LEADER 06276nam 2200577Ia 450 001 9910824418103321 005 20240418141327.0 010 $a1-280-75761-2 010 $a0-19-191672-2 010 $a1-4294-5991-3 010 $a0-19-152461-1 035 $a(CKB)24235056100041 035 $a(MiAaPQ)EBC415080 035 $a(MiAaPQ)EBC7037116 035 $a(Au-PeEL)EBL415080 035 $a(CaPaEBR)ebr10271619 035 $a(CaONFJC)MIL75761 035 $a(OCoLC)437092641 035 $a(PPN)116668709 035 $a(EXLCZ)9924235056100041 100 $a20060614d2007 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 13$aAn introduction to quantum computing /$fPhillip Kaye, Raymond Laflamme, Michele Mosca 205 $a1st ed. 210 $aOxford $cOxford University Press$d2007 215 $axi, 274 p. $cill 320 $aIncludes bibliographical references and index. 327 $aIntro -- 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. 327 $a7.3 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. 327 $a10.6 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. 330 $aThis 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. 606 $aQuantum computers 606 $aComputers 615 0$aQuantum computers. 615 0$aComputers. 676 $a004.1 676 $a004.1 700 $aKaye$b Phillip$01621186 701 $aLaflamme$b Raymond$01621187 701 $aMosca$b Michele$0514914 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910824418103321 996 $aAn introduction to quantum computing$93954357 997 $aUNINA