Quantum algorithms via linear algebra: a primer
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge, MA [u.a.]
The MIT Press
2014
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XII, 192 S. graph. Darst. |
| ISBN: | 9780262028394 |
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Record in the Search Index
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| adam_text | Titel: Quantum algorithms via linear algebra
Autor: Lipton, Richard J
Jahr: 2014
Contents
Preface xi
Acknowledgements xiii
1 Introduction 1
1.1 The Model 2
1.2 The Space and the States 3
1.3 The Operations 5
1.4 Where Is the Input? 6
1.5 What Exactly Is the Output? 7
1.6 Summary and Notes 8
2 Numbers and Strings 9
2.1 Asymptotic Notation 11
2.2 Problems 12
2.3 Summary and Notes 13
3 Basic Linear Algebra 15
3.1 Hilbert Spaces 16
3.2 Products and Tensor Products 16
3.3 Matrices 17
3.4 Complex Spaces and Inner Products 19
3.5 Matrices, Graphs, and Sums Over Paths 20
3.6 Problems 23
3.7 Summary and Notes 26
4 Boolean Functions, Quantum Bits, and Feasibility 27
4.1 Feasible Boolean Functions 28
4.2 An Example 30
4.3 Quantum Representation of Boolean Arguments 33
4.4 Quantum Feasibility 35
4.5 Problems 38
4.6 Summary and Notes 40
5 Special Matrices 41
5.1 Hadamard Matrices 41
5.2 Fourier Matrices 42
5.3 Reversible Computation and Permutation Matrices 43
5.4 Feasible Diagonal Matrices 44
5.5 Reflections 45
5.6 Problems 46
5.7 Summary and Notes 49
6 Tricks
6.1 Start Vectors 51
6.2 Controlling and Copying Base States 52
6.3 The Copy-Uncompute Trick 54
6.4 Superposition Tricks 55
6.5 Flipping a Switch 56
6.6 Measurement Tricks 58
6.7 Partial Transforms 59
6.8 Problems 50
6.9 Summary and Notes 62
7 Phil s Algorithm 63
7.1 The Algorithm 63
7.2 The Analysis 63
7.3 An Example 64
7.4 A Two-Qubit Example 64
7.5 Phil Measures Up 66
7.6 Quantum Mazes versus Circuits versus Matrices 69
7.7 Problems 71
7.8 Summary and Notes 74
8 Deutsch s Algorithm 77
8.1 The Algorithm 77
8.2 The Analysis 78
8.3 Superdense Coding and Teleportation 82
8.4 Problems 86
8.5 Summary and Notes 87
9 The Deutsch-Jozsa Algorithm 89
9.1 The Algorithm 89
9.2 The Analysis 90
9.3 Problems 92
9.4 Summary and Notes 92
10 Simon s Algorithm 93
10.1 The Algorithm 93
10.2 The Analysis 94
10.3 Problems 95
10.4 Summary and Notes 96
11 Shor s Algorithm 97
11.1 Strategy 97
11.2 Good Numbers 98
11.3 Quantum Part of the Algorithm 99
11.4 Analysis of the Quantum Part 100
11.5 Probability of a Good Number 102
11.6 Using a Good Number 105
11.7 Continued Fractions 106
11.8 Problems 107
11.9 Summary and Notes 108
12 Factoring Integers 109
12.1 Some Basic Number Theory 109
12.2 Periods Give the Order 110
12.3 Factoring 110
12.4 Problems 112
12.5 Summary and Notes 113
13 Graver s Algorithm 115
13.1 Two Vectors 115
13.2 The Algorithm 117
13.3 The Analysis 117
13.4 The General Case, with A: Unknown 118
13.5 Grover Approximate Counting 119
13.5.1 The Algorithm 122
13.5.2 The Analysis 122
13.6 Problems 126
13.7 Summary and Notes 128
14 Quantum Walks 129
14.1 Classical Random Walks 129
14.2 Random Walks and Matrices 130
14.3 An Encoding Nicety 132
14.4 Defining Quantum Walks 133
14.5 Interference and Diffusion 134
14.6 The Big Factor 138
14.7 Problems 139
14.8 Summary and Notes 140
15 Quantum Walk Search Algorithms 143
15.1 Search in Big Graphs 143
15.2 General Quantum Walk for Graph Search 145
15.3 Specifying the Generic Walk 147
15.4 Adding the Data 149
15.5 Toolkit Theorem for Quantum Walk Search 150
15.5.1 The Generic Algorithm 151
15.5.2 The Generic Analysis 152
15.6 Grover Search as Generic Walk 152
15.7 Element Distinctness 153
15.8 Subgraph Triangle Incidence 154
15.9 Finding a Triangle 155
15.10 Evaluating Formulas and Playing Chess 156
15.11 Problems 157
15.12 Summary and Notes 158
16 Quantum Computation and BQP 159
16.1 The Class BQP 159
16.2 Equations, Solutions, and Complexity 161
16.3 A Circuit Labeling Algorithm 163
16.4 Sum-Over-Paths and Polynomial Roots 165
16.5 The Additive Polynomial Simulation 168
16.6 Bounding BQP 169
16.7 Problems 170
16.8 Summary and Notes 173
17 Beyond I75
17.1 Reviewing the Algorithms 175
17.2 Some Further Topics 176
17.3 The Quantum in the Algorithms 179
Bibliography 183
Index 189
|
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| discipline | Physik Informatik Mathematik |
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| spelling | Lipton, Richard J. 1946- Verfasser (DE-588)142572888 aut Quantum algorithms via linear algebra a primer Richard J. Lipton ; Kenneth W. Regan Cambridge, MA [u.a.] The MIT Press 2014 XII, 192 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Quanteninformatik (DE-588)4705961-8 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Quantum computers Computer algorithms Algebras, Linear Quanteninformatik (DE-588)4705961-8 s Algorithmus (DE-588)4001183-5 s Lineare Algebra (DE-588)4035811-2 s DE-604 Regan, Kenneth W. 1959- Verfasser (DE-588)1048755223 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027695069&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lipton, Richard J. 1946- Regan, Kenneth W. 1959- Quantum algorithms via linear algebra a primer Lineare Algebra (DE-588)4035811-2 gnd Quanteninformatik (DE-588)4705961-8 gnd Algorithmus (DE-588)4001183-5 gnd |
| subject_GND | (DE-588)4035811-2 (DE-588)4705961-8 (DE-588)4001183-5 |
| title | Quantum algorithms via linear algebra a primer |
| title_auth | Quantum algorithms via linear algebra a primer |
| title_exact_search | Quantum algorithms via linear algebra a primer |
| title_full | Quantum algorithms via linear algebra a primer Richard J. Lipton ; Kenneth W. Regan |
| title_fullStr | Quantum algorithms via linear algebra a primer Richard J. Lipton ; Kenneth W. Regan |
| title_full_unstemmed | Quantum algorithms via linear algebra a primer Richard J. Lipton ; Kenneth W. Regan |
| title_short | Quantum algorithms via linear algebra |
| title_sort | quantum algorithms via linear algebra a primer |
| title_sub | a primer |
| topic | Lineare Algebra (DE-588)4035811-2 gnd Quanteninformatik (DE-588)4705961-8 gnd Algorithmus (DE-588)4001183-5 gnd |
| topic_facet | Lineare Algebra Quanteninformatik Algorithmus |
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