From classical to quantum coding / Zunaira Babar, Daryus Chandra, Soon Xin Ng, Lajos Hanzo.

Format:

Book

Author/Creator:

Babar, Zunaira, author.

Chandra, Daryus, author.

Ng, Soon Xin, author.

Hanzo, Lajos, 1952- author.

Contributor:

Wiley InterScience (Online service)

Language:

English

Subjects (All):

Error-correcting codes (Information theory).

Quantum computing.

Electronic books.

Physical Description:

1 online resource (416 pages)

Place of Publication:

Piscataway, NJ : IEEE Press, [2026]

Contents:

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 Quantum Irregular Convolutional Codes 248 11.8 Results and Discussion II 252 11.9 Summary and Conclusions 255

12 Near-hashing-bound Quantum Turbo Short-block Codes 257 12.1 Introduction to Iterative Decoding 257 12.2 Quantum Short-block Codes 260 12.3 Quantum Turbo Code Design Using QSBCs 271 12.4 Results and Analysis 274 12.5 Conclusions and Future Research 281

13 EXIT-chart-aided Design of Irregular Multiple-rate Quantum Turbo Block Codes 283 13.1 Introduction 283 13.2 Quantum Short-block Codes 284 13.3 Quantum Turbo Short-block Codes 288 13.4 EXIT-chart Analysis 291 13.5 Multiple-rate Quantum Turbo Short-block Codes 298 13.6 Conclusions 304

14 Quantum Low-density Parity Check Codes 307 14.1 Introduction 307 14.2 Quantum LDPC Code Designs 308 14.3 Iterative Decoding of Quantum LDPC Codes 316 14.4 High-rate QLDPC Codes from Row-circulant Classical LDPCs 323 14.5 Results and Discussions I 326 14.6 Modified Non-binary Decoding 328 14.7 Reweighted BP for Graphs Exhibiting Cycles 335 14.8 Results and Discussions II 336 14.9 Summary and Conclusions 341

15 Summary and Future Research 347 15.1 Summary 347 15.2 Future Research 359

A Construction of Syndrome Former 363 A.1 Convolutional Codes 363 A.2 Turbo Trellis Coded Modulation 365

B Simulation of QLDPC Decoding 367

Glossary 369 References 373 Subject Index 389 Author Index 391.

Notes:

Includes bibliographical references and index.

Electronic reproduction. Hoboken, N.J. Available via World Wide Web.

Description based on online resource; title from digital title page (viewed on March 12, 2026).

Other Format:

Print version:

ISBN:

1394331940

9781394331956

1394331959

9781394331963

1394331967

9781394331949

Publisher Number:

90104286300

CIPO000336889

Access Restriction:

Restricted for use by site license.