Understand the future of wireless communication with this groundbreaking guide

Quantum physics and quantum communications will be integral to the future of computing and telecommunications technology. Quantum technologies have applications in a vast array of advanced technological fields, including wireless technology, where communication speed, encryption, and networking methods promise to be revolutionized by their introduction. For the next generation of engineers and telecommunications experts, a thorough understanding of this groundbreaking area of research will be critical.

Wireless Quantum Networks, Volume 1 promises to help readers build this understanding with a comprehensive guide. It offers thorough coverage of the principles, algorithms, and design elements underlying, due to its implementability, Intelligent Continuous Variable Quantum Technology (ICVQT), which incorporates aspects of quantum machine learning, quantum computing, and advantages in practical implementations compared with Discrete Variable counterpart. The result can be used as a stand-alone introduction to this essential subject or as the first step in a broad-based quantum computing and communication education, supplemented by Volume 2 of this series.

Wireless Quantum Networks, Volume 1 readers will also find:

Detailed treatment of topics including Quantum Information Theory, Deep Quantum Neural Networks, Entanglement, Quantum Network (QN) Routing, QN Topology design, Quantum Coding Theory, Quantum Computing Gates Libraries, and more
Discussions grounded in the latest research, moving naturally from introductory to advanced proficiency
Design examples within each chapter

Wireless Quantum Networks Volume 1 isa must for computer scientists, engineers, and researchers interested in quantum communications, as well as advanced undergraduate and graduate students looking for a grounding in the subject.

Savo Glisic, PhD, is a Research Professor at the Worcester Polytechnic Institute, Massachusetts, USA. He has decades of research experience in the field of wireless communications in both the US and Europe, and has published extensively on quantum communications and related subjects.

