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—DrivenModels
　　2.2 FeatureSpace
　　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 QuantumCircuits
　　4.3 Adiabatic Quantum Computing
　　4.4 QuantumParallelism
　　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 ManifoldEmbedding
　　5.3 K—Means and K—Medians Clustering
　　5.4 Hierarchical Clustering
　　5.5 Density—BasedClustering
　6 Pattern Recogrution 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 KemelFunctions
　　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 Ada Boost
　　9.3 A Family of Convex Boosters
　　9.4 Nonconvex Loss Functions
Part Three Quantum Computing and Machine Learning
　10 Clustering 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 QuantumK—Means
　　10.6 QuantumK—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 Physical 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 Optimal State for Learning
　　13.7 Applying the Unitary and Finding the Parameter for the Input State
　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