Feedback is the core concept in cybernetics and its effective use has made great success in but not limited to the fields of engineering, biology, and computer science. When feedback is used to quantum systems, two major types of feedback control protocols including coherent feedback control (CFC) and measurement-based feedback control (MFC) have been developed. In this paper, we compare the two types of quantum feedback control protocols by focusing on the real-time information used in the feedback loop and the capability in dealing with parameter uncertainty. An equivalent relationship is established between quantum CFC and non-selective quantum MFC in the form of operator-sum representation. Using several examples of quantum feedback control, we show that quantum MFC can theoretically achieve better performance than quantum CFC in stabilizing a quantum state and dealing with Hamiltonian parameter uncertainty. The results enrich understanding of the relative advantages between quantum MFC and quantum CFC, and can provide useful information in choosing suitable feedback protocols for quantum systems.
Feedback is the core concept in cybernetics and its effective use has made great success in but not limited to the fields of engineering, biology, and computer science. When feedback is used to quantum systems, two major types of feedback control protocols including coherent feedback control (CFC) and measurement-based feedback control (MFC) have been developed. In this paper, we compare the two types of quantum feedback control protocols by focusing on the real-time information used in the feedback loop and the capability in dealing with parameter uncertainty. An equivalent relationship is established between quantum CFC and non-selective quantum MFC in the form of operator-sum representation. Using several examples of quantum feedback control, we show that quantum MFC can theoretically achieve better performance than quantum CFC in stabilizing a quantum state and dealing with Hamiltonian parameter uncertainty. The results enrich understanding of the relative advantages between quantum MFC and quantum CFC, and can provide useful information in choosing suitable feedback protocols for quantum systems.
As a key method in dealing with uncertainties, feedback has been understood fairly well in classical control theory. But for quantum control systems, the capability of measurement-based feedback control (MFC) has not been investigated systematically. In contrast to the control of classical systems where the measurement effect is negligible, the quantum measurement will cause a quantum state to collapse, which will inevitably introduce additional uncertainties besides the system initial uncertainty. Therefore, there is a complicated tradeoff between the uncertainty introduced and the information gained by the measurement, and thus a theoretical investigation of the capability of MFC is of fundamental importance. In this paper, inspired by both the Heisenberg uncertainty principle for quantum systems and the investigation of the feedback capability for classical systems, we try to answer the following three basic questions: (i) How to choose the measurement channel appropriately? (ii) Is the MFC still superior to the open loop control in dealing with the system information uncertainties? and (iii) What is the maximum capability or limitation of the MFC? These questions will be answered theoretically by establishing several theorems concerning the asymptotic reachability of eigenstates of a typical class of Hamiltonian control mode.
This paper investigates the potential of adaptive control systems utilizing quantum feedback loops for achieving enhanced control performance in complex dynamic systems. Classical control methods often struggle with the inherent uncertainties and nonlinearities present in many real-world systems. We propose a novel approach that leverages the principles of quantum mechanics, specifically quantum measurement and feedback, to directly influence system dynamics. The core concept involves creating a quantum feedback loop where continuous measurements of the system's state are processed through a quantum measurement apparatus and used to modify the control input. The utilization of quantum entanglement is explored as a mechanism to improve the sensitivity of the feedback loop, potentially leading to dramatically faster and more precise control compared to traditional approaches. This research introduces a theoretical framework and explores the mathematical foundations for such systems, highlighting key advantages and potential challenges. The presented model demonstrates the feasibility of adapting control strategies in real-time, based on quantum measurements, for improved system regulation and stability. This work represents a significant step towards exploring the application of quantum technologies in control engineering.
The paper first briefly introduces the current research on quantum control. Then the quantum open-loop control (no measurement introduced) and the closed-loop control (measurement introduced) was compared through a standard model of coherent control. When using quantum closed-loop control, we need measurement which inevitably brings in the reduction noise. This is different from the classical control systems. On the other hand, measurement-based feedback can reduce the influence of the system uncertainties. Thus, there is a tradeoff between the noise influence brought in by the measurement and the information got by the measurement. The paper demonstrate that in the case without decoherence, the quantum closed-loop control is superior to the open-loop control in dealing with the uncertainty in some sense. In the case with decoherence, we discuss the controllability of the quantum control through two performance indices.
Quantum engineering has seen rapid growth in the past two decades. Physicists, mathematicians and engineers have been working in unison to control a number of diverse systems in the quantum regime. Quantum control involving feedback has become particularly topical, as using information gained from a system can lead to more stable operation of a control protocol. Quantum feedback can be split into two paradigms: measurement based feedback and coherent feedback. Although it is increasingly evident that retaining the coherence of the feedback signal provides an intrinsic advantage over measurement-based feedback, coherent feedback is still a new paradigm. In particular, there are a limited number of options for coherently estimating a state within a feedback loop. As a step towards better understanding and implementation of quantum feedback, this thesis reports on modelling, estimation and control of quantum systems. The first topic is physical realisability of a variety of quantum systems, especially finite level systems and their outgrowths. Bilinear quantum stochastic differential equations (QSDEs) have to be employed to characterise these systems, which is a significant complement to the previous work on linear QSDEs. In light of the fact that direct and indirect couplings play a vital role in quantum network and control, we also provide state-space models for different classes of coupled open quantum systems incorporating both bidirectional and directional interactions. The second topic is coherent observers and optimal filtering. It is well established that classically estimation using the Kalman filter can provide improved performance over direct feedback schemes, and similar demonstrations have been performed for measurement-based quantum feedback. In this thesis I present coherent observers, including least mean squares estimators, which are driven by the coherent output of a specified quantum plant and designed such that some subset of the observer and plant's expectation values converge in the asymptotic limit. Not only can estimators "observe" mean quantities of quantum plant, but also they can "estimate" quantum correlations such as entanglement. This is of much importance to coherent feedback design in the absence of measurement steps without loss of fidelity. Last but not least, several topics regarding stabilisation and control design of quantum systems are discussed in my thesis. To be specific, tools for quantum stability analysis (e.g. Lyapunov conditions) are provided. Both measurement-based feedback and coherent feedback control design are taken into account. A measurement-based optimal controller for opto-mechanical systems aimed at synchronising different mechanical modes is presented, which is application-oriented. Moreover, A general observer-based coherent feedback control framework is studied, and I demonstrate a pole-placement approach via coherent observers that can be applied to various scenarios.
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 computers hold immense promise for solving problems intractable for classical machines, yet their practical realization is hindered by the fragility of quantum states. Quantum Error Correction (QEC) is indispensable for protecting quantum information from environmental noise and operational imperfections. Traditional QEC schemes often rely on measurement-based feedback, which involves performing measurements, processing the classical outcomes, and then applying corrective operations. This process introduces latency, consumes significant resources, and can itself be a source of errors due to the invasive nature of quantum measurement and the classical-quantum interface. Coherent feedback control offers a compelling alternative by allowing the controller to directly interact with the quantum system using quantum fields, without intermediate measurement and classical processing. This maintains the coherence of the quantum information throughout the feedback loop, potentially leading to more robust and faster error correction. This paper explores the theoretical framework and potential advantages of employing coherent feedback control for autonomous QEC. We review existing QEC paradigms, delve into the principles of coherent feedback, and propose how this approach can be integrated into autonomous QEC architectures. Specifically, we investigate its application to bosonic codes and stabilizer codes, discussing the engineering challenges and the prospects for achieving truly fault-tolerant quantum computation by minimizing the classical overhead and enhancing real-time error suppression.