Читать книгу Artificial Intelligence and Quantum Computing for Advanced Wireless Networks - Savo G. Glisic - Страница 4

1 Chapter 2Figure 2.1 If X and Y are two jointly normally distributed random variables,...Figure 2.2 The regression line for predicting Y* from X* is not the 45° line...Figure 2.3 Decision tree.Figure 2.4 Tree terminology.Figure 2.5 Data classification.Figure 2.6 Classification with outliers.Figure 2.7 Classifiers with nonlinear transformations.Figure 2.8 Illustration of the nearest neighbor (NN) classification algorith...Figure 2.9 Illustration of the plane partitioning of a two‐dimensional datas...Figure 2.10 Illustration of the nearest neighbor (NN) decision boundary.Figure 2.11 Example of clustering.Figure 2.12 k‐Means algorithm.Figure 2.13 k = 3 means clustering on 2D dataset.Figure 2.14 Concept of data projection.Figure 2.15 Successive data projections.Figure 2.16 Decision tree presenting response to direct mailing.Figure 2.17 Predicting email spam.Figure 2.18 Top‐down algorithmic framework for decision tree induction. The ...Figure 2.19 Black circles represent the input data, x_n; red squares repres...

2 Chapter 3Figure 3.1 From biological to mathematical simplified model of a neuron.Figure 3.2 Block diagram of feedforward network.Figure 3.3 Schematic representation of supervised learning.Figure 3.4 Illustration of backpropagation.Figure 3.5 Finite impulse response (FIR) neuron and neural network.Figure 3.6 Finite impulse response (FIR) network unfolding.Figure 3.7 Temporal backpropagation.Figure 3.8 Oversimplified finite impulse response (FIR) network.Figure 3.9 Network prediction configuration.Figure 3.10 Nonlinear AR/ARMA predictors.Figure 3.11 Recurrent neural network.Figure 3.12 Canonical form of a recurrent neural network for prediction.Figure 3.13 Recurrent neural network (RNN) architectures: (a) activation fee...Figure 3.14 General locally recurrent–globally feedforward (LRGF) architectu...Figure 3.15 An example of Elman recurrent neural network (RNN).Figure 3.16 An example of Jordan recurrent neural network (RNN).Figure 3.17 A fully connected recurrent neural network (RNN; Williams–Zipser...Figure 3.18 Nonlinear IIR filter structures. (a) A recurrent nonlinear neura...Figure 3.19 A long short‐term memory (LSTM) memory cell.Figure 3.20 A bidirectional recurrent neural network (BRNN). (for more detai...Figure 3.21 (Top) Cellular neural networks (CeNN) architecture, (bottom) cir...Figure 3.22 Memristor‐based cellular nonlinear/neural network (MCeNN).Figure 3.23 Illustration of the convolution operation. If we overlap the con...Figure 3.24 RGB image/three channels and three kernels. (for more details se...Figure 3.25 Computing∂z/∂X. (for more details see the color fig...Figure 3.26 Illustration of pooling layer operation. (for more details see t...Figure 3.27 Illustration of preprocessing in a cooperative neural network (C...

3 Chapter 4Figure 4.1 (a) Neural network (NN) as a classifier, (b) NN during the releva...Figure 4.2 Relevance propagation.Figure 4.3 Relevance propagation (heat map; relevance is presented by the in...Figure 4.4 Example of membership functions versus the traffic volume and net...Figure 4.5 A schematic representation of the Mamdani inference algorithm.Figure 4.6 Illustration of the soft margin for a linear support vector machi...

4 Chapter 5Figure 5.1 Operation of GraphSAGE: (a) sample neighborhood, (b) aggregate fe...Figure 5.2 Illustrations of ConvGNN network: (a) A ConvGNN with multiple gra...Figure 5.3 2D Convolution versus graph convolution: (a) 2D convolution. Anal...Figure 5.4 Parametric graph convolution: (a) Conventional graph convolutiona...Figure 5.5 A ConvGNN with pooling and readout layers for graph classificatio...Figure 5.6 A graph autoencoder (GAE) for network embedding. The encoder uses...Figure 5.7 A STGNN for spatial‐temporal graph forecasting. A graph convoluti...Figure 5.8 A subset of the Web.Figure 5.9 Graph and the neighborhood of a node. The state x₁ of node 1 depe...Figure 5.10 Graph (on the top, left), the corresponding encoding network (to...Figure 5.B.1 A directed graph and the corresponding matrices.

