Оглавление
Savo G. Glisic. Artificial Intelligence and Quantum Computing for Advanced Wireless Networks
Table of Contents
List of Tables
List of Illustrations
Guide
Pages
Artificial Intelligence and Quantum Computing for Advanced Wireless Networks
Preface
1 Introduction. 1.1 Motivation
1.2 Book Structure
References
2 Machine Learning Algorithms
2.1 Fundamentals. 2.1.1 Linear Regression
2.1.2 Logistic Regression
2.1.3 Decision Tree: Regression Trees Versus Classification Trees
2.1.4 Trees in R and Python
2.1.5 Bagging and Random Forest
2.1.6 Boosting GBM and XGBoost
2.1.7 Support Vector Machine
2.1.8 Naive Bayes, kNN, k‐Means
Example 2.1
Design Example 2.1
Example 2.2
Example 2.3
Example 2.4
2.1.9 Dimensionality Reduction
Design Example 2.2
2.2 ML Algorithm Analysis. 2.2.1 Logistic Regression
2.2.2 Decision Tree Classifiers
Design Example 2.3
Design Example 2.4
2.2.3 Dimensionality Reduction Techniques
Design Example 2.5
References
3 Artificial Neural Networks. 3.1 Multi‐layer Feedforward Neural Networks. 3.1.1 Single Neurons
3.1.2 Weights Optimization
3.2 FIR Architecture. 3.2.1 Spatial Temporal Representations
3.2.2 Neural Network Unfolding
Example
3.2.3 Adaptation
Design Example 3.1
3.3 Time Series Prediction
3.3.1 Adaptation and Iterated Predictions
3.4 Recurrent Neural Networks. 3.4.1 Filters as Predictors
3.4.2 Feedback Options in Recurrent Neural Networks
3.4.3 Advanced RNN Architectures
3.5 Cellular Neural Networks (CeNN)
3.6 Convolutional Neural Network (CoNN)
3.6.1 CoNN Architecture
3.6.2 Layers in CoNN
References
4 Explainable Neural Networks
4.1 Explainability Methods
4.1.1 The Complexity and Interoperability
4.1.2 Global Versus Local Interpretability
4.1.3 Model Extraction
4.2 Relevance Propagation in ANN
4.2.1 Pixel‐wise Decomposition
4.2.2 Pixel‐wise Decomposition for Multilayer NN
4.3 Rule Extraction from LSTM Networks
4.4 Accuracy and Interpretability
4.4.1 Fuzzy Models
Design Example 4.1
Design Example 4.2
Design Example 4.3
Algorithm 4.1 Mamdani (max‐min) inference
Design Example 4.4
Design Example 4.5
4.4.2 SVR
4.4.3 Combination of Fuzzy Models and SVR
References
5 Graph Neural Networks
5.1 Concept of Graph Neural Network (GNN)
5.1.1 Classification of Graphs
5.1.2 Propagation Types
5.1.3 Graph Networks
5.2 Categorization and Modeling of GNN
5.2.1 RecGNNs
5.2.2 ConvGNNs
5.2.3 Graph Autoencoders (GAEs)
5.2.4 STGNNs
5.3 Complexity of NN
5.3.1 Labeled Graph NN (LGNN)
Theorem 5.1
Theorem 5.2
5.3.2 Computational Complexity
Appendix 5.A Notes on Graph Laplacian
Proposition 5.1
Proposition 5.2
Appendix 5.B Graph Fourier Transform
References
6 Learning Equilibria and Games. 6.1 Learning in Games
Fictitious Play
Design Example 6.1
Definition 6.1
Definition 6.2
Proposition 6.1
6.1.1 Learning Equilibria of Games
Definition 6.3
Definition 6.4
Definition 6.5
Theorem 6.1
Theorem 6.2
Lemma 6.1
Theorem 6.3
Definition 6.6
Lemma 6.2
Corollary 6.1
Lemma 6.3
Lemma 6.4
Theorem 6.4
Corollary 6.2
Theorem 6.5
6.1.2 Congestion Games
Algorithm 1 GRAPHICALGAMES
Definition 6.7
Theorem 6.6:
Corollary 6.3
Definition 6.8
Algorithm 2 PARALLELLINKS
Lemma 6.5
Lemma 6.6
Lemma 6.7
Theorem 6.7:
Lemma 6.8
Lemma 6.9
Algorithm 3 PARALLELLINKS AVOIDING OVER‐QUERIES
Theorem 6.8
Lemma 6.10
Definition 6.9
Definition 6.10
Algorithm 4 ProcessK
Lemma 6.11
Lemma 6.12
Algorithm 5 ProcessD
Lemma 6.13
Lemma 6.14
Lemma 6.15
Algorithm 6 FINDKBRIDGES (k)
Lemma 6.16
Lemma 6.17
Algorithm 7 MULTIPROCESSK
Lemma 6.18
Theorem 6.9
6.2 Online Learning of Nash Equilibria in Congestion Games
Design Example 6.2
