The Second Edition of Quantum Information Processing, Quantum Computing, and Quantum Error Correction: An Engineering Approach presents a self-contained introduction to all aspects of the area, teaching the essentials such as state vectors, operators, density operators, measurements, and dynamics of a quantum system. In additional to the fundamental principles of quantum computation, basic quantum gates, basic quantum algorithms, and quantum information processing, this edition has been brought fully up to date, outlining the latest research trends. These include:
Key topics include:
This fully up-to-date new edition will be of use to engineers, computer scientists, optical engineers, physicists and mathematicians.
1. Chapter 1 Introduction - p. 1 2. Chapter 2 Quantum Mechanics Fundamentals - p. 31 3. 2.1: Introduction - p. 32 4. 2.2: Eigenkets as Base Kets - p. 34 5. 2.3: Matrix Representations - p. 36 6. 2.4: Pauli Operators and Hadamard Gate - p. 39 7. 2.5: Density Operators - p. 42 8. 2.6: Quantum Measurements - p. 44 9. 2.7: Uncertainty Principle - p. 48 10. 2.8: Change of Basis - p. 51 11. 2.9: Time Evolution—Schrödinger Equation - p. 56 12. 2.10: Harmonic Oscillator - p. 60 13. 2.11: Angular Momentum - p. 64 14. 2.12: Spin-1/2 Systems - p. 73 15. 2.13: Hydrogen-Like Atoms and Beyond - p. 84 16. 2.14: Summary - p. 89 17. 2.15: Problems - p. 90 18. Chapter 3 Quantum Circuits and Modules - p. 97 19. Chapter 4 Quantum Information Processing Fundamentals - p. 125 20. Chapter 5 Quantum Algorithms and Methods - p. 159 21. Chapter 6 Information Theory and Classical Error Correcting Codes - p. 193 22. 6.1: Classical Information Theory Fundamentals - p. 194 23. 6.2: Channel Coding Preliminaries - p. 207 24. 6.3: Linear Block Codes - p. 209 25. 6.4: Cyclic Codes - p. 222 26. 6.5: Bose–Chaudhuri–Hocquenghem Codes - p. 228 27. 6.6: Reed–Solomon Codes, Concatenated Codes, and Product Codes - p. 238 28. 6.7: Concluding Remarks - p. 242 29. 6.8: Problems - p. 242 30. Chapter 7 Quantum Information Theory Fundamentals - p. 251 31. 7.1: Introductory Remarks - p. 252 32. 7.2: Von Neumann Entropy - p. 252 33. 7.3: Holevo Information, Accessible Information, and Holevo Bound - p. 258 34. 7.4: Data Compression and Schumacher's Noiseless Quantum Coding Theorem - p. 261 35. 7.5: Quantum Channels - p. 270 36. 7.6: Quantum Channel Coding and Holevo–Schumacher–Westmoreland Theorem - p. 273 37. 7.7: Summary - p. 282 38. 7.8: Problems - p. 283 39. Chapter 8 Quantum Error Correction - p. 287 40. 8.1: Pauli Operators (Revisited) - p. 288 41. 8.2: Quantum Error Correction Concepts - p. 292 42. 8.3: Quantum Error Correction - p. 303 43. 8.4: Important Quantum Coding Bounds - p. 316 44. 8.5: Quantum Operations (Superoperators) and Quantum Channel Models - p. 321 45. 8.6: Summary - p. 329 46. 8.7: Problems - p. 330 47. Chapter 9 Quantum Stabilizer Codes and Beyond - p. 337 48. 9.1: Stabilizer Codes - p. 338 49. 9.2: Encoded Operators - p. 343 50. 9.3: Finite Geometry Interpretation - p. 347 51. 9.4: Standard Form of Stabilizer Codes - p. 350 52. 9.5: Efficient Encoding and Decoding - p. 355 53. 9.6: Nonbinary Stabilizer Codes - p. 368 54. 9.7: Subsystem Codes - p. 373 55. 9.8: Topological Codes - p. 381 56. 9.9: Surface Codes - p. 387 57. 9.10: Entanglement-Assisted Quantum Codes - p. 388 58. 9.11: Summary - p. 411 59. 9.12: Problems - p. 411 60. Chapter 10 Quantum LDPC Codes - p. 425 61. Chapter 11 Fault-Tolerant Quantum Error Correction and Fault-Tolerant Quantum Computing - p. 469 62. 11.1: Fault-Tolerance Basics - p. 470 63. 11.2: Fault-Tolerant Quantum Computation Concepts - p. 472 64. 11.3: Fault-Tolerant Quantum Error Correction - p. 477 65. 11.3.1: Fault-Tolerant Syndrome Extraction - p. 479 66. 