【目 录】
Preface
Notations
Part One Fundamental Concepts
1 Introduction
1.1 Learning Theory and Data Mining
1.2 Why Quantum Computers?
1.3 A Heterogeneous Model
1.4 An Overview of Quantum Machine Learning Algorithms
1.5 Quantum-Like Learning on Classical Computers
2 Machine Learning
2.1 Data-Driven Models
2.2 Feature Space
2.3 Supervised and Unsupervised Learning
2.4 Generalization Performance
2.5 Model Complexity
2.6 Ensembles
2.7 Data Dependencies and Computational Complexity
3 Quantum Mechanics
3.1 States and Superposition
3.2 Density Matrix Representation and Mixed States
3.3 Composite Systems and Entanglement
3.4 Evolution
3.5 Measurement
3.6 Uncertainty Relations
3.7 Tunneling
3.8 Adiabatic Theorem
3.9 No-Cloning Theorem
4 Quantum Computing
4.1 Qubits and the Bloch Sphere
4.2 Quantum Circuits
4.3 Adiabatic Quantum Computing
4.4 Quantum Parallelism
4.5 Grover’s Algorithm
4.6 Complexity Classes
4.7 Quantum Information Theory
Part Two Classical Learning Algorithms
5 Unsupervised Learning
5.1 Principal Component Analysis
5.2 Manifold Embedding
5.3 K-Means and K-Medians Clustering
5.4 Hierarchical Clustering
5.5 Density-Based Clustering
6 Pattern Recognition and Neural Networks
6.1 The Perceptron
6.2 Hopfield Networks
6.3 Feedforward Networks
6.4 Deep Learning
6.5 Computational Complexity
7 Supervised Learning and Support Vector Machines
7.1 K-Nearest Neighbors
7.2 Optimal Margin Classifiers
7.3 Soft Margins
7.4 Nonlinearity and Kernel Functions
7.5 Least-Squares Formulation
7.6 Generalization Performance
7.7 Multiclass Problems
7.8 Loss Functions
7.9 Computational Complexity
8 Regression Analysis
8.1 Linear Least Squares
8.2 Nonlinear Regression
8.3 Nonparametric Regression
8.4 Computational Complexity
9 Boosting
9.1 Weak Classifiers
9.2 AdaBoost
9.3 A Family of Convex Boosters
9.4 Nonconvex Loss Functions
Part Three Quantum Computing and Machine Learning
10Clustering Structure and Quantum Computing
10.1 Quantum Random Access Memory
10.2 Calculating Dot Products
10.3 Quantum Principal Component Analysis
10.4 Toward Quantum Manifold Embedding
10.5 Quantum K-Means
10.6 Quantum K-Medians
10.7 Quantum Hierarchical Clustering
10.8 Computational Complexity
11 Quantum Pattern Recognition
11.1 Quantum Associative Memory
11.2 The Quantum Perceptron
11.3 Quantum Neural Networks
11.4 Physica1 Realizations
11.5 Computational Complexity
12 Quantum Classification
12.1 Nearest Neighbors
12.2 Support Vector Machines with Grover's Search
12.3 Support Vector Machines with Exponential Speedup
12.4 Computational Complexity
13 Quantum Process Tomography and Regression
13.1 Channel-State Duality
13.2 Quantum Process Tomography
13.3 Groups,compact Lie Groups,and the Unitary Group
13.4 Representation Theory
13.5 Parallel Application and Storage of the Unitary
13.6 Optima1 State for Learning
13.7 Applying the Unitary and Finding the Parameter for theInputState
14 Boosting and Adiabatic Quantum Computing
14.1 Quantum Annealing
14.2 Quadratic Unconstrained Binary Optimization
14.3 Ising Model
14.4 QBoost
14.5 Nonconvexity
14.6 Sparsity,Bit Depth,and Generalization Performance
14.7 Mapping to Hardware
14.8 Computational Complexity
Bibliography