From Classical to Quantum Coding - Zunaira Babar

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Résumé :

An expert discussion of the potential evolution of quantum codes

In From Classical to Quantum Coding, a team of distinguished researchers deliver a seamless book on the subject of quantum error correction codes (QECC) designed for mitigating the environment-induced decoherence imposed on quantum computing and communications. Commencing from first principles, Part I is dedicated to readers familiar with classical coding and wishing to move into quantum coding. Part II focuses on near-term quantum codes requiring a modest to moderate number of qubits. Finally, Part III of the book offers an outlook on the classical to quantum evolution of QECCs, to advanced codes that rely on numerous qubits as quantum technology matures.

The book incorporates several advanced topics, including the universal decoding of arbitrary linear codes, iterative short turbo block codes, turbo convolutional codes, and the family of low-density parity check codes. The powerful design tool of extrinsic information transfer charts plays a central role in the associated near-hashing-bound designs.

Readers will also find:

• An easy-reading introduction to quantum information processing and quantum coding
• An evolutionary portrayal of the classical to quantum coding paradigm
• Practical discussions of near-term quantum topological error correction codes and how they protect quantum gates from decoherence
• Detailed treatments of syndrome-based decoding of diverse quantum turbo codes and quantum low-density parity check codes

From Classical to Quantum Coding will benefit doctoral students, and industrial and academic researchers wishing to expand their expertise from the classical to the quantum field of signal processing, computing and communications....

Biographie:

Zunaira Babar is a Senior Algorithm Engineer at VIAVI Solutions Inc.

Daryus Chandra is a Senior Quantum Error Correction Researcher at Photonic Inc.

Soon Xin Ng, PhD, is a Full Professor of Telecommunications at the University of Southampton, UK.

Lajos Hanzo is a Fellow of the Royal Academy of Engineering and a Foreign Member of the Hungarian Academy of Sciences....

Sommaire:

About the Authors xiii
List of Acronyms xv
Preface xvii
Acknowledgments xix

Part I From Classical to Quantum Codes 1

1 Introduction 3
1.1 Motivation 3
1.2 Historical Overview 6
1.3 Outline of the Book 17

2 Preliminaries on Quantum Information 21
2.1 Introduction 21
2.2 A Brief Review of Quantum Information 21
2.3 Quantum Information Processing 24
2.4 Quantum Decoherence 28
2.5 No-cloning Theorem 33
2.6 Quantum Entanglement 34
2.7 Quantum Channels 35
2.8 Summary and Conclusions 38

3 From Classical to Quantum Coding 39
3.1 Introduction 39
3.2 A Brief Review of Classical Syndrome-based Decoding 40
3.3 A Brief Review of Quantum Stabilizer Codes 43
3.4 Protecting a Single Qubit: Design Examples 46
3.5 Summary and Conclusions 57

4 Revisiting Classical Syndrome Decoding 59
4.1 Introduction 59
4.2 Look-up Table-based Syndrome Decoding 61
4.3 Trellis-based Syndrome Decoding 62
4.4 Block Syndrome Decoding 70
4.5 Results and Discussion 74
4.6 Summary and Conclusions 79

5 Near-capacity Codes for Entanglement-aided Classical Communication 83
5.1 Introduction 83
5.2 Review of the SD Coding Protocol 84
5.3 Entanglement-assisted Classical Capacity 87
5.4 Bit-based Code Structure 90
5.5 Near-capacity Design 91
5.6 Results and Discussion I 95
5.7 Symbol-based Code Structure 101
5.8 Results and Discussion II 101
5.9 Summary and Conclusion 104

Part II Near-term Quantum Codes 109

6 Quantum Coding Bounds and a Closed-form Approximation of the Minimum Distance Versus Quantum Coding Rate 111
6.1 Introduction 111
6.2 On Classical to Quantum Coding Bounds 111
6.3 Quantum Coding Bounds in the Asymptotical Limit 114
6.4 Quantum Coding Bounds on Finite-length Codes 118
6.5 The Bounds on Entanglement-assisted Quantum Stabilizer Codes 122
6.6 Summary and Conclusions 126

7 Quantum Topological Error Correction Codes: The Classical-to-quantum Isomorphism Perspective 127
7.1 Introduction 127
7.2 Classical Topological Error Correction Codes: Design Examples 127
7.3 Quantum Topological Error Correction Codes: Design Examples 135
7.4 Performance of Quantum Topological Error Correction Codes 141
7.5 Summary and Conclusions 151

8 Protecting Quantum Gates Using Quantum Topological Error Correction Codes 153
8.1 Introduction 153
8.2 Protecting Transversal Gates 154
8.3 Design Examples 159
8.4 Error Model 164
8.5 Simulation Results and Performance Analysis 169
8.6 Conclusions and Future Research 179

9 Universal Decoding of Quantum Stabilizer Codes via Classical Guesswork 181
9.1 Introduction 181
9.2 Decoding Classical FEC Codes via Guesswork 182
9.3 Quantum Stabilizer Codes 184
9.4 Decoding Quantum Stabilizer Codes 185
9.5 Results and Discussion 192
9.6 Conclusions and Future Work 197

Part III Advanced Quantum Codes 201

10 Revisiting the Classical to Quantum Coding Evolution 203
10.1 Introduction 203
10.2 Review of Classical Linear Block Codes 204
10.3 Quantum Stabilizer Codes 206
10.4 Quantum Convolutional Codes 218
10.5 Entanglement-assisted Quantum Codes 221
10.6 Summary and Conclusions 222

11 EXIT-chart Aided Near-hashing-bound Concatenated Quantum Codes 225
11.1 Introduction 225
11.2 Design Objectives 226
11.3 Circuit-based Representation of Stabilizer Codes 228
11.4 Revisiting Concatenated Quantum Codes 234
11.5 EXIT Chart Aided Quantum Code Design 239
11.6 Results and Discussion I 242
11.7 Quantu...