5 Chapter 6Figure 6.1 Routing game with two populations of players. Source: Krichene et...Figure 6.2 Examples of different types of stage games.Figure 6.3 In brackets: original version of Pigou’s network. no brackets: no...Figure 6.4 Braess’s paradox. (a) Initial network, (b) augmented network. The...Figure 6.5 (a) In atomic instances with affine cost functions, different equ...Figure 6.6 (Left) Example of embedding problems with zero‐cost cycles. Wavy ...

6 Chapter 7Figure 7.1 Algorithm for autonomous channel and power level selection.Figure 7.2 Major use cases of each self‐organizing network (SON) function....Figure 7.3 Transfer learning (TL)‐based network state information updating....Figure 7.4 Transition kernel: Markov decision process model of the system dy...Figure 7.5 Simulation scenario: network and traffic parameters.Figure 7.6 Time‐averaged parameters.Figure 7.7 Cell cluster example.Figure 7.8 Popularity profiles modeled as Markov chains. (a) Global populari...Figure 7.9 Performance of the algorithms.Figure 7.10 Datasets and the sources of data available to the network operat...Figure 7.11 Network function virtualization (NFV) service function chain.Figure 7.12 Graph neural network (GNN)‐based resource forecasting model for ...Figure 7.13 Service function chain (SFC) modeling: virtualized network funct...Figure 7.14 States and features from the virtualized network function compon...Figure 7.15 Virtualized network function 2 (VNF 2): Clearwater cloud IP mult...Figure 7.16 Network function virtualization (NFV) implementation used for ev...Figure 7.17 (a) Total forecasting error (t‐training iteration each involving...Figure 7.18 (a) Homer CPU utilization, (b) Homestead processing delay (t‐tes...Figure 7.19 (a) Percentage error on delay prediction, (b) percentage CPU for...Figure 7.20 (a) Effect on processing latency, (b) effect on calls dropped (t...Figure 7.21 Cumulative call drops (t‐test number).Figure 7.22 Results of change point detection for a nonstationary traffic se...Figure 7.23 Learned traffic parameters and predicted resource demands for da...Figure 7.24 Distribution of VNF packet processing delay for both the synthes...Figure 7.25 QoS performance comparison between resource demand prediction sc...Figure 7.26 Episodic average reward versus the episode number for the three ...Figure 7.27 (a) System model, (b) local control loop used to stabilize the u...Figure 7.28 Numerical experiments with different M under N = 100.Figure 7.29 Illustrative example of structural role proximity.Figure 7.30 Conceptual view of network representation learning (NRL).Figure 7.31 Taxonomy to summarize network representation learning (NRL) tech...Figure 7.32 Categorization of network structure.

7 Chapter 8Figure 8.1 The 2D representation of a qubit, when the amplitudes of its quan...Figure 8.2 The generic 3D representation of a qubit using a Bloch sphere, wh...Figure 8.3 Qubit represented by two electronic levels in an atom.Figure 8.4 Beam splitting of light.Figure 8.5 Wave and particle nature of light. (for more details see the colo...Figure 8.6 (a) Einstein–Podolsky–Rosen (EPR) paradox description using He at...Figure 8.7 Circuit representation of the Hadamard gate H, of the three Pauli...Figure 8.8 Quantum teleportation using entanglement.Figure 8.9 The five complex fifth roots of 1.Figure 8.10 QFT_M/2 and a Hadamard gate correspond to FFT_M/2 on the odd and e...Figure 8.11 QFT_M is reduced to QFT_M/2 and M additional gates.Figure 8.12 Quantum Fourier transform (QFT) iterations.Figure 8.13 General block diagram of QFT processor.