11.3.2: Fault-Tolerant Encoded Operations - p. 486 67. 11.3.3: Measurement Protocol - p. 492 68. 11.3.4: Fault-Tolerant Stabilizer Codes - p. 496 69. 11.3.5: The [5,1,3] Fault-Tolerant Stabilizer Code - p. 503 70. 11.4: Fault-Tolerant Quantum Computation - p. 506 71. 11.5: Accuracy Threshold Theorem - p. 512 72. 11.6: Surface Codes and Large-Scale Quantum Computing - p. 514 73. 11.7: Summary - p. 524 74. 11.8: Problems - p. 524 75. Chapter 12 Cluster State-based Quantum Computing - p. 531 76. Chapter 13 Physical Implementations of Quantum Information Processing - p. 563 77. 13.1: Physical Implementation Basics - p. 564 78. 13.2: Nuclear Magnetic Resonance in Quantum Computing - p. 566 79. 13.3: Trapped Ions in Quantum Computing - p. 573 80. 13.4: Photonic Quantum Implementations - p. 580 81. 13.5: Photonic Implementation of Quantum Relay - p. 596 82. 13.6: Implementation of Quantum Encoders and Decoders - p. 598 83. 13.7: Cavity Quantum Electrodynamics-Based Quantum Information Processing - p. 604 84. 13.8: Quantum Dots in Quantum Information Processing - p. 610 85. 13.9: Summary - p. 612 86. 13.10: Problems - p. 612 87. Chapter 14 Quantum Machine Learning - p. 619 88. 14.1: Machine Learning Fundamentals - p. 620 89. 14.1.1: Machine Learning Basics - p. 621 90. 14.1.2: Principal Component Analysis - p. 628 91. 14.1.3: Support Vector Machines - p. 633 92. 14.1.4: Clustering - p. 638 93. 14.1.5: Boosting - p. 647 94. 14.1.6: Regression Analysis - p. 649 95. 14.1.7: Neural Networks - p. 651 96. 14.2: The Ising Model, Adiabatic Quantum Computing, and Quantum Annealing - p. 659 97. 14.3: Quantum Approximate Optimization Algorithm and Variational Quantum Eigensolver - p. 663 98. 14.4: Quantum Boosting - p. 669 99. 14.5: Quantum Random Access Memory - p. 671 100. 14.6: Quantum Matrix Inversion - p. 673 101. 14.7: Quantum Principal Component Analysis - p. 675 102. 14.8: Quantum Optimization-Based Clustering - p. 677 103. 14.9: Grover Algorithm-Based Global Quantum Optimization - p. 678 104. 14.10: Quantum K-Means - p. 680 105. 14.11: Quantum Support Vector Machine - p. 684 106. 14.12: Quantum Neural Networks - p. 686 107. 14.13: Summary - p. 693 108. 14.14: Problems - p. 694 109. Chapter 15 Quantum Key Distribution - p. 703 110. 15.1: Cryptography Basics - p. 704 111. 15.2: QKD Basics - p. 706 112. 15.3: No-Cloning Theorem and Distinguishing of Quantum States - p. 708 113. 15.4: Discrete Variable QKD Protocols - p. 709 114. 15.5: QKD Security - p. 717 115. 15.6: The Decoy-State Protocols - p. 722 116. 15.7: Measurement Device-Independent QKD Protocols - p. 725 117. 15.8: Twin-Field QKD Protocols - p. 732 118. 15.9: Information Reconciliation and Privacy Amplification - p. 736 119. 15.10: Quantum Optics and Gaussian Quantum Information Theory - p. 742 120. 15.11: Continuous Variable QKD - p. 754 121. 15.12: Summary - p. 771 122. 15.13: Problems - p. 772 123. Appendix Abstract Algebra Fundamentals - p. 785 124. Index - p. 803
The Second Edition of Quantum Information Processing, Quantum Computing, and Quantum Error Correction: An Engineering Approach presents a self-contained introduction to all aspects of the area, teaching the essentials such as state vectors, operators, density operators, measurements, and dynamics of a quantum system. In additional to the fundamental principles of quantum computation, basic quantum gates, basic quantum algorithms, and quantum information processing, this edition has been brought fully up to date, outlining the latest research trends. These include:
Key topics include:
This fully up-to-date new edition will be of use to engineers, computer scientists, optical engineers, physicists and mathematicians.
