量子机器学习中数据挖掘的量子计算方法PDF电子书下载

Part One Fundamental Concepts 1

1 Introduction 3

1.1 Learning Theory and Data Mining 5

1.2 Why Quantum Computers? 6

1.3 AHeterogeneous Model 7

1.4 An Overview of Quantum Machine Learning Algorithms 7

1.5 Quantum-Like Learning on Classical Computers 9

2 Machine Learning 11

2.1 Data-Driven Models 12

2.2 Feature Space 12

2.3 Supervised and Unsupervised Learning 15

2.4 Generalization Performance 18

2.5 Model Complexity 20

2.6 Ensembles 22

2.7 Data Dependencies and Computational Complexity 23

3 Quantum Mechanics 25

3.1 States and Superposition 26

3.2 Density Matrix Representation and Mixed States 27

3.3 Composite Systems and Entanglement 29

3.4 Evolution 32

3.5 Measurement 34

3.6 Uncertainty Relations 36

3.7 Tunneling 37

3.8 Adiabatic Theorem 37

3.9 No-Cloning Theorem 38

4 Quantum Computing 41

4.1 Qubits and the Bloch Sphere 41

4.2 Quantum Circuits 44

4.3 Adiabatic Quantum Computing 48

4.4 Quantum Parallelism 49

4.5 Grover's Algorithm 49

4.6 Complexity Classes 51

4.7 Quantum Information Theory 52

Part Two Classical Learning Algorithms 55

5 Unsupervised Learning 57

5.1 Principal Component Analysis 57

5.2 Manifold Embedding 58

5.3 K-Means and K-Medians Clustering 59

5.4 Hierarchical Clustering 60

5.5 Density-Based Clustering 61

6 Pattern Recognition and Neural Networks 63

6.1 The Perceptron 63

6.2 Hopfield Networks 65

6.3 Feedforward Networks 67

6.4 DeepLearning 69

6.5 Computational Complexity 70

7 Supervised Learning and Support Vector Machines 73

7.1 K-Nearest Neighbors 74

7.2 Optimal Margin Classifiers 74

7.3 Soft Margins 76

7.4 Nonlinearity and Kernel Functions 77

7.5 Least-Squares Formulation 80

7.6 Generalization Performance 81

7.7 Multiclass Problems 81

7.8 Loss Functions 83

7.9 Computational Complexity 83

8 Regression Analysis 85

8.1 LinearLeast Squares 85

8.2 Nonlinear Regression 86

8.3 Nonparametric Regression 87

8.4 Computational Complexity 87

9 Boosting 89

9.1 Weak Classifers 89

9.2 AdaBoost 90

9.3 A Family of Convex Boosters 92

9.4 Nonconvex Loss Functions 94

Part Three Quantum Computing and Machine Learning 97

10 Clustering Structure and Quantum Computing 99

10.1 Quantum Random Access Memory 99

10.2 Calculating Dot Products 100

10.3 Quantum Principal Component Analysis 102

10.4 Toward Quantum Manifold Embedding 104

10.5 QuantumK-Means 104

10.6 Quantum K-Medians 105

10.7 Quantum Hierarchical Clustering 106

10.8 Computational Complexity 107

11 Quantum Pattern Recognition 109

11.1 Quantum Associative Memory 109

11.2 The Quantum Perceptron 114

11.3 QuantumNeural Networks 115

11.4 Physical Realizations 116

11.5 Computational Complexity 118

12 Quantum Classification 119

12.1 Nearest Neighbors 119

12.2 Support Vector Machines with Grover's Search 121

12.3 Support Vector Machines with Exponential Speedup 122

12.4 Computational Complexity 123

13 Quantum Process Tomography and Regression 125

13.1 Channel-State Duality 126

13.2 Quantum Process Tomography 127

13.3 Groups,Compact Lie Groups,and the Unitary Group 128

13.4 Representation Theory 130

13.5 Parallel Application and Storage of the Unitary 133

13.6 Optimal State for Learning 134

13.7 Applying the Unitary and Finding the Parameter for the Input State 136

14 Boosting and Adiabatic Quantum Computing 139

14.1 Quantum Annealing 140

14.2 Quadratic Unconstrained Binary Optimization 141

14.3 Ising Model 142

14.4 QBoost 143

14.5 Nonconvexity 143

14.6 Sparsity,Bit Depth,and Generalization Performance 145

14.7 Mapping to Hardware 147

14.8 Computational Complexity 151

Bibliography 153