Algorithm 8 Online Learning Framework for the Congestion Game
6.3 Minority Games
6.4 Nash Q‐Learning
6.4.1 Multi‐agentQ‐Learning
6.4.2 Convergence
Lemma 6.19
Assumption*)
Lemma 6.20
6.5 Routing Games
6.5.1 Nonatomic Selfish Routing
Design Example 6.3
Design Example 6.4 Braess’s Paradox
6.5.2 Atomic Selfish Routing
Design Example 6.5
6.5.3 Existence of Equilibrium
Theorem 6.10
Theorem 6.11
6.5.4 Reducing the POA
Theorem 6.12
Design Example 6.6
Theorem 6.13
Corollary 6.4
6.6 Routing with Edge Priorities
Theorem 6.14
Proposition *)
Theorem 6.15
Theorem 6.16
6.6.1 Computing Equilibria
References
Notes
7 AI Algorithms in Networks. 7.1 Review of AI‐Based Algorithms in Networks
7.1.1 Traffic Prediction
7.1.2 Traffic Classification
7.1.3 Traffic Routing
7.1.4 Congestion Control
7.1.5 Resource Management
7.1.6 Fault Management
7.1.7 QoS and QoE Management
7.1.8 Network Security
7.2 ML for Caching in Small Cell Networks
7.2.1 System Model
7.3 Q‐Learning‐Based Joint Channel and Power Level Selection in Heterogeneous Cellular Networks
7.3.1 Stochastic Noncooperative Game
7.3.2 Multi‐Agent Q‐Learning
7.3.3 Q‐Learning for Channel and Power Level Selection
7.4 ML for Self‐Organizing Cellular Networks
7.4.1 Learning in Self‐Configuration
7.4.2 RL for SON Coordination
7.4.3 SON Function Model
7.4.4 Reinforcement Learning
Design Example 7.1
Design Example 7.2
7.5 RL‐Based Caching
7.5.1 System Model
7.5.2 Optimality Conditions
Design Example 7.3
7.6 Big Data Analytics in Wireless Networks
7.6.1 Evolution of Analytics
7.6.2 Data‐Driven Network Optimization
7.7 Graph Neural Networks. 7.7.1 Network Virtualization
7.7.2 GNN‐Based Dynamic Resource Management
7.7.3 Learning and Adaptation
Design Example 7.4
7.8 DRL for Multioperator Network Slicing
7.8.1 System Model
7.8.2 System Optimization
7.8.3 Game Equilibria by DRL
Lemma 7.1
Theorem 7.1
7.9 Deep Q‐Learning for Latency‐Limited Network Virtualization
7.9.1 System Model
7.9.2 Learning and Prediction
7.9.3 DRL for Dynamic VNF Migration
Design Example 7.5
7.10 Multi‐Armed Bandit Estimator (MBE)
7.10.1 System Model
Lemma 7.2
Lemma 7.3
Lemma 7.4
Theorem 7.2:
Corollary 7.1
7.10.2 System Performance
Definition2)
Lemma 7.5
Design Example 7.6
7.11 Network Representation Learning
7.11.1 Network Properties
7.11.2 Unsupervised NRL
7.11.2.1 Unsupervised Structure Preserving
7.11.2.1.1 Microscopic Structure Preserving NRL
7.11.2.1.2 Mesoscopic Structure
Structural Role Proximity Preserving NRL
Intra‐community Proximity Preserving NRL
7.11.2.1.3 Macroscopic Structure Preserving NRL
7.11.2.2 Unsupervised Content Augmented NRL
7.11.2.2.1 Text‐Associated DeepWalk (TADW)
7.11.2.2.2 Homophily, Structure, and Content Augmented Network Representation Learning (HSCA)
7.11.2.2.3 Paired Restricted Boltzmann Machine (pRBM)
7.11.2.2.4 User Profile Preserving Social Network Embedding (UPP‐SNE)
7.11.2.2.5 Property Preserving Network Embedding (PPNE)
7.11.3 Semi‐Supervised NRL
7.11.3.1 Semi‐Supervised Structure Preserving NRL
7.11.3.1.1 Discriminative Deep Random Walk (DDRW)
7.11.3.1.2 Max‐Margin DeepWalk (MMDW)
7.11.3.1.3 Transductive LINE (TLINE)
7.11.3.1.4 Group Enhanced Network Embedding (GENE)
7.11.3.1.5 Semi‐supervised Network Embedding (SemiNE)
7.11.3.2 Semi‐supervised Content Augmented NRL
7.11.3.2.1 Tri‐Party Deep Network Representation (TriDNR)
7.11.3.2.2 Linked Document Embedding (LDE)
7.11.3.2.3 Discriminative Matrix Factorization (DMF)
7.11.3.2.4 Predictive Labels and Neighbors with Embeddings Transductively or Inductively from Data (Planetoid)
7.11.3.2.5 Label informed Attribute Network Embedding (LANE)
