The control of quantum multipartite mechanical systems is an emerging research topic in the quantum field due to the rapid development of technologies such as solid state physics and quantum optics. In this dissertation, we propose a quantum multi-channel decoupling methodology that facilitates the control of quantum multipartite mechanical systems and the design of complex quantum networks. Our approach uses bilinear input affine system models to express desired quantum control systems. This setting allows us to adopt various useful techniques from modern control theory, with some non-trivial modifications. In the quantum realm, we deal with the domain problem, and therefore the decoupling control of infinite-dimensional quantum systems is also included in our work. Our analysis is based on the operator algorithm, whose nature is the matrix operation. For quantum multipartite mechanical systems, the whole system's dimension is the product of all the single components' dimensions, yet in classical systems it is simply the sum of them. Thus, we use the tensor product method to analyze and design quantum multipartite mechanical systems. We give the conditions under which quantum multi-channel decoupling can be achieved and design the feedback control law.
The control of quantum multipartite mechanical systems is an emerging research topic in the quantum field due to the rapid development of technologies such as solid state physics and quantum optics. In this dissertation, we propose a quantum multi-channel decoupling methodology that facilitates the control of quantum multipartite mechanical systems and the design of complex quantum networks. Our approach uses bilinear input affine system models to express desired quantum control systems. This setting allows us to adopt various useful techniques from modern control theory, with some non-trivial modifications. In the quantum realm, we deal with the domain problem, and therefore the decoupling control of infinite-dimensional quantum systems is also included in our work. Our analysis is based on the operator algorithm, whose nature is the matrix operation. For quantum multipartite mechanical systems, the whole system's dimension is the product of all the single components' dimensions, yet in classical systems it is simply the sum of them. Thus, we use the tensor product method to analyze and design quantum multipartite mechanical systems. We give the conditions under which quantum multi-channel decoupling can be achieved and design the feedback control law.
We study multiple-input multiple-output (MIMO) quantum systems and explore quantum decoupling techniques that can be used to facilitate the design of quantum networks. We provide a quantum state feedback control law to change the structure of a quantum system in order to decouple the multiple channels. We show that an MIMO quantum system can be decoupled as an aggregate of n separated single-input single-output (SISO) quantum systems from an input-output point of view. We also discuss the conditions under which quantum decoupling can be achieved. We illustrate our method with several qubit and atomic systems.
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.
This paper investigates the dynamic control of quantum states and the engineering of multi-body entanglement. The core claim centers on leveraging dynamic quantum state manipulation to construct and control multi-body entanglement, ultimately enabling effective coupling between quantum information and physical systems. This work proposes a mechanism utilizing precise control of quantum bit rotations and phases to dynamically generate and manipulate multi-body entanglement. The potential applications include advanced quantum computing and quantum sensing. The research represents a significant advancement by moving beyond the static nature of traditional quantum entanglement, offering novel opportunities for quantum technologies. We explore theoretical frameworks and potential pathways for realizing this complex entanglement structure. The key mathematical concepts used are represented as follows: |ψ⟩ denotes a quantum state, ⊗ represents the tensor product for multi-body systems, R(θ, φ) is a rotation operator, U(φ) is a phase operator, ⟨ψ|ψ⟩ represents the probability of a specific state, H(ρ) represents the Hamiltonian operator, Tr(ρ) represents the trace of a density matrix, I is the identity operator, and ε is a small parameter used in perturbation theory. The goal is to develop robust methods for creating and maintaining entanglement across multiple particles, addressing challenges related to decoherence and control fidelity. This work lays the foundation for future research into more complex entangled systems and their applications.
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.
The study of open quantum systems forms one of the main problems of modern physics. This thesis aims at contributing to this field, and focuses on the investigation of non-Markovian dynamics of open quantum systems. Here, as a special case, quantum many-body systems provide for a rich field of research. With the ability to control them being of essential importance for the development of quantum technologies, the characterization of their dynamical properties has also drawn a lot of interest lately. One of the main methodological tasks in the study of open quantum systems is to reduce the infinite degrees of freedom of the total system. In order to achieve this, the thesis makes use of the tensor network method matrix product states and combines it with the picture of the quantum stochastic Schrödinger equation. However, when computing the dynamics of many-body systems of system size N, even the reduced system dynamics scale with 2N, making larger system sizes difficult to access. Therefore, especially when computing non-Markovian time-dynamics where the information backflow from the reservoir has to be taken into account, efficiently constructed algorithms are required. This thesis proposes these type of algorithms and demonstrates their application. They enable an access to larger system sizes, thus making it possible to investigate non-equilibrium steady-states of quantum many-body systems in a non-Markovian interaction for system sizes up to N=30. This thesis consists of three parts. The first part provides an introduction to the theory of open quantum systems and to the methodology for modeling them. The second part examines many-body system-reservoir interaction in the non-Markovian regime by investigating the case of fully coherent self-feedback. It uses the one-dimensional Heisenberg spin-1/2 chain as a paradigmatic and recently intensely studied many-body system. It is demonstrated that this gives rise to new conditions for the feedback phase and to highly non-trivial states within the system as well as to the possibility of partially characterizing the system non-invasively and storing excitation within it. Next, a novel approach to the boundary-driven Heisenberg chain is presented, where the chain is exposed to a coherent driving field, thus enabling a comparison to the well-studied incoherently driven model. The third part demonstrates the use of an external pump to control the feedback phase of a Lambda-type three-level system, where the external pump pulse is shown to be a new control parameter. The thesis concludes with the proposition to enhance the indistinguishability of two photons by feedback control.
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.