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Introduction to Classical and Quantum Computing

Last updated Aug 10, 2022

# Introduction to Classical and Quantum Computing

Metadata

  • CiteKey:: wongIntroductionClassicalQuantum
  • Type:: book
  • Author:: Thomas Wong
  • Year:: 2022
  • Tags:: #Source/Zotero, #Source/Book
  • Format:: PDF
  • Rating:: 10

Abstract

I wrote a FREE introductory quantum computing textbook! The only prerequisite is trigonometry. It is not a conceptual overview, however. Rather, it teaches the math (including basic linear algebra) along the way.The textbook is based on an introductory quantum computing course that I’ve been teaching at Creighton University since 2018. From the beginning, I wrote all my lecture notes and homework problems in a textbook format using LaTeX, and now they’re available to everyone.

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Tags and Collections

  • Keywords:: Book; Quantum Computing; 📥

Table of contents

  1. Chapter 1 - Classical Information and Computation
  2. Bits
  3. Coins
  4. Dice
  5. Encoding Information
  6. Physical Bits
  7. Binary
  8. ASCII
  9. Logic Gates
  10. Single-Bit Gates
  11. Two-Bit Gates
  12. Logic Gates as Physical Circuits
  13. Universal Gates
  14. Adders and Verilog
  15. Adding Binary Numbers by Hand
  16. Half Adder
  17. Full Adder
  18. Ripple-Carry Adder
  19. Ripple-Carry with Full Adders
  20. Circuit Complexity
  21. Circuit Simplification and Boolean Algebra
  22. Order of Operations
  23. Association, Commutivity, and Distribution
  24. Identities Involving Zero and One
  25. Single-Variable Identities
  26. Two-Variable Identities and De Morgan’s Laws
  27. Circuit Simplification
  28. Reversible Logic Gates
  29. Reversible Gates
  30. Irreversible Gates
  31. Toffoli Gate: A Reversible AND Gate
  32. Making Irreversible Gates Reversible
  33. Error Correction
  34. Errors in Physical Devices
  35. Error Detection
  36. Error Correction
  37. Computational Complexity
  38. Asymptotic Notation
  39. Complexity Classes
  40. Turing Machines
  41. Components
  42. Incrementing Binary Numbers
  43. Church-Turing Thesis
  44. Summary
  45. Chapter 2 - One Quantum Bit
  46. Qubit Touchdown: A Quantum Computing Board Game
  47. Superposition
  48. Zero or One
  49. Superposition
  50. Review of Complex Numbers
  51. Measurement
  52. Measurement in the Z-Basis
  53. Normalization
  54. Measurement in Other Bases
  55. Consecutive Measurements
  56. Bloch Sphere Mapping
  57. Global and Relative Phases
  58. Bloch Sphere
  59. Physical Qubits
  60. Quantum Gates
  61. Linear Maps
  62. Classical Reversible Gates
  63. Common One-Qubit Quantum Gates
  64. General One-Qubit Gates
  65. Quantum Circuits
  66. Summary
  67. Chapter 3 - Linear Algebra
  68. Quantum States
  69. Column Vectors
  70. Row Vectors
  71. Inner Products
  72. Inner Products Are Scalars
  73. Orthonormality
  74. Projection, Measurement, and Change of Basis
  75. Quantum Gates
  76. Gates as Matrices
  77. Common One-Qubit Gates as Matrices
  78. Sequential Quantum Gates
  79. Circuit Identities
  80. Unitarity
  81. Reversibility
  82. Outer Products
  83. Outer Products Are Matrices
  84. Completeness Relation
  85. Summary
  86. Chapter 4 - Multiple Quantum Bits
  87. Entanglion: A Quantum Computing Board Game
  88. Mechanics
  89. Connection to Quantum Computing
  90. States and Measurement
  91. Tensor Product
  92. Kronecker Product
  93. Measuring Individual Qubits
  94. Sequential Single-Qubit Measurements
  95. Entanglement
  96. Product States
  97. Entangled States
  98. Quantum Gates
  99. One-Qubit Quantum Gates
  100. Two-Qubit Quantum Gates
  101. Toffoli Gate
  102. No-Cloning Theorem
  103. Quantum Adders
  104. Classical Adder