Ch 1 INTRODUCTION

1.1 Motivation

1.2 Structure of the book

Ch 2 ADVANCES IN ML

2.1 Lifelong ML

2.1.1 Multi-Task Learning [MTL]

2.2 Lifelong Supervised Learning

2.3 Lifelong Neural Networks

2.4 Cumulative Learning

2.4.1 Open (World) Classification or Learning

2.4.2 Open World Learning for Unseen Class Detection

2.5 Efficient Lifelong Learning Algorithm: ELLA

2.6 Lifelong Sentiment Classification: LSC

2.7 Lifelong Unsupervised Learning

2.7.1 Lifelong Topic Modeling

2.7.1.1 Lifelong Topic Model for Small Data: AMC

2.7.2 Lifelong Information Extraction (LIE)

2.7.3 Lifelong Relaxation Labeling (Lifelong‐RL)

2.8 Lifelong Reinforcement Learning

2.8.1 LRL Through Multiple Environments

2.8.2 Hierarchical Bayesian LRL

2.8.3 Policy Gradient ELLA (PG‐ELLA)

REFERENCES

Ch 3 DEEP NN and FEDERATED LEARNING

3.1 Optimization Algorithm Approximation by DNN

3.1.1 Generic Optimization Problem

3.1.2 Algorithm Approximation Background

3.2 Spatial Scheduling by DNN

3.2.1 Wireless Link Scheduling

3.2.2 Scheduling by DNN

3.2.2.1 Learning Based on Geographic Location Information

3.2.2.2 DNN Structure

3.2.2.3 Training Process

3.2.2.4 Link Deactivation

3.3 Spatial Scheduling by DNN with Proportional Fairness

3.3.1. Proportional Fairness Scheduling

3.3.2. Learning to Maximize Weighted Sum Rate

3.3.3 Weighted Sum Rate Maximization via Binary Weights

3.3.4 Utility Analysis of Binary Reweighting Scheme

3.4 DNN in Vehicular Networks

3.4.1 System Model

3.4.1.1 Channel Model

3.4.1.2 Modeling AoI

3.4.1.3 Link Clustering

3.4.2 Network Optimization

3.4.2.1 AoI‐Aware RRM Objectives

3.4.2.2 Bellman’s Equation

3.4.2.3 DRL Algorithm

3.5 Federated Learning

3.5.1 Preliminaries

3.5.2 Algorithms Classification

3.5.3 FLS Architecture

3.6 FL and Block Chains

3.6.1 Basics of Block Chains

3.6.2 CASE STUDY: Blockchain‐based

Federated Learning (BFL) in Vehicular Network

3.6.2.1 System Model

3.6.2.2 BFL Block Arrival Process

3.6.2.3 System Optimization

REFERENCES

Ch 4 QC WITH CONTINUOUS VARIABLE

4.1 Preliminaries

4.1.1. Position and momentum space

4.1.2 Momentum Operator

4.1.3 Translation Operator in Quantum Mechanics

4.1.4 Wave Function

4.1.5 Hamiltonian Operator

4.1.6 Schrödinger equation

4.1.7 Relativistic wave equations

4.2 Gaussian Quantum Information

4.2.1 Elements of Gaussian Quantum Information Theory

4.2.2 Distinguishability of Gaussian States

4.2.2.1 Measures of distinguishability

4.2.2.2 Distinguishing optical coherent states

4.2.3 Examples of Gaussian Quantum Protocols

4.2.3.1 Quantum teleportation and variants

4.2.3.2 Quantum cloning

4.2.4 Bosonic Gaussian Channels

4.2.4.1 Preliminaries

4.2.4.2 One‐mode Gaussian channels

4.2.4.3 Classical capacity of Gaussian channels

4.2.4.4 Quantum capacity of Gaussian channels

4.2.4.5 Quantum dense coding and entanglement‐assisted classical capacity

4.2.4.6. Entanglement distribution and secret‐key capacities

4.2.4.7. Gaussian channel discrimination and applications

Appendix

REERENCES

Ch 5 ENTENGLEMENT

5.1 Quantum information with continuous variables

5.1.1 Continuous Variables in Quantum Optics

5.1.1.1 The quadratures of the quantized field

5.1.1.2 Phase‐space distribution

5.1.1.3 Gaussian states

5.1.1.4 Linear optics

5.1.1.5. Nonlinear optics

5.1.1.6. Polarization and spin

5.1.1.7 Phase reference

5.1.2 Continuous‐Variable Entanglement

5.1.2.1. Bipartite entanglement

5.1.2.2. Multipartite entanglement

5.1.2.3 Nonlocality

5.2 Remote Entanglement Distribution

Appendix A: Schmidt decomposition

Appendix B: Mermin‐Klyshko inequalities

Appendix C: The classification of tripartite three‐mode Gaussian states

Appendix C1: Points of Intersection

REFERENCES

Ch 6 ACHIEVABLE TRANSMISSION RATES

6.1 Bosonic Gaussian channels (BGCs)

6.1.1. Multi‐mode BGCs

6.1.1.1. Notation and preliminaries

6.1.1.2. BGCs

6.1.2. Unitary dilation theorem

6.1.2.1. General dilations

6.1.2.2. Reducing the number of environmental modes

6.1.2.3. Minimal noise channels

6.1.2.4. Additive classical noise channel

6.1.2.5. Canonical form for generic channels

