Quantum Machine Learning
What Quantum Computing Means to Data Mining
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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
Readership
Math, physics, computing students, researchers, industry
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
- 1. Introduction
- 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
- 6. Pattern Recognition and Neural Networks
- 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
- 10. Clustering Structure and Quantum Computing
- Bibliography
Product details
- No. of pages: 176
- Language: English
- Copyright: © Academic Press 2014
- Published: August 13, 2014
- Imprint: Academic Press
- Paperback ISBN: 9780128100400
- eBook ISBN: 9780128010990
About the Author
Peter Wittek
Peter Wittek received his PhD in Computer Science from the National University of Singapore, and he also holds an MSc in Mathematics. He is interested in interdisciplinary synergies, such as scalable learning algorithms on supercomputers, computational methods in quantum simulations, and quantum machine learning. He collaborated on these topics during research stints to various institutions, including the Indian Institute of Science, Barcelona Supercomputing Center, Bangor University, Tsinghua University, the Centre for Quantum Technologies, and the Institute of Photonic Sciences. He has been involved in major EU research projects, and obtained several academic and industry grants.
Affiliations and Expertise
Research Associate Professor, University of Borås, Sweden