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Quantum Computing

Author: Mikio Nakahara
Publisher: CRC Press
ISBN: 9781420012293
Size: 79.67 MB
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Covering both theory and progressive experiments, Quantum Computing: From Linear Algebra to Physical Realizations explains how and why superposition and entanglement provide the enormous computational power in quantum computing. This self-contained, classroom-tested book is divided into two sections, with the first devoted to the theoretical aspects of quantum computing and the second focused on several candidates of a working quantum computer, evaluating them according to the DiVincenzo criteria. Topics in Part I Linear algebra Principles of quantum mechanics Qubit and the first application of quantum information processing—quantum key distribution Quantum gates Simple yet elucidating examples of quantum algorithms Quantum circuits that implement integral transforms Practical quantum algorithms, including Grover’s database search algorithm and Shor’s factorization algorithm The disturbing issue of decoherence Important examples of quantum error-correcting codes (QECC) Topics in Part II DiVincenzo criteria, which are the standards a physical system must satisfy to be a candidate as a working quantum computer Liquid state NMR, one of the well-understood physical systems Ionic and atomic qubits Several types of Josephson junction qubits The quantum dots realization of qubits Looking at the ways in which quantum computing can become reality, this book delves into enough theoretical background and experimental research to support a thorough understanding of this promising field.

Diversities In Quantum Computation And Quantum Information

Author: Mikio Nakahara
Publisher: World Scientific
ISBN: 9814425982
Size: 13.90 MB
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This book is a collection of lecture notes and contributions in "Summer School on Diversities in Quantum Computation/Information" held on 1-5 August, 2010 at U-Community Hotel, Higashi-Osaka, Japan. Lecturers are world class authorities in respective areas in quantum information and quantum computing including physics, mathematics, chemistry and information science. They lectured on cutting-edge research frontiers where they are currently working, including quantum error correction, relativistic quantum information, quantum computing of link polynomials, quantum algorithms, etc. Each lecture note is written in a self-contained manner so that it may be used as a textbook for one semester graduate course or advanced undergraduate course. Contributions report current research subjects also in a self-contained manner. We believe that these articles are accessible to the readers form various disciplines.

Quantum Computer Science

Author: Marco Lanzagorta
Publisher: Morgan & Claypool Publishers
ISBN: 1598297325
Size: 67.92 MB
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In this text we present a technical overview of the emerging field of quantum computation along with new research results by the authors. What distinguishes our presentation from that of others is our focus on the relationship between quantum computation and computer science. Specifically, our emphasis is on the computational model of quantum computing rather than on the engineering issues associated with its physical implementation. We adopt this approach for the same reason that a book on computer programming doesn't cover the theory and physical realization of semiconductors. Another distinguishing feature of this text is our detailed discussion of the circuit complexity of quantum algorithms. To the extent possible we have presented the material in a form that is accessible to the computer scientist, but in many cases we retain the conventional physics notation so that the reader will also be able to consult the relevant quantum computing literature. Although we expect the reader to have a solid understanding of linear algebra, we do not assume a background in physics. This text is based on lectures given as short courses and invited presentations around the world, and it has been used as the primary text for a graduate course at George Mason University. In all these cases our challenge has been the same: how to present to a general audience a concise introduction to the algorithmic structure and applications of quantum computing on an extremely short period of time. The feedback from these courses and presentations has greatly aided in making our exposition of challenging concepts more accessible to a general audience. Table of Contents: Introduction / The Algorithmic Structure of Quantum Computing / Advantages and Limitations of Quantum Computing / Amplitude Amplification / Case Study: Computational Geometry / The Quantum Fourier Transform / Case Study: The Hidden Subgroup / Circuit Complexity Analysis of Quantum Algorithms / Conclusions / Bibliography

Transactions On Computational Science Xxiv

Author: Marina L. Gavrilova
Publisher: Springer
ISBN: 3662457113
Size: 27.72 MB
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The LNCS journal Transactions on Computational Science reflects recent developments in the field of Computational Science, conceiving the field not as a mere ancillary science but rather as an innovative approach supporting many other scientific disciplines. The journal focuses on original high-quality research in the realm of computational science in parallel and distributed environments, encompassing the facilitating theoretical foundations and the applications of large-scale computations and massive data processing. It addresses researchers and practitioners in areas ranging from aerospace to biochemistry, from electronics to geosciences, from mathematics to software architecture, presenting verifiable computational methods, findings, and solutions and enabling industrial users to apply techniques of leading-edge, large-scale, high performance computational methods. This, the 24th issue of the Transactions on Computational Science journal, guest edited by Himanshu Thapliyal and Nagarajan Ranganathan, is devoted to the topic of reversible computing. It is comprised of eight selected papers on reversible energy recovery designs, design of reversible logic gates and arithmetic circuits in optical computing, reversible basic linear algebra subprograms, quantum circuit description language, and reversible circuit and logic synthesis.