6.1.3. Weak degradability

6.1.3.1. A criterion for weak degradability

6.1.4. Two‐mode BGCs

6.1.4.1. Weak‐degradability properties

6.2 Entanglement‐Assisted Classical Capacity

of Noisy Quantum Channels

6.3 Entanglement- assisted classical capacity

6.3.1 The BSST Theorem

6.3.2 Entanglement‐Assisted vs Unassisted Capacities

6.4 Entanglement‐assisted capacity of quantum channel with additive constraint

6.4.1. Classical Quantum Chanel with Additive Constraint

6.4.2. Quantum-Quantum Chanel

6.4.3. Entanglement‐Assisted Capacity

6.5 Entanglement in Quantum channels with cv

6.5.1 The entanglement‐assisted classical capacity

6.5.2 Entanglement‐assisted versus unassisted classical capacities

6.5.3 On continuity of the entanglement‐assisted capacity

6.5.4. Coherent information and a measure of private classical information

6.6 Fundamental Limits of Quantum Communications: Summary

6.6.1 Adaptive protocols and two‐way capacities

6.6.2 General bounds for two‐way capacities

6.6.3 Simulation of quantum channels

6.6.4 Teleportation covariance

6.6.5 Teleportation stretching of adaptive protocols.

6.6.6 REE as a single‐letter converse bound

6.6.7 Generalizations

6.6.8 Achievable rates in bosonic communications

6.6.9 Achievable rates in quantum optical communications

6.6.10 Achievable rates in quantum communications with Gaussian noise

6.6.11 Limits on achievable rates in qubit communications

6.7 Simplification of the main results

6.8 Summary of Analytical Tools

6.9 Performance Bounds

6.10 Simplified Models for Bosonic Gaussian Channels

6.11 Simplified Models for Discrete‐Variable Channels

6.2 Simplified Bounds for QKD Protocols Rates

6.3 Algorithms Upgrades

REFERENCES

Ch 7 QUANTUM NETWORK ROUTING

7.1 Routing over Virtual Quantum Network

7.1.1 Preliminaries

7.1.2 Ring Network

7.1.3 Sphere Network

7.1.3.1 Definition of the VQN architecture

7.1.3.2 Routing Algorithm

7.2 Minimum Cost Routing

7.2.1 Quantum Routing Parameters

7.2.2 Entanglement‐Gradient Routing

7.3 Entanglement Distribution

7.3.1 Preliminaries

7.3.2 The optimal RED protocol

7.3.3 Stationary Protocol

7.4 Quantum graph

7.5 Multipoint entanglement distribution (multi-partite entanglement)

REFERENCES

Ch 8 Dynamic QUANTUM NETWORK TOPOLOGY DESIGN

8.1 Quantum graph states

8.1.1. Interaction pattern.

8.1.2. Stabilizer formalism.

8.1.3 Local Clifford group and LC equivalence.

8.1.4 Weyl operators and Heisenberg group

8.2. Evaluation of the Degree of Entanglement for Graph States

8.2.1 Schmidt measure

8.2.2. Generalization of the evaluation rules

8.3 Quantum State Graph Reconfiguration

8.3.1 Vertex‐deletions and local complementations

8.3.2 Circle graphs

8.3.3 Examples of vertices

8.3.4 Graph Reconfiguration Algorithms

REFERENCES

Ch 9 ELEMENTS of QUANTUM CODING THEORY

9.1 Quantum coding theorems

9.1.1 Preliminaries

9.1.2 Quantum coding theorem

9.1.3 Reliability function

9.1.4 Reliability Function for Different Quantum Channel Examples

9.2 Error Correction Limits for Quantum Metrology

9.2.1. Quantum Metrology in Presence of Impairments

9.2.2 Error Correction Enhanced Quantum Metrology

9.2.2.1. Noiseless Ancilla and Perfect Error Correction

9.2.2.2. Noisy Ancilla and Perfect Error Correction

9.2.2.3. Noiseless Ancilla and Imperfect Error Correction

9.2.2.4. Limitations of Current Quantum Technologies

9.2.3. Other Error Correction Strategies

9.3 Stabilizer Codes

9.3.1 Stabilizer Coding

9.4 Quantum LDPC Codes

9.4.1 An Introduction to classical LDPC Codes

9.4.1.1 Representations of LPDC Codes

9.4.1.2 LDPC Code Design Techniques

9.4.1.3 Iterative Decoding Algorithms

9.4.2 Constructing regular quantum LDPC codes

9.5 Homological family of quantum LDPC codes

9.5.1 Code construction based on a Regular Tessellation of Hyperbolic Space

9.5.2 Hyperbolic 4‐space and its Regular Tessellation by Hypercubes

9.5.3 Compact Manifolds

9.5.4 Code Performance

9.5.5 Decoders

REFERENCES

Ch 10 QUANTUM MACHINE LEARNING

10.1. Quantum Neural Networks with DV

10.1.1 Error Backpropagation in Quantum ANN

