Mathematics of Quantum Computation and Quantum Technology

Author: Louis Kauffman
Publisher: CRC Press
ISBN: 9781584889007
Format: PDF, Docs
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Research and development in the pioneering field of quantum computing involve just about every facet of science and engineering, including the significant areas of mathematics and physics. Based on the firm understanding that mathematics and physics are equal partners in the continuing study of quantum science, Mathematics of Quantum Computation and Quantum Technology explores the rapid mathematical advancements made in this field in recent years. Novel Viewpoints on Numerous Aspects of Quantum Computing and Technology Edited by a well-respected team of experts, this volume compiles contributions from specialists across various disciplines. It contains four main parts, beginning with topics in quantum computing that include quantum algorithms and hidden subgroups, quantum search, algorithmic complexity, and quantum simulation. The next section covers quantum technology, such as mathematical tools, quantum wave functions, superconducting quantum computing interference devices (SQUIDs), and optical quantum computing. The section on quantum information deals with error correction, cryptography, entanglement, and communication. The final part explores topological quantum computation, knot theory, category algebra, and logic. The Tools You Need to Tackle the Next Generation of Quantum Technology This book facilitates both the construction of a common quantum language and the development of interdisciplinary quantum techniques, which will aid efforts in the pursuit of the ultimate goal-a "real" scalable quantum computer.

Mathematical Aspects of Quantum Computing 2007

Author: Mikio Nakahara
Publisher: World Scientific
ISBN: 9812814485
Format: PDF, ePub
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This book provides a comprehensive overview of the mathematical aspects of quantum computing. It will be useful for graduate students and researchers interested in quantum computing from different areas of physics, mathematics, informatics and computer science. The lecture notes in this volume are written in a self-contained style, and hence are accessible for graduate students and researchers with even less background in the topics. Sample Chapter(s). Quantum Computing: An Overview (804 KB). Contents: Quantum Computing: An Overview (M Nakahara); Braid Group and Topological Quantum Computing (T Ootsuka & K Sakuma); An Introduction to Entanglement Theory (D J H Markham); Holonomic Quantum Computing and Its Optimization (S Tanimura et al.); Playing Games in Quantum Mechanical Settings: Features of Quantum Games (u K uzdemir et al.); Quantum Error-Correcting Codes (M Hagiwara); Controled Teleportation of an Arbitrary Unknown Two-Qubit Entangled State (V Ebrahimi et al.); Notes on the Dr-Cirac Classification (Y Ota et al.); Bang-Bang Control of Entanglement in Spin-Bus-Boson Model (R Rahimi et al.); Numerical Computation of Time-Dependent Multipartite Nonclassical Correlation (A SaiToh et al.); On Classical No-Cloning Theorem Under Liouville Dynamics and Distances (T Yamano & O Iguchi). Readership: Advanced undergraduate students, graduate students and researchers in physics, mathematics, informatics and computer science.

Mathematics of Quantum Computation

Author: Ranee K. Brylinski
Publisher: CRC Press
ISBN: 1420035371
Format: PDF, ePub
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Among the most exciting developments in science today is the design and construction of the quantum computer. Its realization will be the result of multidisciplinary efforts, but ultimately, it is mathematics that lies at the heart of theoretical quantum computer science. Mathematics of Quantum Computation brings together leading computer scientists, mathematicians, and physicists to provide the first interdisciplinary but mathematically focused exploration of the field's foundations and state of the art. Each section of the book addresses an area of major research, and does so with introductory material that brings newcomers quickly up to speed. Chapters that are more advanced include recent developments not yet published in the open literature. Information technology will inevitably enter into the realm of quantum mechanics, and, more than all the atomic, molecular, optical, and nanotechnology advances, it is the device-independent mathematics that is the foundation of quantum computer and information science. Mathematics of Quantum Computation offers the first up-to-date coverage that has the technical depth and breadth needed by those interested in the challenges being confronted at the frontiers of research.

