From Distributed Quantum Computing to Quantum Internet Computing

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.

• About the Author xPreface xiAcknowledgments xiv1 Introduction 11.1 The New Quantum Age and the Second Quantum Revolution 11.2 Distributed Quantum Computing and the Rise of Quantum Internet Computing 41.2.1 Distributed Quantum Computing 51.2.2 Quantum Internet Computing 81.3 Aim and Scope of the Book 91.4 Outline of this Book 101.5 Related Books and Resources 112 Preliminaries 172.1 Qubit and Qubit States 172.2 Quantum Gates and Quantum Circuits 232.2.1 Single Qubit Gates 242.2.2 Measurement Operators 262.2.2.1 Measurement Postulate (General Measurement) 272.2.2.2 POVM 272.2.2.3 Projective Measurements 282.2.3 Multiple Qubit Gates 292.2.4 Quantum Circuits 292.2.5 Universal Quantum Computer and Gate Sets 322.3 Entanglement 332.4 Teleportation and Superdense Coding 392.5 Summary 422.6 Further Reading and Resources on Quantum Computing 423 Distributed Quantum Computing–Classical and Quantum 453.1 The Power of Entanglement for Distributed Computing 463.1.1 Enabling Distributed Computations with Fewer Bits of Communication 463.1.1.1 The Distributed Three-Party Product Problem 473.1.1.2 The Distributed Deutsch–Jozsa Promise Problem 493.1.1.3 The Distributed Intersection Problem 523.1.1.4 Discussion 563.1.2 Enabling Distributed Computations Not Possible Classically 563.1.2.1 Greenberger–Horne–Zeilinger and Mermin (GHZ&M) Game 563.1.2.2 Clauser–Horne–Shimony–Holt (CHSH) 603.1.2.3 Discussion 673.2 Other Quantum Protocols 673.2.1 Quantum Coin Flipping 673.2.1.1 Classical Coin Flipping 673.2.1.2 Quantum Coin Flipping 743.2.2 Quantum Leader Election 773.2.3 Quantum Key Distribution (QKD) 793.2.4 Quantum Anonymous Broadcasting 903.2.5 Quantum Voting 973.2.6 Quantum Byzantine Generals Solution 993.2.7 Quantum Secret Sharing 1043.2.8 Quantum Oblivious Transfer (OT) 1053.2.9 Discussion 1073.3 Summary 1074 Distributed Quantum Computing – Distributed Control of Quantum Gates 1134.1 Performing a Distributed CNOT 1134.1.1 Using Teleportation 1134.1.2 A More Efficient MethodWith Cat-Like States 1144.2 Beyond the Distributed CNOT 1184.2.1 Same Control Qubit for Multiple Target Qubits on Different Machines 1184.2.2 Multiple Control Qubits for the Same Target Qubit on a Different Machine 1234.2.3 Cat-Entangler and Cat-Disentangler Modules 1264.3 Distributing Quantum Circuits and Compilation for Distributed Quantum Programs 1274.4 Control and Scheduling for Distributed Quantum Computers 1294.5 Distributed Quantum Computing Without Internode Entanglement 1324.6 Summary 1335 Delegating Quantum Computations 1375.1 Delegating Private Quantum Computations 1375.2 How to Verify Delegated Private Quantum Computations 1495.2.1 X Gate Gadget 1505.2.2 Z Gate Gadget 1515.2.3 CNOT Gate Gadget 1515.2.4 R Gate Gadget 1515.2.5 H Gate Gadget 1555.3 Quantum Computing-as-a-Service 1585.4 Summary 1586 The Quantum Internet 1616.1 Entanglement Over Longer Distances 1616.1.1 Bell States and Bell State Measurement 1626.1.2 Entanglement Swapping 1636.1.3 Transmission of Qubits Using Tree-Cluster States 1656.2 Entanglement with Higher Fidelity 1726.2.1 Fidelity 1726.2.2 Twirling Map 1746.2.3 Quality of Distributed Entanglement and Entanglement Purification 1776.3 Distributed Quantum Computation Over the Quantum Internet – Challenges 1836.4 Summary 187References 1877 Conclusion 191References 192Index 193