Trends In Quantum Computing Research

Quantum information processing is an exciting new emergent and interdisciplinary field. It combines questions of national security (When will today's public key cryptography be broken?) to questions of fundamental science (What are the fundamental limits to information processing?). It has thrived through the collaboration between the computer, engineering, mathematical and physical sciences. It is a field that is challenging our understanding of information, communication, computation, and of the fundamental laws of nature. This book brings together leading research in the field.

Quantum mechanics, the subfield of physics that describes the behavior of very small (quantum) particles, provides the basis for a new paradigm of computing. First proposed in the 1980s as a way to improve computational modeling of quantum systems, the field of quantum computing has recently garnered significant attention due to progress in building small-scale devices. However, significant technical advances will be required before a large-scale, practical quantum computer can be achieved. Quantum Computing: Progress and Prospects provides an introduction to the field, including the unique characteristics and constraints of the technology, and assesses the feasibility and implications of creating a functional quantum computer capable of addressing real-world problems. This report considers hardware and software requirements, quantum algorithms, drivers of advances in quantum computing and quantum devices, benchmarks associated with relevant use cases, the time and resources required, and how to assess the probability of success.

D. Hilbert, in his famous program, formulated many open mathematical problems which were stimulating for the development of mathematics and a fruitful source of very deep and fundamental ideas. During the whole 20th century, mathematicians and specialists in other fields have been solving problems which can be traced back to Hilbert's program, and today there are many basic results stimulated by this program. It is sure that even at the beginning of the third millennium, mathematicians will still have much to do. One of his most interesting ideas, lying between mathematics and physics, is his sixth problem: To find a few physical axioms which, similar to the axioms of geometry, can describe a theory for a class of physical events that is as large as possible. We try to present some ideas inspired by Hilbert's sixth problem and give some partial results which may contribute to its solution. In the Thirties the situation in both physics and mathematics was very interesting. A.N. Kolmogorov published his fundamental work Grundbegriffe der Wahrschein lichkeitsrechnung in which he, for the first time, axiomatized modern probability theory. From the mathematical point of view, in Kolmogorov's model, the set L of ex perimentally verifiable events forms a Boolean a-algebra and, by the Loomis-Sikorski theorem, roughly speaking can be represented by a a-algebra S of subsets of some non-void set n.

By the year 2020, the basic memory components of a computer will be the size of individual atoms. At such scales, the current theory of computation will become invalid. "Quantum computing" is reinventing the foundations of computer science and information theory in a way that is consistent with quantum physics - the most accurate model of reality currently known. Remarkably, this theory predicts that quantum computers can perform certain tasks breathtakingly faster than classical computers – and, better yet, can accomplish mind-boggling feats such as teleporting information, breaking supposedly "unbreakable" codes, generating true random numbers, and communicating with messages that betray the presence of eavesdropping. This widely anticipated second edition of Explorations in Quantum Computing explains these burgeoning developments in simple terms, and describes the key technological hurdles that must be overcome to make quantum computers a reality. This easy-to-read, time-tested, and comprehensive textbook provides a fresh perspective on the capabilities of quantum computers, and supplies readers with the tools necessary to make their own foray into this exciting field. Topics and features: concludes each chapter with exercises and a summary of the material covered; provides an introduction to the basic mathematical formalism of quantum computing, and the quantum effects that can be harnessed for non-classical computation; discusses the concepts of quantum gates, entangling power, quantum circuits, quantum Fourier, wavelet, and cosine transforms, and quantum universality, computability, and complexity; examines the potential applications of quantum computers in areas such as search, code-breaking, solving NP-Complete problems, quantum simulation, quantum chemistry, and mathematics; investigates the uses of quantum information, including quantum teleportation, superdense coding, quantum data compression, quantum cloning, quantum negation, and quantum cryptography; reviews the advancements made towards practical quantum computers, covering developments in quantum error correction and avoidance, and alternative models of quantum computation. This text/reference is ideal for anyone wishing to learn more about this incredible, perhaps "ultimate," computer revolution. Dr. Colin P. Williams is Program Manager for Advanced Computing Paradigms at the NASA Jet Propulsion Laboratory, California Institute of Technology, and CEO of Xtreme Energetics, Inc. an advanced solar energy company. Dr. Williams has taught quantum computing and quantum information theory as an acting Associate Professor of Computer Science at Stanford University. He has spent over a decade inspiring and leading high technology teams and building business relationships with and Silicon Valley companies. Today his interests include terrestrial and Space-based power generation, quantum computing, cognitive computing, computational material design, visualization, artificial intelligence, evolutionary computing, and remote olfaction. He was formerly a Research Scientist at Xerox PARC and a Research Assistant to Prof. Stephen W. Hawking, Cambridge University.

This volume presents papers on the topics covered at the National Academy of Engineering's 2018 US Frontiers of Engineering Symposium. Every year the symposium brings together 100 outstanding young leaders in engineering to share their cutting-edge research and innovations in selected areas. The 2018 symposium was held September 5-7 and hosted by MIT Lincoln Laboratory in Lexington, Massachusetts. The intent of this book is to convey the excitement of this unique meeting and to highlight innovative developments in engineering research and technical work.

This book targets computer scientists and engineers who are familiar with concepts in classical computer systems but are curious to learn the general architecture of quantum computing systems. It gives a concise presentation of this new paradigm of computing from a computer systems' point of view without assuming any background in quantum mechanics. As such, it is divided into two parts. The first part of the book provides a gentle overview on the fundamental principles of the quantum theory and their implications for computing. The second part is devoted to state-of-the-art research in designing practical quantum programs, building a scalable software systems stack, and controlling quantum hardware components. Most chapters end with a summary and an outlook for future directions. This book celebrates the remarkable progress that scientists across disciplines have made in the past decades and reveals what roles computer scientists and engineers can play to enable practical-scale quantum computing.

A self-contained, graduate-level textbook that develops from scratch classical results as well as advances of the past decade.

As the amount of accumulated data across a variety of fields becomes harder to maintain, it is essential for a new generation of computational theories and tools to assist humans in extracting knowledge from this rapidly growing digital data. Global Trends in Intelligent Computing Research and Development brings together recent advances and in depth knowledge in the fields of knowledge representation and computational intelligence. Highlighting the theoretical advances and their applications to real life problems, this book is an essential tool for researchers, lecturers, professors, students, and developers who have seek insight into knowledge representation and real life applications.