1. Chapter 1 Introduction - p. 1 2. Chapter 2 Quantum Mechanics Fundamentals - p. 31 3. 2.1: Introduction - p. 32 4. 2.2: Eigenkets as Base Kets - p. 34 5. 2.3: Matrix Representations - p. 36 6. 2.4: Pauli Operators and Hadamard Gate - p. 39 7. 2.5: Density Operators - p. 42 8. 2.6: Quantum Measurements - p. 44 9. 2.7: Uncertainty Principle - p. 48 10. 2.8: Change of Basis - p. 51 11. 2.9: Time Evolution—Schrödinger Equation - p. 56 12. 2.10: Harmonic Oscillator - p. 60 13. 2.11: Angular Momentum - p. 64 14. 2.12: Spin-1/2 Systems - p. 73 15. 2.13: Hydrogen-Like Atoms and Beyond - p. 84 16. 2.14: Summary - p. 89 17. 2.15: Problems - p. 90 18. Chapter 3 Quantum Circuits and Modules - p. 97 19. Chapter 4 Quantum Information Processing Fundamentals - p. 125 20. Chapter 5 Quantum Algorithms and Methods - p. 159 21. Chapter 6 Information Theory and Classical Error Correcting Codes - p. 193 22. 6.1: Classical Information Theory Fundamentals - p. 194 23. 6.2: Channel Coding Preliminaries - p. 207 24. 6.3: Linear Block Codes - p. 209 25. 6.4: Cyclic Codes - p. 222 26. 6.5: Bose–Chaudhuri–Hocquenghem Codes - p. 228 27. 6.6: Reed–Solomon Codes, Concatenated Codes, and Product Codes - p. 238 28. 6.7: Concluding Remarks - p. 242 29. 6.8: Problems - p. 242 30. Chapter 7 Quantum Information Theory Fundamentals - p. 251 31. 7.1: Introductory Remarks - p. 252 32. 7.2: Von Neumann Entropy - p. 252 33. 7.3: Holevo Information, Accessible Information, and Holevo Bound - p. 258 34. 7.4: Data Compression and Schumacher's Noiseless Quantum Coding Theorem - p. 261 35. 7.5: Quantum Channels - p. 270 36. 7.6: Quantum Channel Coding and Holevo–Schumacher–Westmoreland Theorem - p. 273 37. 7.7: Summary - p. 282 38. 7.8: Problems - p. 283 39. Chapter 8 Quantum Error Correction - p. 287 40. 8.1: Pauli Operators (Revisited) - p. 288 41. 8.2: Quantum Error Correction Concepts - p. 292 42. 8.3: Quantum Error Correction - p. 303 43. 8.4: Important Quantum Coding Bounds - p. 316 44. 8.5: Quantum Operations (Superoperators) and Quantum Channel Models - p. 321 45. 8.6: Summary - p. 329 46. 8.7: Problems - p. 330 47. Chapter 9 Quantum Stabilizer Codes and Beyond - p. 337 48. 9.1: Stabilizer Codes - p. 338 49. 9.2: Encoded Operators - p. 343 50. 9.3: Finite Geometry Interpretation - p. 347 51. 9.4: Standard Form of Stabilizer Codes - p. 350 52. 9.5: Efficient Encoding and Decoding - p. 355 53. 9.6: Nonbinary Stabilizer Codes - p. 368 54. 9.7: Subsystem Codes - p. 373 55. 9.8: Topological Codes - p. 381 56. 9.9: Surface Codes - p. 387 57. 9.10: Entanglement-Assisted Quantum Codes - p. 388 58. 9.11: Summary - p. 411 59. 9.12: Problems - p. 411 60. Chapter 10 Quantum LDPC Codes - p. 425 61. Chapter 11 Fault-Tolerant Quantum Error Correction and Fault-Tolerant Quantum Computing - p. 469 62. 11.1: Fault-Tolerance Basics - p. 470 63. 11.2: Fault-Tolerant Quantum Computation Concepts - p. 472 64. 11.3: Fault-Tolerant Quantum Error Correction - p. 477 65. 11.3.1: Fault-Tolerant Syndrome Extraction - p. 479 66. 