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Quantum Computing

Author: Mikio Nakahara
Publisher: CRC Press
ISBN: 9781420012293
Size: 78.97 MB
Format: PDF
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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.

Quantum Computing

Author: Mikio Nakahara
Publisher: CRC Press
ISBN: 9780750309837
Size: 29.66 MB
Format: PDF, ePub, Docs
View: 2790
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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.

Quantum Algorithms Via Linear Algebra

Author: Richard J. Lipton
Publisher: MIT Press
ISBN: 0262323575
Size: 46.17 MB
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This introduction to quantum algorithms is concise but comprehensive, covering many key algorithms. It is mathematically rigorous but requires minimal background and assumes no knowledge of quantum theory or quantum mechanics. The book explains quantum computation in terms of elementary linear algebra; it assumes the reader will have some familiarity with vectors, matrices, and their basic properties, but offers a review of all the relevant material from linear algebra. By emphasizing computation and algorithms rather than physics, this primer makes quantum algorithms accessible to students and researchers in computer science without the complications of quantum mechanical notation, physical concepts, and philosophical issues.After explaining the development of quantum operations and computations based on linear algebra, the book presents the major quantum algorithms, from seminal algorithms by Deutsch, Jozsa, and Simon through Shor's and Grover's algorithms to recent quantum walks. It covers quantum gates, computational complexity, and some graph theory. Mathematical proofs are generally short and straightforward; quantum circuits and gates are used to illuminate linear algebra; and the discussion of complexity is anchored in computational problems rather than machine models. Quantum Algorithms via Linear Algebra is suitable for classroom use or as a reference for computer scientists and mathematicians.

Quantum Computation And Quantum Information

Author: Michael A. Nielsen
Publisher: Cambridge University Press
ISBN: 9780521635035
Size: 38.82 MB
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First-ever comprehensive introduction to the major new subject of quantum computing and quantum information.

Quantum Computer Science

Author: Marco Lanzagorta
Publisher: Morgan & Claypool Publishers
ISBN: 1598297325
Size: 51.29 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

Classical And Quantum Information

Author: Dan C. Marinescu
Publisher: Academic Press
ISBN: 9780123838759
Size: 60.52 MB
Format: PDF, Kindle
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A new discipline, Quantum Information Science, has emerged in the last two decades of the twentieth century at the intersection of Physics, Mathematics, and Computer Science. Quantum Information Processing is an application of Quantum Information Science which covers the transformation, storage, and transmission of quantum information; it represents a revolutionary approach to information processing. Classical and Quantum Information covers topics in quantum computing, quantum information theory, and quantum error correction, three important areas of quantum information processing. Quantum information theory and quantum error correction build on the scope, concepts, methodology, and techniques developed in the context of their close relatives, classical information theory and classical error correcting codes. Presents recent results in quantum computing, quantum information theory, and quantum error correcting codes Covers both classical and quantum information theory and error correcting codes The last chapter of the book covers physical implementation of quantum information processing devices Covers the mathematical formalism and the concepts in Quantum Mechanics critical for understanding the properties and the transformations of quantum information

Problems And Solutions In Quantum Computing And Quantum Information

Author:
Publisher: World Scientific Publishing Company
ISBN: 9813238429
Size: 72.52 MB
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Quantum computing and quantum information are two of the fastest growing and most exciting research fields in physics. Entanglement, teleportation and the possibility of using the non-local behavior of quantum mechanics to factor integers in random polynomial time have also added to this new interest. This book presents a huge collection of problems in quantum computing and quantum information together with their detailed solutions, which will prove to be invaluable to students as well as researchers in these fields. Each chapter gives a comprehensive introduction to the topics. All the important concepts and areas such as quantum gates and quantum circuits, product Hilbert spaces, entanglement and entanglement measures, teleportation, Bell states, Bell measurement, Bell inequality, Schmidt decomposition, quantum Fourier transform, magic gate, von Neumann entropy, quantum cryptography, quantum error corrections, quantum games, number states and Bose operators, coherent states, squeezed states, Gaussian states, coherent Bell states, POVM measurement, quantum optics networks, beam splitter, phase shifter and Kerr Hamilton operator are included. A chapter on quantum channels has also been added. Furthermore a chapter on boolean functions and quantum gates with mapping bits to qubits is included. The topics range in difficulty from elementary to advanced. Almost all problems are solved in detail and most of the problems are self-contained. Each chapter also contains supplementary problems to challenge the reader. Programming problems with Maxima and SymbolicC++ implementations are also provided.

Quantum Computing

Author: Eleanor G. Rieffel
Publisher: MIT Press
ISBN: 0262015064
Size: 73.73 MB
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A thorough exposition of quantum computing and the underlying concepts of quantum physics, with explanations of the relevant mathematics and numerous examples.

Classical And Quantum Computation

Author: Alexei Yu. Kitaev
Publisher: American Mathematical Soc.
ISBN: 0821832298
Size: 64.47 MB
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This book presents a concise introduction to an emerging and increasingly important topic, the theory of quantum computing. The development of quantum computing exploded in 1994 with the discovery of its use in factoring large numbers--an extremely difficult and time-consuming problem when using a conventional computer. In less than 300 pages, the authors set forth a solid foundation to the theory, including results that have not appeared elsewhere and improvements on existing works. The book starts with the basics of classical theory of computation, including NP-complete problems and the idea of complexity of an algorithm. Then the authors introduce general principles of quantum computing and pass to the study of main quantum computation algorithms: Grover's algorithm, Shor's factoring algorithm, and the Abelian hidden subgroup problem. In concluding sections, several related topics are discussed (parallel quantum computation, a quantum analog of NP-completeness, and quantum error-correcting codes). This is a suitable textbook for a graduate course in quantum computing. Prerequisites are very modest and include linear algebra, elements of group theory and probability, and the notion of an algorithm (on a formal or an intuitive level). The book is complete with problems, solutions, and an appendix summarizing the necessary results from number theory.

Introduction To Quantum Computers

Author: Gennady P Berman
Publisher: World Scientific
ISBN: 9814496103
Size: 33.21 MB
Format: PDF, ePub
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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