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Cambridge University Press eBooks

Quantum feedback control

Kurt A. Jacobs

Published Aug 14, 2014• 2 citations

Abstract

Introduction The notion of feedback control comes to us from the classical world of mechanical and electrical engineering. Machines designed to operate a certain way may deviate because of small errors in their physical construction, because of inherent instability, or because of external sources of noise. Such deviations can be controlled by monitoring a machine’s behavior, and using this information to apply forces that periodically or continuously correct the motion. This is called feedback control, and the device that receives the measurement signal, and translates it into the appropriate correcting forces, is called the “feedback controller” (or “controller” for short). We will usually refer to the system to be controlled as the primary, and the system that acts as a feedback controller as the auxiliary. The device(s) that actually apply the forces to the system are often called the actuator(s), and the prescription by which the control forces are chosen based on the measurement results is variously called the control algorithm, law, strategy, or protocol. Here we exclusively use the terms strategy and protocol. Feedback control is also known as closed-loop control, because the flow of information to the controller, and the flow back to the system via actuators, are thought of as forming a loop. As a historical note, Maxwell appears to have been the first to perform a mathematical analysis of a feedback control system. He studied “governors,” mechanical devices that control the speed of an engine by using the centrifugal force generated by the engine to control the flow of fuel [413]. In fact the use of centrifugal governors goes back even further, as they were used to control the pressure between millstones in windmills in the 17th century [253].

DOI: 10.1017/cbo9781139179027.006

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Introduction The notion of feedback control comes to us from the classical world of mechanical and electrical engineering. Machines designed to operate a certain way may deviate because of small errors in their physical construction, because of inherent instability, or because of external sources of noise. Such deviations can be controlled by monitoring a machine’s behavior, and using this information to apply forces that periodically or continuously correct the motion. This is called feedback control, and the device that receives the measurement signal, and translates it into the appropriate correcting forces, is called the “feedback controller” (or “controller” for short). We will usually refer to the system to be controlled as the primary, and the system that acts as a feedback controller as the auxiliary. The device(s) that actually apply the forces to the system are often called the actuator(s), and the prescription by which the control forces are chosen based on the measurement results is variously called the control algorithm, law, strategy, or protocol. Here we exclusively use the terms strategy and protocol. Feedback control is also known as closed-loop control, because the flow of information to the controller, and the flow back to the system via actuators, are thought of as forming a loop. As a historical note, Maxwell appears to have been the first to perform a mathematical analysis of a feedback control system. He studied “governors,” mechanical devices that control the speed of an engine by using the centrifugal force generated by the engine to control the flow of fuel [413]. In fact the use of centrifugal governors goes back even further, as they were used to control the pressure between millstones in windmills in the 17th century [253].

In the conventional picture of quantum feedback control, sensors perform measurements on the system, a classical controller processes the results of the measurements, and actuators supply semiclassical potentials to alter the behavior of the quantum system. In this picture, the sensors tend to destroy coherence in the process of making measurements, and although the controller can use the actuators to act coherently on the quantum system, it is processing and feeding back classical information. This paper proposes an alternative method for quantum feedback control, in which the sensors, controller, and actuators are quantum systems that interact coherently with the system to be controlled. In this picture, the controller gets, processes, and feeds back quantum information. Controllers that operate using such quantum feedback loops can perform tasks such as entanglement transfer that are not possible using classical feedback. Necessary and sufficient conditions are presented for Hamiltonian quantum systems to be controllable and observable using both classical and quantum feedback.

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.

In the conventional picture of quantum feedback, control sensors make measurements on a quantum system, a classical controller processes the results of the measurements, and semiclassical actuators act back on the system to alter its behavior. We describe and provide an experimental demonstration of an alternative method for quantum feedback control, in which the sensors, controller, and actuators of conventional feedback control are replaced with quantum systems that interact coherently with the system to be controlled. The resulting control system represents a fully coherent quantum feedback loop.

This paper proposes and analyzes an adaptive quantum feedback control system designed to optimize the performance of quantum devices. The core of the system lies in a real-time monitoring and adjustment mechanism utilizing a quantum sensor to measure the state of the quantum system. This measurement data is then fed back into a control algorithm, which dynamically adjusts the system parameters to achieve precise control. Unlike traditional control systems that are sensitive to parameter uncertainties, this adaptive approach leverages the inherent properties of quantum systems to enhance stability and performance. The theoretical framework presented here establishes a foundation for future research and development in adaptive quantum control, addressing key challenges in quantum device operation and manipulation. The system aims to provide a robust and flexible solution for controlling quantum systems with varying characteristics. The primary focus is on the control loop design and the feedback algorithm implementation, with an emphasis on achieving optimal performance under conditions of parameter uncertainty. This work contributes to the growing field of quantum control by introducing a novel adaptive strategy that can significantly improve the operational capabilities of quantum devices.

Quantum control theory is profitably reexamined from the perspective of quantum information, two results on the role of quantum information technology in quantum feedback control are presented and two quantum feedback control schemes, teleportation-based distant quantum feedback control and quantum feedback control with quantum cloning, are proposed. In the first feedback scheme, the output from the quantum system to be controlled is fed back into the distant actuator via teleportation to alter the dynamics of system. The result theoretically shows that it can accomplish some tasks such as distant feedback quantum control that Markovian or Bayesian quantum feedback can not complete. In the second feedback strategy, the design of quantum feedback control algorithms is separated into a state recognition step, which gives "on-off" signal to the actuator through recognizing some copies from the cloning machine, and a feedback (control) step using another copies of cloning machine. A compromise between information acquisition and measurement disturbance is established, and this strategy can perform some quantum control tasks with coherent feedback.

In the conventional picture of quantum feedback control, sensors make measurements on a quantum system, a classical controller processes the results of the measurements, and semi-classical actuators act back on the system to alter its behavior. Quantum measurements are well known to yield probabilistic results and to introduce unavoidable disturbances in the system measured. Accordingly, quantum feedback is traditionally considered to be both probabilistic and destructive. This paper proposes and provides an experimental demonstration of an alternative method for quantum feedback control, in which sensors, controller, and actuators are themselves quantum systems that interact coherently with the system to be controlled. The resulting feedback loop preserves quantum coherence. Such coherent quantum feedback control is deterministic, non-destructive, and can be used to perform actions such as transferring quantum entanglement that are not possible using conventional feedback control of quantum systems. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.