References
8 Fundamentals of Quantum Communications. 8.1 Introduction
8.2 Quantum Gates and Quantum Computing
8.2.1 Quantum Circuits
8.2.2 Quantum Algorithms
8.3 Quantum Fourier Transform (QFT)
Design Example 8.1
Design Example 8.2
8.3.1 QFT Versus FFT Revisited
References
9 Quantum Channel Information Theory
9.1 Communication Over a Channel
9.2 Quantum Information Theory
9.2.1 Density Matrix and Trace Operator
9.2.2 Quantum Measurement
Design Example 9.1
9.3 Channel Description
Design Example 9.2 Partial Trace
9.3.1 Channel Entropy
9.3.2 Some History
9.4 Channel Classical Capacities
9.4.1 Capacity of Classical Channels
9.4.2 The Private Classical Capacity
9.4.3 The Entanglement‐Assisted Classical Capacity
9.4.4 The Classical Zero‐Error Capacity
9.4.5 Entanglement‐Assisted Classical Zero‐Error Capacity
Design Example 9.3
9.5 Channel Quantum Capacity
9.5.1 Preserving Quantum Information
9.5.2 Quantum Coherent Information
9.5.3 Connection Between Classical and Quantum Information
9.6 Quantum Channel Examples
9.6.1 Channel Maps
9.6.2 Capacities
9.6.3 Q Channel Parameters
Design Example 9.4
References
10 Quantum Error Correction
Design Example 10.1
Design Example 10.2
Design Example 10.3
Design Example 10.4
Design Example 10.5
10.1 Stabilizer Codes
Design Example 10.6 COMMUTATION PROPERTIES FOR PAULI OPERATORS
Design Example 10.7 THE [[4, 2, 2]] DETECTION CODE
Design Example 10.8 THE SHOR [[9, 1, 3]] CODE
10.2 Surface Code
Design Example 10.9 THE [[5,1,2]] SURFACE CODE
10.2.1 The Rotated Lattice
10.3 Fault‐Tolerant Gates
10.3.1 Fault Tolerance
10.4 Theoretical Framework
10.4.1 Classical EC
Design Example 10.10 ERROR CORRECTION
Design Example 10.11
10.4.2 Theory of QEC. 10.4.2.1 Preliminaries
10.4.2.2 Basics of QEC Theory
10.4.2.3 Code Construction
Design Example 10.12 CODES
10.4.2.4 More on Coding and Syndrome Extractions
10.A Binary Fields and Discrete Vector Spaces
10.B Some Noise Physics
References
11 Quantum Search Algorithms
11.1 Quantum Search Algorithms. 11.1.1 The Deutsch Algorithm [2]
11.1.2 The Deutsch–Jozsa Algorithm
11.1.3 Simon’s Algorithm
11.1.4 Shor’s Algorithm
11.1.5 Quantum Phase Estimation Algorithm
11.1.6 Grover’s Quantum Search Algorithm
Design Example 11.1
11.1.7 Boyer–Brassard–Høyer–Tapp QSA
11.1.8 Dürr–Høyer QSA
11.1.9 Quantum Counting Algorithm
11.1.10 Quantum Heuristic Algorithm
11.1.11 Quantum GA
11.1.12 Harrow–Hassidim–Lloyd Algorithm
11.1.13 Quantum Mean Algorithm
11.1.14 Quantum Weighted Sum Algorithm
11.2 Physics of Quantum Algorithms
11.2.1 Implementation of Deutsch’s Algorithm
11.2.2 Implementation of Deutsch–Jozsa Algorithm
11.2.3 Bernstein and Vazirani’s Implementation
11.2.4 Implementation of QFT
11.2.5 Estimating Arbitrary Phases
11.2.6 Improving Success Probability When Estimating Phases
11.2.7 The Order‐Finding Problem
Design Example 11.2
11.2.8 Concatenated Interference
Design Example 11.3
Design Example 11.4 Grover’s Algorithm
Design Example 11.5 Simon’s Algorithm
Design Example 11.6 Shor’s Algorithm
Definition 1
Theorem 1
Theorem 2
Design Example 11.7 QC Implementation of Shor’s Algorithm
References
12 Quantum Machine Learning
12.1 QML Algorithms
12.2 QNN Preliminaries
12.3 Quantum Classifiers with ML: Near‐Term Solutions
12.3.1 The Circuit‐Centric Quantum Classifier
Design Example 12.1
12.3.2 Training
12.4 Gradients of Parameterized Quantum Gates
12.5 Classification with QNNs
12.5.1 Representation
12.5.2 Learning
12.6 Quantum Decision Tree Classifier
12.6.1 Model of the Classifier
Appendix 12.7 Matrix Exponential
Design Example 12.2
