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

Andrew C. Doherty, Doyle, J.

Published Sep 1, 2000• 0 citations
OpenAlex

Abstract

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...

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 25, 2004•1 citation
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...
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.
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).
Recent theoretical and experimental advances mean that it is now possible to control physical systems at the quantum level. Indeed, developments in quantum technology provide strong motivation for the feedback control of quantum systems. This paper will discuss both measurement feedback and coherent feedback control for quantum systems. Measurement feedback involves conditioning on the measurement information, and so we describe the Belavkin quantum filter and its use in quantum control. In contrast, coherent feedback does not involve any measurements, and we discuss some recent results on coherent feedback control.
The goal of quantum control is to enable robust quantum information processing in noisy environments. Quantum feedback control is one of the most established strategies, but its reliance on measurement and real-time feedback imposes intrinsic limitations from measurement backaction and latency. Here, we propose and experimentally realize a measurement-free quantum feedforward control scheme, together with a composite framework that sequentially combines quantum feedforward control and quantum feedback control. We demonstrate both theoretically and experimentally that quantum feedforward control effectively protects nonorthogonal quantum states without measurement, while the composite strategy achieves superior performance when measurement is available, which makes it a practical alternative to quantum feedback control. These results establish quantum feedforward control as an independent control approach beyond quantum feedback control and highlight the advantages of the composite scheme, providing a new route toward high-fidelity quantum information processing in noisy environments.
Summary form only given. Although real-time feedback of measured signals is an essential component of sensing and control in classical settings, models for quantum feedback that are rigorous yet useful have only become possible since the advent of measurement-based quantum trajectory theory. The quantum feedback scenario introduces new concerns of coherence and measurement backaction, but recent work has shown that these can be treated properly in a formal integration of quantum trajectory theory with standard state-space formulations of filtering and control theory. Pioneering studies by H. M. Wiseman have shown that such models can be used to design and to analyze realistic schemes for adaptive homodyne measurement and for feedback control of atomic motion. Much of the ongoing research in our group focuses on the experimental implementation of such schemes. For a broad range of quantum feedback scenarios, certain recurring technical issues arise out of the need to perform complex, high-bandwidth processing of measured signals. We are developing a "rapid-prototyping" approach to refining signal processing and feedback algorithms via quantum trajectory simulation on a PC, followed by translation of the algorithms into hardware Description language (HDL).
In many optical and atomic systems it is now possible to monitor an individual quantum system with high signal to noise and feed back by altering the system dynamics in real time. This motivates further development of quantum mechanical descriptions of feedback control. We discuss recent work on closed loop control of open quantum systems, focusing on general linear systems for which the statistics of the problem are Gaussian. Such systems may be realized with linear optics, parametric amplifiers and homodyne detection. This problem allows a direct comparison with the classical linear, quadratic cost, Gaussian noise (LQG) optimal control problem. This highlights the key distinction between the quantum and classical theories for linear systems: that increased measurement sensitivity may run counter to the control objectives since it increases the backaction noise. While in an idealized classical control problem it is always preferable to obtain a better sensor, quantum mechanical problems generically have an optimal sensitivity since quantum mechanical measurements irreducibly disturb the system. The general theory will be illustrated by reference to specific simple examples.