Topological Quantum Computation

Author: Zhenghan Wang
Publisher: American Mathematical Soc.
ISBN: 0821849301
Format: PDF, ePub
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Topological quantum computation is a computational paradigm based on topological phases of matter, which are governed by topological quantum field theories. In this approach, information is stored in the lowest energy states of many-anyon systems and processed by braiding non-abelian anyons. The computational answer is accessed by bringing anyons together and observing the result. Besides its theoretical esthetic appeal, the practical merit of the topological approach lies in its error-minimizing hypothetical hardware: topological phases of matter are fault-avoiding or deaf to most local noises, and unitary gates are implemented with exponential accuracy. Experimental realizations are pursued in systems such as fractional quantum Hall liquids and topological insulators. This book expands on the author's CBMS lectures on knots and topological quantum computing and is intended as a primer for mathematically inclined graduate students. With an emphasis on introducing basic notions and current research, this book gives the first coherent account of the field, covering a wide range of topics: Temperley-Lieb-Jones theory, the quantum circuit model, ribbon fusion category theory, topological quantum field theory, anyon theory, additive approximation of the Jones polynomial, anyonic quantum computing models, and mathematical models of topological phases of matter.

Quantum Computation and Information

Author: Samuel J. Lomonaco
Publisher: American Mathematical Soc.
ISBN: 0821821407
Format: PDF, Kindle
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This book is a collection of papers given by invited speakers at the first AMS Special Session on Quantum Computation and Information held at the January 2000 Annual Meeting of the AMS in Washington, DC. The papers in this volume give readers a broad introduction to the many mathematical research challenges posed by the new and emerging field of quantum computation and quantum information. Of particular interest is a long paper by Lomonaco and Kauffman discussing mathematical and computational aspects of the so-called hidden subgroup algorithm. This book is the companion volume to Quantum Computation: A Grand Mathematical Challenge for the Twenty-First Century and the Millennium, Volume 58 in the Proceedings of Symposia in Applied Mathematics series.

Quantum Information

Author: Stephen Barnett
Publisher: Oxford University Press
ISBN: 0198527624
Format: PDF, ePub
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Quantum information is an area of science, which brings together physics, information theory, computer science & mathematics. This book, which is based on two successful lecture courses, is intended to introduce readers to the ideas behind new developments including quantum cryptography, teleportation & quantum computing.

Bio Inspired and Nanoscale Integrated Computing

Author: Mary Mehrnoosh Eshaghian-Wilner
Publisher: John Wiley & Sons
ISBN: 0470429976
Format: PDF, Docs
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Brings the latest advances in nanotechnology and biology to computing This pioneering book demonstrates how nanotechnology can create even faster, denser computing architectures and algorithms. Furthermore, it draws from the latest advances in biology with a focus on bio-inspired computing at the nanoscale, bringing to light several new and innovative applications such as nanoscale implantable biomedical devices and neural networks. Bio-Inspired and Nanoscale Integrated Computing features an expert team of interdisciplinary authors who offer readers the benefit of their own breakthroughs in integrated computing as well as a thorough investigation and analyses of the literature. Carefully edited, the book begins with an introductory chapter providing a general overview of the field. It ends with a chapter setting forth the common themes that tie the chapters together as well as a forecast of emerging avenues of research. Among the important topics addressed in the book are modeling of nano devices, quantum computing, quantum dot cellular automata, dielectrophoretic reconfigurable nano architectures, multilevel and three-dimensional nanomagnetic recording, spin-wave architectures and algorithms, fault-tolerant nanocomputing, molecular computing, self-assembly of supramolecular nanostructures, DNA nanotechnology and computing, nanoscale DNA sequence matching, medical nanorobotics, heterogeneous nanostructures for biomedical diagnostics, biomimetic cortical nanocircuits, bio-applications of carbon nanotubes, and nanoscale image processing. Readers in electrical engineering, computer science, and computational biology will gain new insights into how bio-inspired and nanoscale devices can be used to design the next generation of enhanced integrated circuits.