Solution
Remark 1:
Remark 2:
Design Example 12.3
Solution
Design Example 12.4
Design Example 12.5
Solution 1: (Use Diagonalization)
Solution 3: (Use Fundamental Solutions and Avoid Complex Exponential Functions)
References
13 QC Optimization. 13.1 Hybrid Quantum‐Classical Optimization Algorithms
13.1.1 QAOA
Design Example 13.1
13.2 Convex Optimization in Quantum Information Theory
Theorem 13.1
Theorem 13.2
Corollary 13.3
Corollary
13.2.1 Relative Entropy of Entanglement
Theorem 13.5
Theorem 13.6
13.3 Quantum Algorithms for Combinatorial Optimization Problems
Design Example 13.2
Design Example 13.2
13.4 QC for Linear Systems of Equations
Problem Statement
13.4.1 Algorithm in Brief
13.4.2 Detailed Description of the Algorithm
13.4.3 Error Analysis
Design Example 13.4 QC FOR MULTIPLE REGRESSION
13.5 Quantum Circuit
13.6 Quantum Algorithm for Systems of Nonlinear Differential Equations
References
14 Quantum Decision Theory
14.1 Potential Enablers for Qc
14.2 Quantum Game Theory (QGT)
14.2.1 Definitions
Design Example 14.1
14.2.2 Quantum Games
Definition 14.1
Design Example 14.2
14.2.3 Quantum Game for Spectrum Sharing
14.3 Quantum Decision Theory (QDT)
14.3.1 Model: QDT
Design Example 14.3
14.3.1.1 Decision Tasks and Participants
14.4 Predictions in QDT
14.4.1 Utility Factors
14.4.2 Classification of Lotteries by Attraction Indices
Design Example 14.4
14.4.2.1 Lotteries with Gains [77]
14.4.2.2 Lotteries with Losses
References
15 Quantum Computing in Wireless Networks
15.1 Quantum Satellite Networks
15.1.1 Satellite‐Based QKD System
15.1.2 QSN Architecture
15.1.3 Routing and Resource Allocation Algorithm
Algorithm 1 Joint GEO‐LEO Routing and Key Allocation Algorithm
Algorithm 2 Joint GEO‐LEO Access Algorithm
Algorithm 3 Separated GEO and LEO Access Algorithm
Design Example 15.111
15.2 QC Routing for Social Overlay Networks
15.2.1 Social Overlay Network
15.2.2 Multiple‐Objective Optimization Model
Definition 1
Definition 2
15.3 QKD Networks
15.3.1 QoS in QKD Overlay Networks
15.3.2 Adaptive QoS‐QKD Networks
15.3.3 Routing Protocol for QKD Network
Design Example 15.222
References
Notes
16 Quantum Network on Graph
16.1 Optimal Routing in Quantum Networks
16.1.1 Network Model
16.1.2 Entanglement
16.1.3 Optimal Quantum Routing
Algorithm 1 Expected Entanglement Rate
Algorithm 2 Auxiliary Functions
Algorithm 3 Optimal Path Selection
Design Example 16.1 [17]
16.2 Quantum Network on Symmetric Graph
Design Example 16.2
16.3 QWs
16.3.1 DQWL
16.3.2 Performance Study of DQWL
16.4 Multidimensional QWs
16.4.1 The Quantum Random Walk
16.4.2 Quantum Random Walks on General Graphs
16.4.3 Continuous‐Time Quantum Random Walk
16.4.4 Searching Large‐Scale Graphs
References
17 Quantum Internet
17.1 System Model
17.1.1 Routing Algorithms
Algorithm 1 Distributed Routing Algorithms (s, e, , D, cap)
Algorithm 2 Modified Greedy: PathDisc(s, e, , Ds,e)
Algorithm 3 Local Best Effort: PathDisc(s, e, , Ds,e)
Algorithm 4 NoN Local Best Effort: PathDisc(s, e, , Ds,e)
17.1.2 Quantum Network on General Virtual Graph
17.1.3 Quantum Network on Ring and Grid Graph
Design Example 17.1
17.1.4 Quantum Network on Recursively Generated Graphs (RGGs)
17.1.5 Recursively Generated Virtual Graph
17.2 Quantum Network Protocol Stack
17.2.1 Preliminaries
Protocol 1 Steiner (S, x)
Assumptions
17.2.2 Quantum Network Protocol Stack
17.2.3 Layer 3 – Reliable State Linking
17.2.4 Layer 4 – Region Routing
Protocol 2 Region Routing(S)
Design Example 17.2 Region Routing [44]
References
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