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From Distributed Quantum Computing to Quantum Internet Computing

An Introduction

Loke, Seng W.


1. Edition December 2023
208 Pages, Hardcover
Wiley & Sons Ltd

ISBN: 978-1-394-18551-1
John Wiley & Sons

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From Distributed Quantum Computing to Quantum Internet Computing

Understand the future of the internet with this accessible guide

Quantum computing, which draws upon the principles of quantum mechanics to perform computing functions unrestricted by the binary language of ordinary computing, has developed with extraordinary speed in recent years. Progress in quantum computing and its related technological subfields, including quantum internet, has been rapid enough to suggest that we are living in a "new Quantum Age." To understand the future of the internet, it's now essential to understand the present and future of quantum computing and quantum internet computing.

This book provides a groundbreaking overview of this field of technology and its latest developments. It provides readers with a working knowledge of the key topics required to connect quantum computing to the future of distributed computing and the internet, including important issues like quantum protocols, distributed quantum computations, fundamental computations in the quantum internet architecture, and more. The result is an accessible and essential reference for any reader looking to better understand quantum technologies.

From Distributed Quantum Computing to Quantum Internet Computing readers will also find:
* Detailed discussion of topics including qubit states, entanglement, quantum gates, and more.
* Mathematical background for underlying key concepts.
* Worked out examples that aim to initiate readers into the emerging area of quantum internet computing.

This book is ideal for researchers and graduate students in quantum computing, quantum internet, quantum communications, and related fields, as well as Computer Scientists and Information Technology students and researchers who want an introductory overview to quantum internet computing.

About the Author x

Preface xi

Acknowledgments xiv

1 Introduction 1

1.1 The New Quantum Age and the Second Quantum Revolution 1

1.2 Distributed Quantum Computing and the Rise of Quantum Internet Computing 4

1.2.1 Distributed Quantum Computing 5

1.2.2 Quantum Internet Computing 8

1.3 Aim and Scope of the Book 9

1.4 Outline of this Book 10

1.5 Related Books and Resources 11

2 Preliminaries 17

2.1 Qubit and Qubit States 17

2.2 Quantum Gates and Quantum Circuits 23

2.2.1 Single Qubit Gates 24

2.2.2 Measurement Operators 26 Measurement Postulate (General Measurement) 27 POVM 27 Projective Measurements 28

2.2.3 Multiple Qubit Gates 29

2.2.4 Quantum Circuits 29

2.2.5 Universal Quantum Computer and Gate Sets 32

2.3 Entanglement 33

2.4 Teleportation and Superdense Coding 39

2.5 Summary 42

2.6 Further Reading and Resources on Quantum Computing 42

3 Distributed Quantum Computing-Classical and Quantum 45

3.1 The Power of Entanglement for Distributed Computing 46

3.1.1 Enabling Distributed Computations with Fewer Bits of Communication 46 The Distributed Three-Party Product Problem 47 The Distributed Deutsch-Jozsa Promise Problem 49 The Distributed Intersection Problem 52 Discussion 56

3.1.2 Enabling Distributed Computations Not Possible Classically 56 Greenberger-Horne-Zeilinger and Mermin (GHZ&M) Game 56 Clauser-Horne-Shimony-Holt (CHSH) 60 Discussion 67

3.2 Other Quantum Protocols 67

3.2.1 Quantum Coin Flipping 67 Classical Coin Flipping 67 Quantum Coin Flipping 74

3.2.2 Quantum Leader Election 77

3.2.3 Quantum Key Distribution (QKD) 79

3.2.4 Quantum Anonymous Broadcasting 90

3.2.5 Quantum Voting 97

3.2.6 Quantum Byzantine Generals Solution 99

3.2.7 Quantum Secret Sharing 104

3.2.8 Quantum Oblivious Transfer (OT) 105

3.2.9 Discussion 107

3.3 Summary 107

4 Distributed Quantum Computing - Distributed Control of Quantum Gates 113

4.1 Performing a Distributed CNOT 113

4.1.1 Using Teleportation 113

4.1.2 A More Efficient MethodWith Cat-Like States 114

4.2 Beyond the Distributed CNOT 118

4.2.1 Same Control Qubit for Multiple Target Qubits on Different Machines 118

4.2.2 Multiple Control Qubits for the Same Target Qubit on a Different Machine 123

4.2.3 Cat-Entangler and Cat-Disentangler Modules 126

4.3 Distributing Quantum Circuits and Compilation for Distributed Quantum Programs 127

4.4 Control and Scheduling for Distributed Quantum Computers 129

4.5 Distributed Quantum Computing Without Internode Entanglement 132

4.6 Summary 133

5 Delegating Quantum Computations 137

5.1 Delegating Private Quantum Computations 137

5.2 How to Verify Delegated Private Quantum Computations 149

5.2.1 X Gate Gadget 150

5.2.2 Z Gate Gadget 151

5.2.3 CNOT Gate Gadget 151

5.2.4 R Gate Gadget 151

5.2.5 H Gate Gadget 155

5.3 Quantum Computing-as-a-Service 158

5.4 Summary 158

6 The Quantum Internet 161

6.1 Entanglement Over Longer Distances 161

6.1.1 Bell States and Bell State Measurement 162

6.1.2 Entanglement Swapping 163

6.1.3 Transmission of Qubits Using Tree-Cluster States 165

6.2 Entanglement with Higher Fidelity 172

6.2.1 Fidelity 172

6.2.2 Twirling Map 174

6.2.3 Quality of Distributed Entanglement and Entanglement Purification 177

6.3 Distributed Quantum Computation Over the Quantum Internet - Challenges 183

6.4 Summary 187

References 187

7 Conclusion 191

References 192

Index 193
Seng W. Loke, PhD, is a Professor in Computer Science for the School of Information Technology, Deakin University, Australia, as well as Director of the Centre for Software, Systems and Society (CS3) and Co-Director of the Internet of Things Platforms and Applications Lab in the Centre for Internet of Things Ecosystem Research and Experimentation (CITECORE). He has published extensively on Internet of Things, context-aware computing, mobile and pervasive computing, and related subjects.

S. W. Loke, School of Information Technology, Deakin University, Australia