11.3.2: Fault-Tolerant Encoded Operations - p. 486 67. 11.3.3: Measurement Protocol - p. 492 68. 11.3.4: Fault-Tolerant Stabilizer Codes - p. 496 69. 11.3.5: The [5,1,3] Fault-Tolerant Stabilizer Code - p. 503 70. 11.4: Fault-Tolerant Quantum Computation - p. 506 71. 11.5: Accuracy Threshold Theorem - p. 512 72. 11.6: Surface Codes and Large-Scale Quantum Computing - p. 514 73. 11.7: Summary - p. 524 74. 11.8: Problems - p. 524 75. Chapter 12 Cluster State-based Quantum Computing - p. 531 76. Chapter 13 Physical Implementations of Quantum Information Processing - p. 563 77. 13.1: Physical Implementation Basics - p. 564 78. 13.2: Nuclear Magnetic Resonance in Quantum Computing - p. 566 79. 13.3: Trapped Ions in Quantum Computing - p. 573 80. 13.4: Photonic Quantum Implementations - p. 580 81. 13.5: Photonic Implementation of Quantum Relay - p. 596 82. 13.6: Implementation of Quantum Encoders and Decoders - p. 598 83. 13.7: Cavity Quantum Electrodynamics-Based Quantum Information Processing - p. 604 84. 13.8: Quantum Dots in Quantum Information Processing - p. 610 85. 13.9: Summary - p. 612 86. 13.10: Problems - p. 612 87. Chapter 14 Quantum Machine Learning - p. 619 88. 14.1: Machine Learning Fundamentals - p. 620 89. 14.1.1: Machine Learning Basics - p. 621 90. 14.1.2: Principal Component Analysis - p. 628 91. 14.1.3: Support Vector Machines - p. 633 92. 14.1.4: Clustering - p. 638 93. 14.1.5: Boosting - p. 647 94. 14.1.6: Regression Analysis - p. 649 95. 14.1.7: Neural Networks - p. 651 96. 14.2: The Ising Model, Adiabatic Quantum Computing, and Quantum Annealing - p. 659 97. 14.3: Quantum Approximate Optimization Algorithm and Variational Quantum Eigensolver - p. 663 98. 14.4: Quantum Boosting - p. 669 99. 14.5: Quantum Random Access Memory - p. 671 100. 14.6: Quantum Matrix Inversion - p. 673 101. 14.7: Quantum Principal Component Analysis - p. 675 102. 14.8: Quantum Optimization-Based Clustering - p. 677 103. 14.9: Grover Algorithm-Based Global Quantum Optimization - p. 678 104. 14.10: Quantum K-Means - p. 680 105. 14.11: Quantum Support Vector Machine - p. 684 106. 14.12: Quantum Neural Networks - p. 686 107. 14.13: Summary - p. 693 108. 14.14: Problems - p. 694 109. Chapter 15 Quantum Key Distribution - p. 703 110. 15.1: Cryptography Basics - p. 704 111. 15.2: QKD Basics - p. 706 112. 15.3: No-Cloning Theorem and Distinguishing of Quantum States - p. 708 113. 15.4: Discrete Variable QKD Protocols - p. 709 114. 15.5: QKD Security - p. 717 115. 15.6: The Decoy-State Protocols - p. 722 116. 15.7: Measurement Device-Independent QKD Protocols - p. 725 117. 15.8: Twin-Field QKD Protocols - p. 732 118. 15.9: Information Reconciliation and Privacy Amplification - p. 736 119. 15.10: Quantum Optics and Gaussian Quantum Information Theory - p. 742 120. 15.11: Continuous Variable QKD - p. 754 121. 15.12: Summary - p. 771 122. 15.13: Problems - p. 772 123. Appendix Abstract Algebra Fundamentals - p. 785 124. Index - p. 803
