-time manipulation of quantum bits (qubits).

Journal of Quantum Science and Technology.Jul 2, 20240 citations

Transfer function approach to quantum control- part I: dynamics of quantum feedback systems

M. Yanagisawa, Hidenori Kimura

This paper gives a unified approach to feedback control theory of quantum mechanical systems of bosonic modes described by noncommutative operators. A quantum optical closed-loop, including a plant and controller, is developed and its fundamental structural properties are analyzed extensively from a purely quantum mechanical point of view, in order to facilitate the use of control theory in microscopic world described by quantum theory. In particular, an input-output description of quantum mechanical systems which is essential in describing the behavior of the feedback systems is fully formulated and developed. This would then provide a powerful tool for quantum control and pave an avenue that connects control theory to quantum dynamics. This paper is divided into two parts. The first part is devoted to the basic formulation of quantum feedback control via quantum communication and local operations on an optical device, cavity, that can be regarded as a unit of quantum dynamics of bosonic modes. The formulation introduced in this paper presents the feature intrinsic in quantum feedback systems based on quantum stochastic differential equations. The input-output description provides a basis for developing quantum feedback control through the transfer function representation of quantum feedback systems. In the follow-up paper, the quantum mechanical representation of feedback is further elaborated to yield the control theoretical representation of fundamental notions of quantum theory, uncertainty principle, e.g., and some applications are presented.

IEEE Transactions on Automatic ControlDec 1, 2003217 citations

Quantum feedback control

Howard M. Wiseman, Gerard J Milburn

Introduction In the preceding chapter we introduced quantum trajectories: the evolution of the state of a quantum system conditioned on monitoring its outputs. As discussed in the preface, one of the chief motivations for modelling such evolution is for quantum feedback control. Quantum feedback control can be broadly defined as follows. Consider a detector continuously producing an output, which we will call a current. Feedback is any process whereby a physical mechanism makes the statistics of the present current at a later time depend upon the current at earlier times. Feedback control is feedback that has been engineered for a particular purpose, typically to improve the operation of some device. Quantum feedback control is feedback control that requires some knowledge of quantum mechanics to model. That is, there is some part of the feedback loop that must be treated (at some level of sophistication) as a quantum system. There is no implication that the whole apparatus must be treated quantum mechanically. The structure of this chapter is as follows. The first quantum feedback experiments (or at least the first experiments specifically identified as such) were done in the mid 1980s by two groups [WJ85a, MY86]. They showed that the photon statistics of a beam of light could be altered by feedback. In Section 5.2 we review such phenomena and give a theoretical description using linearized operator equations. Section 5.3 considers the changes that arise when one allows the measurement to involve nonlinear optical processes.

Cambridge University Press eBooksNov 12, 20093 citations

Quantum feedback for measurement and control

Leigh S. Martin

The standard quantum formalism introduced at the undergraduate level treats measurement as an instantaneous collapse. In reality however, no physical process can occur over a truly infinitesimal time interval. A more subtle investigation of open quantum systems lead to the theory of continuous measurement and quantum trajectories, in which wave function collapse occurs over a finite time scale associated with an interaction. Within this formalism, it becomes possible to ask many new questions that would be trivial or even ill-defined in the context of the more basic measurement model. In this thesis, we investigate both theoretically and experimentally what fundamentally new capabilities arise when an experimental apparatus can resolve the continuous dynamics of a measurement. Theoretically, we show that when one can perform feedback operations on the timescale of the measurement process, the resulting tools provide significantly more control over entanglement generation, and in some settings can generate it optimally. We derive these results using a novel formalism which encompasses most known quantum feedback protocols. Experimentally, we show that continuous measurement allows one to observe the dynamics of a system undergoing simultaneous non-commuting measurements, which provides a reinterpretation of the Heisenberg uncertainty principle. Finally, we combine the theoretical focus on quantum feedback with the experimental capabilities of superconducting circuits to implement a feedback controlled quantum amplifier. The resulting system is capable of adaptive measurement, which we use to perform the first canonical phase measurement.

arXiv:2004.09766Apr 21, 20200 citations