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Quantum Machine Learning bridges the gap between abstract developments in quantum computing and the applied research on machine learning. Paring down the complexity of the disciplines involved, it focuses on providing a synthesis that explains the most important machine learning algorithms in a quantum framework. Theoretical advances in quantum computing are hard to follow for computer scientists, and sometimes even for researchers involved in the field. The lack of a step-by-step guide hampers the broader understanding of this emergent interdisciplinary body of research.

Quantum Machine Learning sets the scene for a deeper understanding of the subject for readers of different backgrounds. The author has carefully constructed a clear comparison of classical learning algorithms and their quantum counterparts, thus making differences in computational complexity and learning performance apparent. This book synthesizes of a broad array of research into a manageable and concise presentation, with practical examples and applications.

Key Features
Bridges the gap between abstract developments in quantum computing with the applied research on machine learning
Provides the theoretical minimum of machine learning, quantum mechanics, and quantum computing
Gives step-by-step guidance to a broader understanding of this emergent interdisciplinary body of research



Table of Contents
Preface
Notations
Part One: Fundamental Concepts
1. Introduction
Abstract
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
Abstract
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
Abstract
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
Abstract
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
5. Unsupervised Learning
Abstract
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
Part Two: Classical Learning Algorithms
6. Pattern Recognition and Neural Networks
Abstract
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
Abstract
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
Abstract
8.1 Linear Least Squares
8.2 Nonlinear Regression
8.3 Nonparametric Regression
8.4 Computational Complexity
9. Boosting
Abstract
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
10. Clustering Structure and Quantum Computing
Abstract
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
Abstract
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
Abstract
12.1 NearestNeighbors
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
Abstract
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
Abstract
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