8 Chapter 9Figure 9.1 Geometrical picture of a noisy qubit quantum channel on the Bloch...Figure 9.2 The channel evolution phase.Figure 9.3 The general model of transmission of information over a noisy c...Figure 9.4 Communication over a noisy channel.Figure 9.5 Detailed model of channel: P purification state, X transmitter ...Figure 9.6 The formal model of a noisy quantum communication channel. The ou...Figure 9.7 Effects of the environment on the transmittable information and o...Figure 9.8 Transmission of classical information over quantum channel with p...Figure 9.9 Transmission of classical information over quantum channel with p...Figure 9.10 Transmission of classical information over quantum channel with ...Figure 9.11 Transmission of classical information over quantum channel with ...Figure 9.12 Model of private classical communication of a channel.Figure 9.13 Entanglement‐assisted capacity of a channel.Figure 9.14 Quantum zero‐error communication system.Figure 9.15 Comparison of single (a) and joint (b) measurement settings. The...Figure 9.16 Confusability graph of a zero‐error code for one channel use. Th...Figure 9.17 Graph of a zero‐error code for two channel uses of a quantum cha...Figure 9.18 Hypergraph and the confusability graph of a given input system w...Figure 9.19 Steps of the entanglement‐assisted zero‐error quantum communicat...Figure 9.20 Hypergraph of an entanglement‐assisted zero‐error quantum code. ...Figure 9.21 Transmission of quantum information through the quantum channel....Figure 9.22 (a) Initially, the quantum system and the reference system are i...Figure 9.23 The conceptual meaning of quantum coherent information. The unit...Figure 9.24 Expression of quantum coherent information. The source entropy o...Figure 9.25 Polarization optics of the QKD transmitter and receiver.

9 Chapter 10Figure 10.1 Circuit diagram for the two‐qubit code.Figure 10.2 The circuit diagram of the three‐qubit code.Figure 10.3 Circuit illustrating the structure of an [[n, k, d]] stabilizer ...Figure 10.4 Circuit diagram for the four‐qubit code.Figure 10.5 The general procedure for active recovery in a quantum error cor...Figure 10.6 The surface code four cycle. (a) Graphical representation. (b) A...Figure 10.7 [50] (a) The [[5, 1, 2]] surface code formed by putting together...Figure 10.8 [50] A distance‐three surface code with parameters [13, 1, 3].Figure 10.9 (a),(b),(c) Rotating a distance 5 lattice to produce another dis...Figure 10.10 Notation for fault‐tolerant circuits.Figure 10.11 Simple example illustrating the principles of quantum error cor...Figure 10.12 Syndrome extraction operation for [[7, 1, 3]] CSS code.

10 Chapter 11Figure 11.1 The quantum circuit employed in Shor’s algorithm for finding the...Figure 11.2 The quantum circuit of the quantum phase estimation algorithm, w...Figure 11.3 Grover operator’s quantum circuit including an oracle, two n‐qub...Figure 11.4 Example of Grover’s QSA, OO‐Oracle Operator, and DO‐Diffusion Op...Figure 11.5 Flowchart of the Boyer–Brassard–Høyer–Tapp (BBHT) quantum search...Figure 11.6 Flowchart of the Dürr–Høyer (DH) quantum search algorithm (QSA)....Figure 11.7 Quantum circuit of the quantum counting algorithm (QCA).Figure 11.8 Quantum circuit of the quantum mean algorithm (QMA).Figure 11.9 Quantum circuit of the quantum weighted sum algorithm (QWSA)....Figure 11.10 Interferometer with two phase shifters.Figure 11.11 Network representation for the phase shift transformation of Eq...Figure 11.12 Network representation of Deutsch’s algorithm.Figure 11.13 Network representation of Deutsch–Jozsa and Bernstein–Vazirani ...Figure 11.14 Network for shown acting on the basis state ∣a1a2⋯am〉...Figure 11.15 Network illustrating estimation of phase φ with j‐bit precision...Figure 11.16 Network representation of Grover’s algorithms. By repeating the...

11 Chapter 12Figure 12.1 Circuit‐centric quantum classifier.Figure 12.2 The circuit‐centric quantum classifier representation.Figure 12.3 Generic model circuit architecture for eight qubits.Figure 12.4 Graphical representation of quantum gates.Figure 12.5 (a) Parameter t₁ and its derivative.Figure 12.5b Parameter t₇ and its derivative.Figure 12.6 Schematic of the quantum neural network (QNN) on a quantum proce...

12 Chapter 13Figure 13.1 Illustration of the three common steps of hybrid quantum‐classic...Figure 13.2 Quantum circuit to evaluate the n‐th component of the grad...Figure 13.3 Fraction of satisfied clauses R₇(γ, β) for circuits o...Figure 13.4 Processing steps of HHL algorithm.Figure 13.5 Quantum circuit for solving a 4 × 4 system of linear equation Ax...

