量子机器学习中数据挖掘的量子计算方法

  • 作者:维特克
  • 责编:张永芹
  • ISBN:978-7-5603-5759-1
  • 出版日期:2016-1-1
  • 所属丛书:
  • 定价:98.00
  • 开本:16
  • 页数:174
  • 图书分类:Q.数学类
  • 中图分类:O数理科学和化学
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【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 Groupscompact Lie Groupsand 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 SparsityBit Depthand Generalization Performance

14.7 Mapping to Hardware

14.8 Computational Complexity

Bibliography