  105. Making the Classical Adder a Quantum Gate
  106. Quantum Setup
  107. Quantum Sum
  108. Quantum Carry
  109. Quantum Ripple-Carry Adder
  110. Circuit Complexity
  111. Adding in Superposition
  112. Universal Quantum Gates
  113. Definition
  114. Components of a Universal Gate Set
  115. Examples of Universal Gate Sets
  116. Solovay-Kitaev Theorem
  117. Quantum Computing without Complex Numbers
  118. Quantum Error Correction
  119. Decoherence
  120. Bit-Flip Code
  121. Phase-Flip Code
  122. Shor Code
  123. Summary
  124. Chapter 5 - Quantum Programming
  125. IBM Quantum Experience
  126. Services
  127. Circuit Composer
  128. Quantum Processor
  129. Simulator
  130. Quantum Assembly Language
  131. OpenQASM
  132. Quantum Experience Standard Header
  133. OpenQASM in IBM Quantum Experience
  134. Quantum Adder
  135. Qiskit
  136. Circuit Composer
  137. Quantum Lab
  138. Simulator
  139. Quantum Processor
  140. Other Quantum Programming Languages
  141. Summary
  142. Chapter 6 - Entanglement and Quantum Protocols
  143. Measurements
  144. Product States
  145. Maximally Entangled States
  146. Partially Entangled States
  147. Bell Inequalities
  148. EPR Paradox and Local Hidden Variables
  149. Bell Inequalities and the CHSH Inequality
  150. Quantum Processor Experiment
  151. Other Experiments
  152. No-Signaling Principle
  153. Other Theories
  154. Monogamy of Entanglement
  155. Classical Correlations
  156. Quantum Entanglement
  157. Superdense Coding
  158. The Problem
  159. Classical Solution
  160. Quantum Solution
  161. Quantum Teleportation
  162. The Problem
  163. Classical Solution
  164. Quantum Solution
  165. Quantum Key Distribution
  166. Encryption
  167. Classical Solution: Public Key Cryptography
  168. Quantum Solution: BB84
  169. Summary
  170. Chapter 7 - Quantum Algorithms
  171. Circuit vs Query Complexity
  172. Circuit Complexity
  173. Query Complexity
  174. Quantum Oracles
  175. Phase Oracle
  176. Parity
  177. The Problem
  178. Classical Solution
  179. Quantum Solution: Deutsch’s Algorithm
  180. Generalization to Additional Bits
  181. Constant vs Balanced Functions
  182. The Problem
  183. Classical Solution
  184. Quantum Solution: Deutsch-Jozsa Algorithm
  185. Secret Dot Product String
  186. The Problem
  187. Classical Solution
  188. Quantum Solution: Bernstein-Vazirani Algorithm
  189. Recursive Problem
  190. Secret XOR Mask
  191. The Problem
  192. Classical Solution
  193. Quantum Solution: Simon’s Algorithm
  194. Summary
  195. Brute-Force Searching
  196. The Problem
  197. Classical Solution
  198. Quantum Solution: Grover’s Algorithm
  199. Reflection About Uniform State
  200. Optimality
  201. Discrete Fourier Transform
  202. Application: Analyzing Music
  203. Classical Solution: Fast Fourier Transform
  204. Quantum Solution: Quantum Fourier Transform
  205. Inverse Quantum Fourier Transform
  206. Eigenvalue Estimation
  207. The Problem
  208. Classical Solution
  209. Quantum Solution
  210. Multiple Eigenstates
  211. Period of Modular Exponentiation
  212. The Problem
  213. Classical Solution
  214. Quantum Solution
  215. Factoring
  216. The Problem
  217. Classical Solution
  218. Quantum Solution: Shor’s Algorithm
  219. Summary
  220. Chapter 8 - Next Steps
  221. Careers in Quantum Computing
  222. Technical Next Steps
  223. Questions
  224. Parting Words
    Answers to Exercises
    Index

# Notes

# By Chapters

  1. Chapter 1 - Classical Information and Computation
  2. Chapter 2 - One Quantum Bit
  3. Chapter 3 - Linear Algebra
  4. Chapter 4 - Multiple Quantum Bits
  5. Chapter 5 - Quantum Programming
  6. Chapter 6 - Entanglement and Quantum Protocols
  7. Chapter 7 - Quantum Algorithms
  8. Chapter 8 - Next Steps