13 Chapter 14Figure 14.1 Braess’s paradox.Figure 14.2 Simulation results.Figure 14.3 Simulation results.Figure 14.4 Cognitive network architecture.Figure 14.5 Circuit that generates the initial entangled state ∣ψ e 〉....Figure 14.6 Ctrl − F₁ gate circuit, where . Looking fro...Figure 14.7 Empirical probability p(L₁) (choice frequency of the risky prosp...Figure 14.8 Empirical probability p(L₁) (choice frequency of the risky prosp...

14 Chapter 15Figure 15.1 Integration of satellite and ground communication networks.Figure 15.2 Principle of trusted‐repeater‐based satellite QKD.Figure 15.3 Basic structure of QKP‐enabled satellite QKD system.Figure 15.4 Architecture of double‐layer quantum satellite networks (QSNs)....Figure 15.5 Route selection for key‐relay services in two scenarios over the...Figure 15.6 Contact and resource graph of quantum satellite network (QSN)....Figure 15.7 Success probability (SP) and SP‐a versus traffic load under diff...Figure 15.8 (a) Success probability (SP) versus traffic load with different ...Figure 15.9 (a) Success probability (SP) versus traffic load with different ...Figure 15.10 Social overlay network.Figure 15.11 Social relationship graph form.Figure 15.12 Adaptive QoS‐QKD network model.Figure 15.13 Simple topology showing the calculation of the threshold .Figure 15.14 Network parameters.Figure 15.15 An example of greedy forwarding.Figure 15.16 The number and average sizes of routing packets.Figure 15.17 Packet delivery ratio (PDR).

15 Chapter 16Figure 16.1 Schematic illustration of the adopted quantum network architectu...Figure 16.2 Expected link entanglement rate ξ_{i, j}(T^ch) between adjacent...Figure 16.3 Expected end‐to‐end entanglement rate between nodes v_i and v_j ...Figure 16.4 Minimum coherence time required for the successful utilization ...Figure 16.5 (a) Butterfly, (b) inverted crown network.Figure 16.6 (a) The G_k network, (b) the grail network.Figure 16.7 Probability distributions of 100‐step discrete quantum walks on ...Figure 16.8 The probability distribution obtained from a computer simulation...Figure 16.9 A graph with various degrees and a labeling of the edges for eac...Figure 16.10 The hypercube in d = 3 dimensions. Vertices correspond to 3‐bit...Figure 16.11 The classical simple random walk on the three‐dimensional hyper...Figure 16.12 The graph G₄. Two binary trees of n = 4 levels are glued togeth...Figure 16.13 The elements of the Hamiltonian of the quantum random walk on GFigure 16.14 Approximation of the finite line by an infinite homogeneous lin...Figure 16.15 A random walk on assignments to the 2‐SAT formula of our exampl...Figure 16.16 The modified graph of Figure 16.12. A big random cycle has been...

16 Chapter 17Figure 17.1 Quantum internet graph G with deterministically chosen virtual l...Figure 17.2 Quantum internet graph G with deterministically chosen virtual l...Figure 17.3 Comparison of different routing algorithms on deterministic virt...Figure 17.4 Recursively generated physical graph and virtual graph at the 0‐...Figure 17.5 Recursively generated physical graph and virtual graph at the fi...Figure 17.6 Network example with three switches (boxes with multiple vertica...Figure 17.7 A quantum network protocol stack comprising four layers: physica...Figure 17.8 Setting of layers 1 and 2.Figure 17.9 Settings of layers 3 and 4.Figure 17.10 Greenberger–Horne–Zeilinger (GHZ) states are very fragile.Figure 17.11 (a) Static phase, (b) adaptive phase.Figure 17.12 (a) Static phase, (b) adaptive phase.Figure 17.13 The goal of a quantum routing protocol.Figure 17.14 Regions and how they connect.Figure 17.15 The state for connecting nine networks in hierarchical regions ...Figure 17.16 Symmetrizing a network state between regions (shown for a three...Figure 17.17 Example network for illustration of Protocol 2.Figure 17.18 (a) Generating the state |GHZ₄〉, (b) generating the state...