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.
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.
Feedback plays an essential role in classical control theory, which has been investigated in depth. However, in quantum control theory, the study of feedback is still in its infancy. The paper continues to explore the fundamental characteristics of quantum feedback control for a typical coherent model based on the results of [3] by highlighting the significant differences between quantum feedback control and classical feedback control due to quantum measurement. The paper compares the control performance of quantum feedback control and quantum open-loop control in the cases with and without environment-induced decoherence. It concludes that in some sense, the quantum feedback control is still superior to the quantum open-loop control despite the complicated tradeoff in the feedback case, and further points out that how the quantum measurement-induced-collapse can play a positive role in the quantum feedback control.
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.
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.
For most practical quantum control systems, it is important and difficult to attain robustness and reliability due to unavoidable uncertainties in the system dynamics or models. Three kinds of typical approaches (e.g., closed-loop learning control, feedback control, and robust control) have been proved to be effective to solve these problems. This work presents a self-contained survey on the closed-loop and robust control of quantum systems, as well as a brief introduction to a selection of basic theories and methods in this research area, to provide interested readers with a general idea for further studies. In the area of closed-loop learning control of quantum systems, we survey and introduce such learning control methods as gradient-based methods, genetic algorithms (GA), and reinforcement learning (RL) methods from a unified point of view of exploring the quantum control landscapes. For the feedback control approach, the paper surveys three control strategies including Lyapunov control, measurement-based control, and coherent-feedback control. Then such topics in the field of quantum robust control as H(∞) control, sliding mode control, quantum risk-sensitive control, and quantum ensemble control are reviewed. The paper concludes with a perspective of future research directions that are likely to attract more attention.
We introduce a general framework, based on collision models and discrete completely positive maps, to describe on an equal footing coherent and measurement-based feedback control of quantum mechanical systems. We apply our framework to prominent tasks in quantum control, ranging from cooling to Hamiltonian control. Unlike other proposed comparisons, where coherent feedback always proves superior, we find that either measurements or coherent manipulations of the controller can be advantageous depending on the task at hand. Measurement-based feedback is typically superior in cooling, while coherent feedback is better at assisting quantum operations. Furthermore, we show that both coherent and measurement-based feedback loops allow one to simulate arbitrary Hamiltonian evolutions, and discuss their respective effectiveness in this regard.
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.