10.1.2 Firing Pattern Selection

10.1.3 Representation of n-to-m Boolean Functions

10.1.4 General Architecture Networks

10.2 Quantum Neural Networks with CV

10.2.1 Continuous Quantum Registers

10.2.2 Discrete Simulation of Continuous Quantum Registers

10.2.3 Quantum Phase Estimation

10.2.4. Quantum Phase Kickback

10.2.5 Quantum Gradients

10.3 Quantum Parametric Optimization

10.3.1 Preliminaries

10.3.1.1. Quantum Feedforward and Backwards Propagation of Phase Errors

10.3.1.2 Full‐batch Effective Phase Kicks

10.3.1.3 Interpretation in classical Hamiltonian dynamics

10.3.2 Quantum Dynamical Descent

10.3.2.1. Basic Algorithm

10.3.2.2. Heisenberg picture update rule

10.3.2.3. Quantum Approximate Optimization Algorithm

10.3.2.4. Quantum Adiabatic Algorithm (QAA)

10.3.3 Extensions of Quantum Descent Methods

10.4 Quantum Neural Network Learning

10.4.1. Quantum‐Coherent Neural Networks

10.4.1.1. Classical‐to‐Quantum Computational Embedding

10.4.1.2. Classical Data Phase Kicking

10.4.1.3. Abstract Quantum Neuron

10.4.1.4. QFB Neural Network

10.4.2. Quantum Phase Error Backpropagation

10.4.2.1. Operator Chain Rule

10.4.2 Implementations of Quantum Coherent Neurons

10.4.2.1. Hybrid CV‐DV Neurons

10.4.2.2. CV‐only

10.5. Quantum Parametric Circuit Learning

10.5.1 Parametric Ansatze & Error Backpropagation

10.5.1.1 From Classic to Quantum Parametrization of Ansatze

10.5.1.2. Quantum Parametric Circuit Error Backpropagation

10.5.2. Quantum State Exponentiation

10.5.2.1. Single state exponentiation

10.5.2.2. Sequential Exponential Batching

10.5.2.3. Quantum Random Access Memory Batching

10.5.3. Quantum State Learning

10.5.3.1. Quantum Pure State Learning

10.5.3.2. Quantum Mixed State Learning

10.5.4. Quantum Unitary & Channel Learning

10.5.4.1. Supervised Unitary Learning

10.5.4.2. Supervised Channel Learning

10.5.4.3. Unsupervised Unitary Learning

10.5.4.4. Unsupervised Channel Learning

10.5.5 Quantum Basic Learning Algorithms

10.5.5.1. Preliminaries

10.5.5.2. Loss Functions

10.5.6. Estimation of Quantum Code

10.5.6.1. Estimation of Quantum Autoencoders: Compression Code

10.5.6.2. Denoising Quantum Autoencoder

10.5.6.3. Quantum Error Correcting Code Learning

10.5.7. Generative Adversarial Quantum Circuits

10.5.7.1. Classical Generative Adversarial Networks Review

10.5.7.2. Generative Adversarial Quantum Circuits

10.5.8. Parametric Hamiltonian Optimization

10.5.8.1. Hamiltonian‐Parallelized Gradient Accumulation

10.5.9. Hybrid Quantum Neural‐Circuit Networks

10.5.9.1. Fully Coherent Hybrid Networks

10.5.9.2. Hybrid Quantum‐Classical Networks

10.6 Quantum Deep Convolutional Neural Networks

10.6.1 Classical Convolutional neural network (CNN)

10.6.1.1 Tensor representation

10.6.1.2 Architecture

10.6.1.3 Mathematical Formulations

10.6.2 Forward Propagation in QCNN

10.6.2.1 Single Quantum Convolution Layer

10.6.2.2 Inner Product Estimation

10.6.2.3 Encoding the amplitude in a register

10.6.2.4 Conditional rotation

10.6.2.5. Amplitude Amplification

10.6.2.6. l_∞ tomography and probabilistic sampling

10.6.2.7 Quantum Pooling

10.6.3. Backward Propagation in QCNN

10.6.3.1 Classical Backpropagation

10.6.3.2 Quantum Algorithm for Backpropagation

10.6.3.3 Gradient Descent and Classical equivalence

REFERENCES

Ch 11 QUANTUM COMPUTING GATES LIBRARIES

11.1 Quantum Gates Library

11.1.1 Classical Logic Gates Library

11.1.2 Quantum Logic Gates Library

11.1.2.1 1- Qubit Gates

11.1.2.2 Rotations About the x‐, y‐, and z‐Axes

11.1.2.3 Controlled Quantum Gates

11.1.2.4 Selected 2‐Qubit Gates Libraries

11.1.2.5 Entangling Power of Quantum Gates

11.1.2.6 Arbitrary 2‐Qubit Gates

11.2 Depth‐Optimal Quantum Circuits

11.2.1 Meet-in-the-Middle (mm) Search Algorithm

11.2.2 Search tree pruning

11.2.3 Implementation Aspects

11.3 Exact Minimization of Quantum Circuits

11.3.1 Preliminaries

11.4 Decomposing CV Operations into a Universal Gate Library

11.4.1 Exact Decompositions of Multi‐Mode Gates

REFERENCES

Index

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