Introduction to Classical and Quantum Computing

Last updated Aug 10, 2022

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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.

Files and Links

• Url:: http://www.thomaswong.net/introduction-to-classical-and-quantum-computing.pdf
• Uri:: http://zotero.org/users/5055703/items/SQNYM3PY
• File:: wong_introduction_to_classical_and_quantum_computing.pdf
• Local Library:: Zotero

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

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