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Autore: | Kaye Phillip |
Titolo: | An introduction to quantum computing / / Phillip Kaye, Raymond Laflamme, Michele Mosca |
Pubblicazione: | Oxford, : Oxford University Press, 2007 |
Edizione: | 1st ed. |
Descrizione fisica: | xi, 274 p. : ill |
Disciplina: | 004.1 |
Soggetto topico: | Quantum computers |
Computers | |
Altri autori: | LaflammeRaymond MoscaMichele |
Nota di bibliografia: | Includes bibliographical references and index. |
Nota di contenuto: | Intro -- Contents -- Preface -- Acknowledgements -- 1 INTRODUCTION AND BACKGROUND -- 1.1 Overview -- 1.2 Computers and the Strong Church-Turing Thesis -- 1.3 The Circuit Model of Computation -- 1.4 A Linear Algebra Formulation of the Circuit Model -- 1.5 Reversible Computation -- 1.6 A Preview of Quantum Physics -- 1.7 Quantum Physics and Computation -- 2 LINEAR ALGEBRA AND THE DIRAC NOTATION -- 2.1 The Dirac Notation and Hilbert Spaces -- 2.2 Dual Vectors -- 2.3 Operators -- 2.4 The Spectral Theorem -- 2.5 Functions of Operators -- 2.6 Tensor Products -- 2.7 The Schmidt Decomposition Theorem -- 2.8 Some Comments on the Dirac Notation -- 3 QUBITS AND THE FRAMEWORK OF QUANTUM MECHANICS -- 3.1 The State of a Quantum System -- 3.2 Time-Evolution of a Closed System -- 3.3 Composite Systems -- 3.4 Measurement -- 3.5 Mixed States and General Quantum Operations -- 3.5.1 Mixed States -- 3.5.2 Partial Trace -- 3.5.3 General Quantum Operations -- 4 A QUANTUM MODEL OF COMPUTATION -- 4.1 The Quantum Circuit Model -- 4.2 Quantum Gates -- 4.2.1 1-Qubit Gates -- 4.2.2 Controlled-U Gates -- 4.3 Universal Sets of Quantum Gates -- 4.4 Efficiency of Approximating Unitary Transformations -- 4.5 Implementing Measurements with Quantum Circuits -- 5 SUPERDENSE CODING AND QUANTUM TELEPORTATION -- 5.1 Superdense Coding -- 5.2 Quantum Teleportation -- 5.3 An Application of Quantum Teleportation -- 6 INTRODUCTORY QUANTUM ALGORITHMS -- 6.1 Probabilistic Versus Quantum Algorithms -- 6.2 Phase Kick-Back -- 6.3 The Deutsch Algorithm -- 6.4 The Deutsch-Jozsa Algorithm -- 6.5 Simon's Algorithm -- 7 ALGORITHMS WITH SUPERPOLYNOMIAL SPEED-UP -- 7.1 Quantum Phase Estimation and the Quantum Fourier Transform -- 7.1.1 Error Analysis for Estimating Arbitrary Phases -- 7.1.2 Periodic States -- 7.1.3 GCD, LCM, the Extended Euclidean Algorithm -- 7.2 Eigenvalue Estimation. |
7.3 Finding-Orders -- 7.3.1 The Order-Finding Problem -- 7.3.2 Some Mathematical Preliminaries -- 7.3.3 The Eigenvalue Estimation Approach to Order Finding -- 7.3.4 Shor's Approach to Order Finding -- 7.4 Finding Discrete Logarithms -- 7.5 Hidden Subgroups -- 7.5.1 More on Quantum Fourier Transforms -- 7.5.2 Algorithm for the Finite Abelian Hidden Subgroup Problem -- 7.6 Related Algorithms and Techniques -- 8 ALGORITHMS BASED ON AMPLITUDE AMPLIFICATION -- 8.1 Grover's Quantum Search Algorithm -- 8.2 Amplitude Amplification -- 8.3 Quantum Amplitude Estimation and Quantum Counting -- 8.4 Searching Without Knowing the Success Probability -- 8.5 Related Algorithms and Techniques -- 9 QUANTUM COMPUTATIONAL COMPLEXITY THEORY AND LOWER BOUNDS -- 9.1 Computational Complexity -- 9.1.1 Language Recognition Problems and Complexity Classes -- 9.2 The Black-Box Model -- 9.2.1 State Distinguishability -- 9.3 Lower Bounds for Searching in the Black-Box Model: Hybrid Method -- 9.4 General Black-Box Lower Bounds -- 9.5 Polynomial Method -- 9.5.1 Applications to Lower Bounds -- 9.5.2 Examples of Polynomial Method Lower Bounds -- 9.6 Block Sensitivity -- 9.6.1 Examples of Block Sensitivity Lower Bounds -- 9.7 Adversary Methods -- 9.7.1 Examples of Adversary Lower Bounds -- 9.7.2 Generalizations -- 10 QUANTUM ERROR CORRECTION -- 10.1 Classical Error Correction -- 10.1.1 The Error Model -- 10.1.2 Encoding -- 10.1.3 Error Recovery -- 10.2 The Classical Three-Bit Code -- 10.3 Fault Tolerance -- 10.4 Quantum Error Correction -- 10.4.1 Error Models for Quantum Computing -- 10.4.2 Encoding -- 10.4.3 Error Recovery -- 10.5 Three- and Nine-Qubit Quantum Codes -- 10.5.1 The Three-Qubit Code for Bit-Flip Errors -- 10.5.2 The Three-Qubit Code for Phase-Flip Errors -- 10.5.3 Quantum Error Correction Without Decoding -- 10.5.4 The Nine-Qubit Shor Code. | |
10.6 Fault-Tolerant Quantum Computation -- 10.6.1 Concatenation of Codes and the Threshold Theorem -- APPENDIX A -- A.1 Tools for Analysing Probabilistic Algorithms -- A.2 Solving the Discrete Logarithm Problem When the Order of a Is Composite -- A.3 How Many Random Samples Are Needed to Generate a Group? -- A.4 Finding r Given k/r for Random k -- A.5 Adversary Method Lemma -- A.6 Black-Boxes for Group Computations -- A.7 Computing Schmidt Decompositions -- A.8 General Measurements -- A.9 Optimal Distinguishing of Two States -- A.9.1 A Simple Procedure -- A.9.2 Optimality of This Simple Procedure -- Bibliography -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- X -- Z. | |
Sommario/riassunto: | This concise, accessible introduction to quantum computing is aimed at advanced undergraduate and beginning graduate students from a variety of scientific backgrounds. The text is technically detailed and clearly illustrated throughout with diagrams and exercises. |
Titolo autorizzato: | An introduction to quantum computing |
ISBN: | 1-280-75761-2 |
0-19-191672-2 | |
1-4294-5991-3 | |
0-19-152461-1 | |
Formato: | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione: | Inglese |
Record Nr.: | 9910824418103321 |
Lo trovi qui: | Univ. Federico II |
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