Technology is the product of understanding physical processes and learning how to control them in order to achieve desired objectives. To be practically usable, technology requires a degree of reliability, which can be achieved by robust system design and control [1].
This review concerns quantum control results and methods that, over the years, have been used in the various operations involving quantum systems. Most of these methods have been originally developed outside the context of quantum physics, and, then, adapted to take into account the specificities of the various quantum physical platforms. Quantum control consists in designing adequate control signals required to efficiently manipulate systems conforming the laws of quantum mechanics in order to ensure the associated desired behaviours and performances. This work attempts to provide a thorough and self-contained introduction and review of the various quantum control theories and their applications. It encompasses issues spanning quantum control modelling, problem formulation, concepts of controllability, as well as a selection of the main control theories. Given the vastness of the field, we tried our best to be as concise as possible, and, for the details, the reader is pointed out to a profusion of references. The contents of the review are organized in the three major classes of control problems - open-loop control, closed-loop learning control, and feedback control - and, for each one of them, we present the main developments in quantum control theory. Finally, concerning the importance of attaining robustness and reliability due to inherent fragility of quantum systems, methods for quantum robust control are also surveyed.
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.
Quantum information science involves the use of precise control over quantum systems to explore new technologies. However, as quantum systems are scaled up they require an ever deeper understanding of many-body physics to achieve the required degree of control. Current experiments are entering a regime which requires active control of a mesoscopic number of coupled quantum systems or quantum bits (qubits). This thesis describes several approaches to this goal and shows how mesoscopic quantum systems can be controlled and utilized for quantum information tasks.
Advances in quantum control theory and optimization techniques have made possible a new phenomena of quantum engineering. Chemical reactions can now be dynamically manipulated using first-principles quantum chemical models, in which a laser field, rather than a catalyst, serve as photonic reagents to selectively break a chemical bond and yield products via intramolecular rearrangement. A field pulse may also be designed to perform ultrasensitive spectroscopy, where compounds with very similar chemical properties are differentiated through their unique interaction with resonant and off-resonant photons. Despite significant progress in theoretical and laboratory quantum control, however, quantum engineering remains principally challenging due to manifestation of noise and uncertainties associated with the input and system parameters. Specifically, a small magnitude of variation in the field and Hamiltonian parameters would cause an otherwise optimal field to deviate from controlling desired quantum state transitions and reaching a particular objective. Thus, an accurate analysis of robustness of controlled quantum dynamics followed by a robust control framework is essential in achieving quantum control in a practical setting. In this work, theoretical foundations for quantum control robustness analysis are presented from both a distributional perspective - in terms of moments of the transition amplitude, interferences, and transition probability - and a worst-case perspective. In addition, an evolutionary control strategy for achieving robust control via open- and closed-loop approach are described with its mechanism of convergence elucidated using the robustness analysis method.
Obtaining reliable state preparation protocols is a key step toward practical implementation of many quantum technologies, and one of the main tasks in quantum control. In this work, different reinforcement learning approaches are used to derive a feedback law for state preparation of a desired state in a target system. In particular, we focus on the robustness of the obtained strategies with respect to different types and amount of noise. Comparing the results indicates that the learned controls are more robust to unmodeled perturbations with respect to simple feedback strategy based on optimized population transfer, and that training on a simulated nominal model retains the same advantages displayed by controllers trained on real data. The possibility of effective off-line training of robust controllers promises significant advantages toward practical implementation.
Quantum mechanics is an advanced and fundamental physical theory that describes the interactions of energy and matter. The development of device fabrication and experimental control has witnessed how quantum mechanics will be used to establish a new technology. This is referred to as emerging quantum technology, which may be defined as the engineering of physical devices and systems that work on quantum principles [1]. Compared to conventional technologies governed by classical mechanics, there are two main imperatives driving the development of quantum technology [2]. The first is that the design of physical devices should be based on quantum principles when the devices are at length scales of nanometers and action scales and approaching Planck’s constant. The second is that quantum principles appearing to offer the promise of excellent performance can hardly be obtained within a classical physical framework.