Quantum computation and quantum information are an emerging research field that involves both physics, computer science, and engineering. The quantum nature of our world can be harnessed to dramatically improve the way we store, transmit, and process information. The first part (Chap. 1) of this thesis presents the theory behind quantum information science and gives a survey of some fascinating topics in this area. The second part (Chap. 2 and 3) studies dissipative quantum systems, which helps us understand the challenges facing all real quantum information processors. The third part (Chap. 4 and 5) discusses how we may use control strategies to fight dissipation and protect quantum information. The last part (Chap. 6 and 7) of this thesis describes circuit-QED systems, a solid state implementation of quantum computers that has become increasingly popular over the years due to great controllability and scalability. Most of my independent contributions are contained in Chap. 3, 4, 5, and Sec. 6.3.1, 7.3.
Quantum computation and quantum information are an emerging research field that involves both physics, computer science, and engineering. The quantum nature of our world can be harnessed to dramatically improve the way we store, transmit, and process information. The first part (Chap. 1) of this thesis presents the theory behind quantum information science and gives a survey of some fascinating topics in this area. The second part (Chap. 2 and 3) studies dissipative quantum systems, which helps us understand the challenges facing all real quantum information processors. The third part (Chap. 4 and 5) discusses how we may use control strategies to fight dissipation and protect quantum information. The last part (Chap. 6 and 7) of this thesis describes circuit-QED systems, a solid state implementation of quantum computers that has become increasingly popular over the years due to great controllability and scalability. Most of my independent contributions are contained in Chap. 3, 4, 5, and Sec. 6.3.1, 7.3.
Quantum information science has blossomed into a major research field over the past decade or so. In doing so, it has established links with several other areas of physics, computer science, and engineering. One of these areas is quantum control – the extension of control theory to physical systems whose dynamics are governed by quantum mechanics. Quantum control, like quantum information, is a fairly young field with remarkable technological consequences, and this cross-pollination is proving to be stimulating. In this thesis we explore some of the connections between quantum information and quantum control. In particular, (i) we examine quantum error correction from a quantum feedback control perspective, and demonstrate new continuous time implementations of quantum error correcting codes; (ii) we consider performing quantum feedback control experiments on a solid-state quantum computing architecture – circuit QED – and propose new measurement schemes that would enable such experiments; and (iii) we consider the problem of optimally estimating quantum processes, and in particular, analyze in detail the problem of optimally estimating a one-parameter quantum process.
In the last 25 years a new understanding has evolved of the role of information in quantum mechanics. At the same time there has been tremendous progress in atomic/optical physics and condensed matter physics, and particularly at the interface between these two formerly distinct fields, in developing experimental systems whose quantum states are long-lived and which can be engineered to perform quantum information processing tasks. These lecture notes will present a brief introduction to the basic theoretical concepts behind this `second quantum revolution.' These notes will also provide an introduction to `circuit QED.' In addition to being a novel test bed for non-linear quantum optics of microwave electrical circuits which use superconducting qubits as artificial atoms, circuit QED offers an architecture for constructing quantum information processors.
Experimental progress in atomic, molecular and optical physics, at the quantum level, as well as in condensed matter physics, has over the last few decades allowed us to not only observe quantum phenomena in nature, but also control them. This has led to the idea of “engineering” quantum systems, where microscopic constituents, such as single atoms, are manipulated in a precise manner to achieve some desired behaviour. By now, this has become a central theme in contemporary low-energy quantum physics. The change in viewpoint, from “observing” to “controlling,” leads to very different goals and opportunities, for experimentalists and theorists alike. This thesis contains seven publications on the following two related topics: i) engineering interactions in quantum systems, allowing for a large degree of control of system parameters, and ii) quantifying and understanding quantum correlations in dynamical quantum systems. The latter is an important goal in quantum information science, necessary to take advantage of quantum systems for information processing tasks, and thus expected to be central for future quantum technologies
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.
Quantum theory and quantum computing in recent years, has raised more and more increasing interest within the scientific community because of various reasons. First, the highly interdisciplinary nature of the subject which involves diverse topics such as, on the theoretical side, information theory and foundational issues of quantum mechanics and on the experimental side, the physics of quantum, optical, atomic and solid state systems. Secondly, the field is extremely promising for revolutionary technological implications in the near future. It is now perfectly clear that one can use quantum mechanics to process and transmit information in a way which does not have a classical analogue, and that using quantum techniques one can implement fully secure cryptographic systems. Recent breakthroughs, such as quantum teleportation, have led to extremely rapid progresses in a fascinating new field and, as a consequence, have attracted the interest of many scientists from varied disciplines. The purpose of this article is to provide a comprehensive overview about the deep involvement of quantum theory in quantum computation to young researchers and newcomers in the field.
In this research notebook on quantum computation and applications for quantum engineers, researchers, and scientists, we will discuss and summarized the core principles and practical application areas of quantum computation. We first discuss the historical prospect from which quantum computing emerged from the early days of computing before the dominance of modern microprocessors. And the re-emergence of that quest with the sunset of Moore's law in the current decade. The mapping of computation onto the behavior of physical systems is a historical challenge vividly illustrate by considering how quantum bits may be realized with a wide variety of physical systems, spanning from atoms to photons, using semiconductors and superconductors. The computing algorithms also change with the underline variety of physical systems and the possibility of encoding the information in the quantum systems compared to the ordinary classical computers because of these new abilities afforded by quantum systems. We will also consider the emerging engineering, science, technology, business, and social implications of these advancements. We will describe a substantial difference between quantum and classical computation paradigm. After we will discuss and understand engineering challenges currently faced by developers of the real quantum computation system. We will evaluate the essential technology required for quantum computers to be able to function correctly. Later on, discuss the potential business application, which can be touch by these new computation capabilities. We utilize the IBM Quantum Experience to run the real-world problem, although on a small scale.