1 option
An introduction to quantum computing / Phillip Kaye, Raymond Laflamme, Michele Mosca.
Loaned to Another Library QA76.889 .K39 2007
By Request
Log in to request item- Format:
- Book
- Author/Creator:
- Kaye, Phillip.
- Language:
- English
- Subjects (All):
- Quantum computers.
- Physical Description:
- xi, 274 pages : illustrations ; 24 cm
- Place of Publication:
- Oxford : Oxford University Press, 2007.
- Summary:
- This concise, accessible text provides a thorough introduction to quantum computing - an exciting emergent field at the interface of the computer, engineering, mathematical and physical sciences. Aimed at advanced undergraduate and beginning graduate students in these disciplines, the text is technically detailed and is clearly illustrated throughout with diagrams and exercises. Some prior knowledge of linear algebra is assumed, including vector spaces and inner products. However, prior familiarity with topics such as tensor products and spectral decomposition is not required, as the necessary material is reviewed in the text.
- Contents:
- 1.2 Computers and the Strong Church-Turing Thesis 2
- 1.3 The Circuit Model of Computation 6
- 1.4 A Linear Algebra Formulation of the Circuit Model 8
- 1.5 Reversible Computation 12
- 1.6 A Preview of Quantum Physics 15
- 1.7 Quantum Physics and Computation 19
- 2 Linear Algebra and the Dirac Notation 21
- 2.1 The Dirac Notation and Hilbert Spaces 21
- 2.2 Dual Vectors 23
- 2.3 Operators 27
- 2.4 The Spectral Theorem 30
- 2.5 Functions of Operators 32
- 2.6 Tensor Products 33
- 2.7 The Schmidt Decomposition Theorem 35
- 2.8 Some Comments on the Dirac Notation 37
- 3 Qubits and the Framework of Quantum Mechanics 38
- 3.1 The State of a Quantum System 38
- 3.2 Time-Evolution of a Closed System 43
- 3.3 Composite Systems 45
- 3.4 Measurement 48
- 3.5 Mixed States and General Quantum Operations 53
- 3.5.1 Mixed States 53
- 3.5.2 Partial Trace 56
- 3.5.3 General Quantum Operations 59
- 4 A Quantum Model of Computation 61
- 4.1 The Quantum Circuit Model 61
- 4.2 Quantum Gates 63
- 4.2.1 1-Qubit Gates 63
- 4.2.2 Controlled-U Gates 66
- 4.3 Universal Sets of Quantum Gates 68
- 4.4 Efficiency of Approximating Unitary Transformations 71
- 4.5 Implementing Measurements with Quantum Circuits 73
- 5 Superdense Coding and Quantum Teleportation 78
- 5.1 Superdense Coding 79
- 5.2 Quantum Teleportation 80
- 5.3 An Application of Quantum Teleportation 82
- 6 Introductory Quantum Algorithms
- 6.1 Probabilistic Versus Quantum Algorithms 86
- 6.2 Phase Kick-Back 91
- 6.3 The Deutsch Algorithm 94
- 6.4 The Deutsch-Jozsa Algorithm 99
- 6.5 Simon's Algorithm 103
- 7 Algorithms with Superpolynomial Speed-Up 110
- 7.1 Quantum Phase Estimation and the Quantum Fourier Transform 110
- 7.1.1 Error Analysis for Estimating Arbitrary Phases 117
- 7.1.2 Periodic States 120
- 7.1.3 GCD, LCM, the Extended Euclidean Algorithm 124
- 7.2 Eigenvalue Estimation 125
- 7.3 Finding-Orders 130
- 7.3.1 The Order-Finding Problem 130
- 7.3.2 Some Mathematical Preliminaries 131
- 7.3.3 The Eigenvalue Estimation Approach to Order Finding 134
- 7.3.4 Shor's Approach to Order Finding 139
- 7.4 Finding Discrete Logarithms 142
- 7.5 Hidden Subgroups 146
- 7.5.1 More on Quantum Fourier Transforms 147
- 7.5.2 Algorithm for the Finite Abelian Hidden Subgroup Problem 149
- 7.6 Related Algorithms and Techniques 151
- 8 Algorithms Based on Amplitude Amplification 152
- 8.1 Grover's Quantum Search Algorithm 152
- 8.2 Amplitude Amplification 163
- 8.3 Quantum Amplitude Estimation and Quantum Counting 170
- 8.4 Searching Without Knowing the Success Probability 175
- 8.5 Related Algorithms and Techniques 178
- 9 Quantum Computational Complexity Theory and Lower Bounds 179
- 9.1 Computational Complexity 180
- 9.1.1 Language Recognition Problems and Complexity Classes 181
- 9.2 The Black-Box Model 185
- 9.2.1 State Distinguishability 187
- 9.3 Lower Bounds for Searching in the Black-Box Model: Hybrid Method 188
- 9.4 General Black-Box Lower Bounds 191
- 9.5 Polynomial Method 193
- 9.5.1 Applications to Lower Bounds 194
- 9.5.2 Examples of Polynomial Method Lower Bounds 196
- 9.6 Block Sensitivity 197
- 9.6.1 Examples of Block Sensitivity Lower Bounds 197
- 9.7 Adversary Methods 198
- 9.7.1 Examples of Adversary Lower Bounds 200
- 9.7.2 Generalizations 203
- 10 Quantum Error Correction 204
- 10.1 Classical Error Correction 204
- 10.1.1 The Error Model 205
- 10.1.2 Encoding 206
- 10.1.3 Error Recovery 207
- 10.2 The Classical Three-Bit Code 207
- 10.3 Fault Tolerance 211
- 10.4 Quantum Error Correction 212
- 10.4.1 Error Models for Quantum Computing 213
- 10.4.2 Encoding 216
- 10.4.3 Error Recovery 217
- 10.5 Three- and Nine-Qubit Quantum Codes 223
- 10.5.1 The Three-Qubit Code for Bit-Flip Errors 223
- 10.5.2 The Three-Qubit Code for Phase-Flip Errors 225
- 10.5.3 Quantum Error Correction Without Decoding 226
- 10.5.4 The Nine-Qubit Shor Code 230
- 10.6 Fault-Tolerant Quantum Computation 234
- 10.6.1 Concatenation of Codes and the Threshold Theorem 237
- A.1 Tools for Analysing Probabilistic Algorithms 241
- A.2 Solving the Discrete Logarithm Problem When the Order of a Is Composite 243
- A.3 How Many Random Samples Are Needed to Generate a Group? 245
- A.4 Finding r Given k/r for Random k 247
- A.5 Adversary Method Lemma 248
- A.6 Black-Boxes for Group Computations 250
- A.7 Computing Schmidt Decompositions 253
- A.8 General Measurements 255
- A.9 Optimal Distinguishing of Two States 258
- A.9.1 A Simple Procedure 258
- A.9.2 Optimality of This Simple Procedure 258.
- Notes:
- Includes bibliographical references and index.
- Local Notes:
- Acquired for the Penn Libraries with assistance from the Sabin W. Colton, Jr., Memorial Fund.
- ISBN:
- 9780198570004
- 0198570007
- 019857049X
- 9780198570493
- OCLC:
- 70398982
The Penn Libraries is committed to describing library materials using current, accurate, and responsible language. If you discover outdated or inaccurate language, please fill out this feedback form to report it and suggest alternative language.