Schr dinger s Killer App

Author: Jonathan P. Dowling
Publisher: Taylor & Francis
ISBN: 1439896747
Format: PDF
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The race is on to construct the first quantum code breaker, as the winner will hold the key to the entire Internet. From international, multibillion-dollar financial transactions to top-secret government communications, all would be vulnerable to the secret-code-breaking ability of the quantum computer. Written by a renowned quantum physicist closely involved in the U.S. government’s development of quantum information science, Schrödinger’s Killer App: Race to Build the World’s First Quantum Computer presents an inside look at the government’s quest to build a quantum computer capable of solving complex mathematical problems and hacking the public-key encryption codes used to secure the Internet. The "killer application" refers to Shor’s quantum factoring algorithm, which would unveil the encrypted communications of the entire Internet if a quantum computer could be built to run the algorithm. Schrödinger’s notion of quantum entanglement—and his infamous cat—is at the heart of it all. The book develops the concept of entanglement in the historical context of Einstein’s 30-year battle with the physics community over the true meaning of quantum theory. It discusses the remedy to the threat posed by the quantum code breaker: quantum cryptography, which is unbreakable even by the quantum computer. The author also covers applications to other important areas, such as quantum physics simulators, synchronized clocks, quantum search engines, quantum sensors, and imaging devices. In addition, he takes readers on a philosophical journey that considers the future ramifications of quantum technologies. Interspersed with amusing and personal anecdotes, this book presents quantum computing and the closely connected foundations of quantum mechanics in an engaging manner accessible to non-specialists. Requiring no formal training in physics or advanced mathematics, it explains difficult topics, including quantum entanglement, Schrödinger’s cat, Bell’s inequality, and quantum computational complexity, using simple analogies.

Quantum Computing Devices

Author: Goong Chen
Publisher: CRC Press
ISBN: 9781420011777
Format: PDF, Mobi
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One of the first books to thoroughly examine the subject, Quantum Computing Devices: Principles, Designs, and Analysis covers the essential components in the design of a "real" quantum computer. It explores contemporary and important aspects of quantum computation, particularly focusing on the role of quantum electronic devices as quantum gates. Largely self-contained and written in a tutorial style, this reference presents the analysis, design, and modeling of the major types of quantum computing devices: ion traps, cavity quantum electrodynamics (QED), linear optics, quantum dots, nuclear magnetic resonance (NMR), superconducting quantum interference devices (SQUID), and neutral atom traps. It begins by explaining the fundamentals and algorithms of quantum computing, followed by the operations and formalisms of quantum systems. For each electronic device, the subsequent chapters discuss physical properties, the setup of qubits, control actions that produce the quantum gates that are universal for quantum computing, relevant measurements, and decoherence properties of the systems. The book also includes tables, diagrams, and figures that illustrate various data, uses, and designs of quantum computing. As nanoelectronics will inevitably replace microelectronics, the development of quantum information science and quantum computing technology is imperative to the future of information science and technology. Quantum Computing Devices: Principles, Designs, and Analysis helps fulfill this need by providing a comprehensive collection of the most promising devices for the future.

Quantum Computing

Author: Mika Hirvensalo
Publisher: Springer Science & Business Media
ISBN: 3662044617
Format: PDF, ePub, Docs
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Mika Hirvensalo maps out the new multidisciplinary research area of quantum computing. The text contains an introduction to quantum computing as well as the most important recent results on the topic. The presentation is uniform and computer science-oriented. Thus, the book differs from most of the previous ones which are mainly physics-oriented. The special style of presentation makes the theory of quantum computing accessible to a larger audience. Many examples and exercises ease the understanding. In this second edition, a new chapter on quantum information has been added and numerous corrections, amendments, and extensions have been incorporated throughout the entire text.