Quantum computing for communications : an engineering approach

Preface.How to use this book.Acknowledgements.List of Figures.Acronyms.PART I: INTRODUCTION TO QUANTUM COMPUTING.1. Motivations.2. Quantum Computing Basics.3. Measurements.PART II: QUANTUM ALGORITHMS.4. Two Simple Quantum Algorithms.5. Quantum Parallelism.6. Quantum Fourier Transform and its Applications.PART III: QUANTUM-ASSISTED SOLUTIONS OF INFOCOM PROBLEMS.7. Searching in an Unsorted Database.8. Quantum Based Multiuser Detection.9. Quantum Based Code Breaking.10. Quantum Based Key Distribution.11. Surfing the WEB on Quantum Basics.PART IV: APPENDICES.12. Mathematical Background.13. Derivations Related to the Generalized Grover Algorithm.14. Complex Baseband-Equivalent Description of Bandlimited Signals.15. Useful Links.References.Solution of Exercises.Index Cover......Page 1 Title page......Page 4 Copyright, ISBN 047086902X......Page 5 Dedication......Page 6 Contents......Page 8 Preface......Page 14 How to use this book......Page 16 Acknowledgments......Page 18 List of Figures......Page 20 Acronyms......Page 26 Part-I: Introduction to QuantumComputing......Page 30 1.1 Life Cycle of a Well-known Invention......Page 32 1.2 What about Computers and Computing?......Page 33 1.3 Let us Play Marbles......Page 36 2.1 Mystery of Probabilistic √I Gate......Page 38 2.2 The Postulates of Quantum Mechanics......Page 43 2.3 Qbits and Qregisters......Page 46 2.4 Elementary Quantum Gates......Page 50 2.5 General Description of the Interferometer......Page 53 2.6.1 A surprising quantum state – entanglement......Page 56 2.6.2 The CNOT gate as classical copy machine and quantum entangler......Page 57 2.6.3 Bell states......Page 59 2.6.4 Entanglement with the environment – decoherence......Page 61 2.6.5 The EPR paradox and the Bell inequality......Page 64 2.7 No Cloning Theorem......Page 69 2.8 How to Prepare an Arbitrary Superposition......Page 71 2.9 Further Reading......Page 72 3.1 General Measurements......Page 74 3.2 Projective Measurements......Page 75 3.2.1 Measurement operators and the 3rd Postulate in the case of projective measurement......Page 76 3.2.2 Measurement using the computational basis states......Page 78 3.2.4 Repeated projective measurement......Page 79 3.2.5 CHSH inequality with entangled particles......Page 80 3.3 Positive Operator Valued Measurement......Page 81 3.3.1 Measurement operators and the 3rd Postulate in the case ofPOVM......Page 83 3.3.2 How to apply POVM operators......Page 85 3.4 Relations among the Measurement Types......Page 87 3.5 Quantum Computing-based Solution of the Game with Marbles......Page 88 3.6 Further Reading......Page 90 Part-II: Quantum Algorithms......Page 92 4.1 Superdense Coding......Page 94 4.2 Quantum Teleportation......Page 96 4.3 Further Reading......Page 99 5.1 Introduction......Page 100 5.2 Deutsch–Jozsa Algorithm......Page 103 5.3 Simon Algorithm......Page 107 5.4 Further Reading......Page 110 6. Quantum Fourier Transform and its Applications......Page 112 6.1 Quantum Fourier Transform......Page 113 6.2.1 Idealistic phase estimation......Page 117 6.2.2 Phase estimation in practical cases......Page 119 6.2.3 Quantitative analysis of the phase estimator......Page 123 6.2.4 Estimating quantum uncertainty......Page 125 6.3.1 Connection between factoring and order finding......Page 131 6.3.2 Quantum-based order finding......Page 133 6.3.3 Error analysis and a numerical example......Page 138 6.4 QFT as generalized Hadamard transform......Page 142 6.5.1 Period finding......Page 146 6.5.2 Two-dimensional period finding and discrete logarithm......Page 147 6.6 Further Reading......Page 150 Part-III: Quantum-assisted Solutions of Infocom Problems......Page 154 7. Searching in an Unsorted Database......Page 156 7.1.1 Initialization – quantum parallelism......Page 157 7.1.2 First stage of G – the Oracle......Page 159 7.1.3 Second stage of G – inversion about the average......Page 160 7.1.4 Required number of iterations......Page 163 7.1.5 Error analysis......Page 166 7.2.1 Quantum counting based on phase estimation......Page 169 7.2.2 Error analysis......Page 171 7.2.3 Replacing quantum counting with indirect estimation onM......Page 176 7.3 Quantum Existence Testing......Page 178 7.3.1 Error analysis......Page 180 7.4 Finding Extreme Values in an Unsorted Database......Page 182 7.5.1 Generalization of the basic Grover database search algorithm......Page 184 7.5.2 Required number of iterations in the generalized Groveralgorithm......Page 188 7.5.3 Design considerations of the generalized Grover operator......Page 193 7.6 Further Reading......Page 197 8.1 Introduction to Code Division Multiple Access and Classical Multi-user Detection......Page 200 8.1.1 DS-CDMA in theory......Page 202 8.1.2 DS-CDMA in practice......Page 203 8.2 Optimal Multi-user Detection......Page 208 8.3 Quantum-based Multi-user Detection......Page 212 8.4 Further Reading......Page 214 9.1 Introduction to Cryptology......Page 216 9.2 Symmetric Key Cryptography......Page 218 9.2.1 Large number of users......Page 219 9.2.2 Length of the key and its randomness......Page 220 9.3 Public Key Cryptography......Page 221 9.3.1 The RSA algorithm......Page 223 9.3.2 Digital signatures......Page 224 9.4.1 Using Grover’s database search algorithm to break RSA......Page 226 9.4.2 Using Shor’s order finding algorithm to break RSA......Page 227 9.5 Further Reading......Page 229 10.1 The BB84 Protocol......Page 232 10.1.1 Idealistic scenario......Page 233 10.1.2 Eve appears on the scene......Page 235 10.1.3 When the channel introduces errors......Page 236 10.2 The B92 Algorithm......Page 237 10.4 Teleportation as a Useful Element in Quantum Cryptography......Page 239 10.5 Further Reading......Page 240 11.1 Introduction to WEB Surfing......Page 244 11.2 Quantum-based Solution of the Guessing Secret Problem......Page 247 Part-IV: Appendices......Page 252 12.1.1 Characterization of random events......Page 254 12.1.2 Decision theory......Page 256 12.2.2 Gaussian elimination......Page 257 12.2.3 Vector spaces......Page 258 12.2.5 Special linear operators......Page 261 12.3.1 Modular arithmetic......Page 263 12.3.2 Definitions......Page 264 12.3.3 Euclid’s algorithm......Page 265 12.3.4 Continued fraction and convergents......Page 266 12.3.5 Useful theorems......Page 268 13.1 Eigenvalues of the Generalized Grover Operator......Page 270 13.2 Eigenvectors of the Generalized Grover Operator......Page 272 14. Complex Baseband-equivalent Description of Bandlimited Signals......Page 276 15. Useful Links......Page 278 References......Page 280 Solutions of Exercises......Page 292 Index......Page 310