Introduction To Quantum Computers

Author: Gennady P Berman
Publisher: World Scientific
ISBN: 9814496103
Size: 78.70 MB
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Quantum computing promises to solve problems which are intractable on digital computers. Highly parallel quantum algorithms can decrease the computational time for some problems by many orders of magnitude. This important book explains how quantum computers can do these amazing things. Several algorithms are illustrated: the discrete Fourier transform, Shor's algorithm for prime factorization; algorithms for quantum logic gates; physical implementations of quantum logic gates in ion traps and in spin chains; the simplest schemes for quantum error correction; correction of errors caused by imperfect resonant pulses; correction of errors caused by the nonresonant actions of a pulse; and numerical simulations of dynamical behavior of the quantum Control-Not gate. An overview of some basic elements of computer science is presented, including the Turing machine, Boolean algebra, and logic gates. The required quantum ideas are explained. Contents:The Turing MachineBinary System and Boolean AlgebraThe Quantum ComputerThe Discrete Fourier TransformQuantum Factorization of IntegersLogic GatesImplementation of Logic Gates Using TransistorsReversible Logic GatesQuantum Logic GatesTwo and Three Qubit Quantum Logic GatesOne-Qubit RotationAj-TransformationBjk-TransformationUnitary Transformations and Quantum DynamicsQuantum Dynamics at Finite TemperaturePhysical Realization of Quantum ComputationsCONTROL-NOT Gate in an Ion TrapAj and Bjk Gates in an Ion TrapLinear Chains of Nuclear SpinsDigital Gates in a Spin ChainNon-resonant Action of π-PulsesExperimental Logic Gates in Quantum SystemsError Correction for Quantum ComputersQuantum Gates in a Two-Spin SystemQuantum Logic Gates in a Spin Ensemble at Room TemperatureEvolution of Four-Spin MoleculesGetting the Desired Density Matrix Readership: Computer scientists, and mathematicians and physicists interested in quantum computing. Keywords:Quantum Computer;Logic Gates;Transistor;Quantum Logic Gates;Quantum Mechanics;Quantum Dynamics;Spin;Shor's Algorithm;Ion Trap;Quantum Dot;Ising Interaction;Density MatrixReviews: “… one of the first books on the market about the basics of quantum computation … A good feature of this is that it is a succinct overview of quantum computation for someone who is just starting in the field.” Contemporary Physics

Differentialgeometrie Topologie Und Physik

Author: Mikio Nakahara
Publisher: Springer-Verlag
ISBN: 3662453002
Size: 43.25 MB
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Differentialgeometrie und Topologie sind wichtige Werkzeuge für die Theoretische Physik. Insbesondere finden sie Anwendung in den Gebieten der Astrophysik, der Teilchen- und Festkörperphysik. Das vorliegende beliebte Buch, das nun erstmals ins Deutsche übersetzt wurde, ist eine ideale Einführung für Masterstudenten und Forscher im Bereich der theoretischen und mathematischen Physik. - Im ersten Kapitel bietet das Buch einen Überblick über die Pfadintegralmethode und Eichtheorien. - Kapitel 2 beschäftigt sich mit den mathematischen Grundlagen von Abbildungen, Vektorräumen und der Topologie. - Die folgenden Kapitel beschäftigen sich mit fortgeschritteneren Konzepten der Geometrie und Topologie und diskutieren auch deren Anwendungen im Bereich der Flüssigkristalle, bei suprafluidem Helium, in der ART und der bosonischen Stringtheorie. - Daran anschließend findet eine Zusammenführung von Geometrie und Topologie statt: es geht um Faserbündel, characteristische Klassen und Indextheoreme (u.a. in Anwendung auf die supersymmetrische Quantenmechanik). - Die letzten beiden Kapitel widmen sich der spannendsten Anwendung von Geometrie und Topologie in der modernen Physik, nämlich den Eichfeldtheorien und der Analyse der Polakov'schen bosonischen Stringtheorie aus einer gemetrischen Perspektive. Mikio Nakahara studierte an der Universität Kyoto und am King’s in London Physik sowie klassische und Quantengravitationstheorie. Heute ist er Physikprofessor an der Kinki-Universität in Osaka (Japan), wo er u. a. über topologische Quantencomputer forscht. Diese Buch entstand aus einer Vorlesung, die er während Forschungsaufenthalten an der University of Sussex und an der Helsinki University of Sussex gehalten hat.

Fft

Author: Elbert Oran Brigham
Publisher:
ISBN: 9783486231779
Size: 41.41 MB
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