QUROPE Quantum Information Processing and Communication in Europe

Our conception of what a computation is has been altered drastically during history, since the times of Leibniz, Babbage and Turing. The result of this remarkable history of ideas – computers as we know them today – has changed our modern society significantly. Yet, the development of computing and communication devices has not come to a stop. Recent developments have shown, in fact, that we are at the beginning of a new era of harnessing the laws of nature, using quantum physics for unprecedented and very powerful ways of information processing. The development of Quantum Information Science (QIS) has been driven by theoretical work of scientists working on the boundary between Physics, Computer Science, Mathematics, and Information Theory. In the early stages of this development, theoretical work has often been far ahead of experimental realization of these ideas. At the same time, theory has provided a number of proposals of how to implement basic ideas and concepts from quantum information in specific physical systems. These ideas are now forming the basis for successful experimental work in the laboratory, driving forward the development of tools that will in turn form the basis for all future technologies which employ, control and manipulate matter and radiation at the quantum level. While the development of QIS has started as early as in the 80’s, the field has gained significant momentum in the last decade. Major triggers were the discovery of fast quantum algorithms and the identification of concrete physical systems in which a quantum computer could be realized. In the meantime, a broad spectrum of research activities can be observed, ranging from the study of fundamental concepts such as quantum entanglement, to novel applications such as quantum simulators, and with significant spin-off also to other fields of research. In many of these activities, European research has played a leading role and has established a strong set of world leading centres. It is important to realize that theoretical activities are often interdisciplinary in nature and span a broad spectrum of research in which the different activities are benefiting from each other to a large degree. Thus it does not seem to be advisable to concentrate research on too narrowly defined topics only. The following list nevertheless tries to highlight the main current areas of quantum information theory as it has been described in more detail in the strategic report.

Quantum algorithms & complexity. Quantum algorithms will be one of the most powerful applications of quantum computers. We know only a few examples up to date, such as Shor’s factoring algorithm, but new techniques and protocols are currently being developed. This area remains one of the cornerstones of research in QIC.

Computational models & architectures. There are many different ideas of how to make quantum systems compute. New computer models, which have only recently been developed, are providing new agendas to formulate quantum algorithms. At the same time, they have opened new ideas for physical implementations of a quantum computer, and we expect new methods for fault-tolerant computation that will make it technologically less challenging to realize scalable devices in the laboratory.

Geometric and topological methods. These methods represent an alternative approach to the realization of quantum computing. They have intrinsic fault-tolerant properties that do not need an active error detection and recovery; however, the overhead that one has to pay are longer operation times, so that much work must still be done to identify which of the available schemes suit better to quantum computation.

Quantum simulations. Quantum simulators may become the first short-term application of quantum computers, since with modest requirements one may be able to perform simulations which are impossible with classical computers. They could be used for a variety of purposes, e.g., to obtain an accurate description of chemical compounds and reactions, to gain deeper understanding of high temperature superconductivity, or to find out the reason why quarks are always confined.

Quantum error correction & purification. Despite its amazing power, a quantum computer will be a rather fragile device, susceptible to disturbances and errors. Fortunately, methods have been developed to protect such a device against disturbances and imperfections, as long as these are small enough. These methods are constantly being improved and refined, but there is still a lot of work to be done until we can run a quantum computer reliably.

Theory of entanglement. Entanglement represents a novel and particularly strong form of correlations which is not present in classical systems. It is a key resource in quantum information science and, at the same time, one of the most prominent features of quantum physics. Insights in the theory of entanglement will continue to have broad implications, and applications will lie not only within the field of QIS itself, but also in other areas of physics, such as field theory and condensed matter physics.

Multi-partite entanglement & applications. Research on multi-particle entanglement has emerged recently, and it is expected to have an impact on novel protocols for quantum information processing. Multi-partite entangled states represent keys resources, both for quantum computers and for novel communication schemes with several users such as quantum-secret sharing, quantum voting etc. Alternatively one can consider multi-partite fingerprinting schemes that would allow for the determination of whether or not a number of databases are identical with very little resources.

Noisy communication channels. In practice, all communication channels such as optical fibres are subject to some level of noise. Such noise can destroy the crucial entanglement or other quantum properties that are needed, e.g., for security or to reduce communication complexity. A proper understanding of how one can communicate via noisy quantum channels and of the capacities of such channels is at the heart of the study of quantum communication tasks.

Fundamental quantum mechanics and decoherence. Quantum information was born, in part, via research on the famous Einstein-Podolski-Rosen paradox and the issue of quantum non-locality. It is now understood that non-locality is one of the central aspects of quantum mechanics. More generally, quantum information profits substantially from studying the fundamental aspects of quantum mechanics and, at the same time, it yields new perspectives, raising hopes of gaining a deeper understanding of the very basis of quantum mechanics. In particular, quantum information theory can provide deeper understanding of dynamics of open quantum systems.

Spin-off to other fields. A very exciting aspect of theoretical work in QIS is the impact that it is beginning to gain on other fields of science. Examples are given by the theory of classical computing, by field theory, and by condensed matter physics. Many of the questions that are now being asked in this area can only be answered or even formulated correctly because of the many insights and techniques gained in the research in entanglement theory in recent years. Theoretical research in QIS in Europe has prospered through the efficient support for collaboration by the European Union, the European Science Foundation and the national funding bodies. In the face of significantly growing international competition from North America, Japan and Australia it will be essential that flexible support compatible with innovative work will continue to be provided.