Quantum computers will revolutionize the way telecommunications networks function.

Quantum computing holds the promise of solving problems that would be intractable with conventional computers by implementing principles from quantum physics in the development of computer hardware, software and communications equipment.

Quantum-assisted computing will be the first step towards full quantum systems, and will cause immense disruption of our traditional networks. The world’s biggest manufacturers are investing large amounts of resources to develop crucial quantum-assisted circuits and devices.

Quantum Computing and Communications:

• Gives an overview of basic quantum computing algorithms and their enhanced versions such as efficient database searching, counting and phase estimation.
• Introduces quantum-assisted solutions for telecom problems including multi-user detection in mobile systems, routing in IP based networks, and secure ciphering key distribution.
• Includes an accompanying website featuring exercises (with solution manual) and sample algorithms from the classical telecom world, corresponding quantum-based solutions, bridging the gap between pure theory and engineering practice.

This book provides telecommunications engineers, as well as graduate students and researchers in the fields of computer science and telecommunications, with a wide overview of quantum computing & communications and a wealth of essential, practical information.

Quantum computers will revolutionize the way telecommunications networks function. Quantum computing holds the promise of solving problems that would be intractable with conventional computers by implementing principles from quantum physics in the development of computer hardware, software and communications equipment. Quantum-assisted computing will be the first step towards full quantum systems, and will cause immense disruption of our traditional networks. The world's biggest manufacturers are investing large amounts of resources to develop crucial quantum-assisted circuits and devices. Quantum Computing and Communications: Gives an overview of basic quantum computing algorithms and their enhanced versions such as efficient database searching, counting and phase estimation. Introduces quantum-assisted solutions for telecom problems including multi-user detection in mobile systems, routing in IP based networks, and secure ciphering key distribution. Includes an accompanying website featuring exercises (with solution manual) and sample algorithms from the classical telecom world, corresponding quantum-based solutions, bridging the gap between pure theory and engineering practice. This book provides telecommunications engineers, as well as graduate students and researchers in the fields of computer science and telecommunications, with a wide overview of quantum computing & communications and a wealth of essential, practical information. Offers an overview of basic quantum computing algorithms and their enhanced versions such as efficient database searching, counting and phase estimation. This book introduces quantum-assisted solutions for telecom problems including multi-user detection in mobile systems, routing in IP based networks, and secure ciphering key distribution.