English | MP4 | AVC 1280×720 | AAC 44KHz 2ch | 284 lectures (11h 53m) | 4.03 GB

Math-Based Introduction to Quantum Computing, Cryptography & Quantum Machine Learning. Code with Python, Q#, & Qiskit

Quantum Computing is the next wave of the software industry. Quantum computers are exponentially faster than classical computers of today. Problems that were considered too difficult for computers to solve, such as simulation of protein folding in biological systems, and cracking RSA encryption, are now possible through quantum computers.

How fast are Quantum Computers? A 64-bit quantum computer can process 36 billion billion bytes of information in each step of computation. Compare that to the 8 bytes that your home computer can process in each step of computation!

Companies like Google, Intel, IBM, and Microsoft are investing billions in their quest to build quantum computers. If you master quantum computing now, you will be ready to profit from this technology revolution.

This course teaches quantum computing from the ground up. The only background you need is 12th grade level high-school Math and Physics.

IMPORTANT: You must enjoy Physics and Math to get the most out of this course. This course is primarily about analyzing the behavior of quantum circuits using Math and Quantum Physics. While everything you need to know beyond 12th grade high school science is explained here, you must be aware that Quantum Physics is an extremely difficult subject. You might frequently need to stop the video and replay the lesson to understand it.

QUANTUM MACHINE LEARNING

It appears that the killer-app for quantum computing will be machine learning and artificial intelligence.

Quantum machine learning algorithms provide a significant speed-up in training. This speed-up can result in more accurate predictions.

While understanding quantum algorithms requires mastery of complex math, using quantum machine learning is relatively simple. Qiskit encapsulates machine learning algorithms inside an API that mimics the popular Scikit-Learn machine-learning toolkit. So you can use quantum machine learning almost as easily as you would traditional ML!

Quantum machine learning can be applied in the back-end to train models, and those trained models can be used in consumer gadgets. This means that quantum machine learning might enhance your everyday life even if quantum computers remain expensive!

COURSE OUTLINE

We begin by learning about basic math. You might have forgotten the math you learned in high-school. I will review linear algebra, probability, Boolean algebra, and complex numbers.

Quantum physics is usually considered unapproachable because it deals with the behavior of extremely tiny particles. But in this course, I will explain quantum physics through the behavior of polarized light. Light is an everyday phenomenon and you will be able to understand it easily.

Next we learn about quantum cryptography. Quantum cryptography is provably unbreakable. I will explain the BB84 quantum protocol for secure key sharing.

Then we will learn about the building-blocks of quantum programs which are quantum gates.

To understand how quantum gates work, we will study quantum superposition and quantum entanglement in depth.

We will apply what we have learned by constructing quantum circuits using Microsoft Q# (QSharp) and IBM Qiskit. For those of you who don’t know the Python programming language, I will provide a crisp introduction of what you need to know.

We will begin with simple circuits and then progress to a full implementation of the BB84 quantum cryptography protocol in Qiskit.

We will learn how to use Qiskit’s implementation of Shor’s algorithm for factoring large numbers.

The killer-app for quantum computing is quantum machine learning.

To understand quantum machine learning, we must first learn how classical machine learning works. I provide a crisp introduction to classical machine learning and neural networks (deep learning).

Finally, we will train a Quantum Support Vector Machine on real-world data and use it to make predictions.

What you’ll learn

- Use quantum cryptography to communicate securely
- Develop, simulate, and debug quantum programs on IBM Qiskit and Microsoft Q#
- Run quantum programs on a real quantum computer through IBM Quantum Experience
- Use Dirac’s notation and quantum physics models to analyze quantum circuits
- Train a Quantum Support Vector Machine (Quantum Machine Learning) on real-world data and use it to make predictions
- Learn Data science and how quantum computing can help in artificial intelligence / machine learning
- Learn why machine learning will be the killer-app for quantum computing

## Table of Contents

**Introduction**

1 Introduction

2 How is Quantum Computing Different

**Quantum Physics Through Photon Polarization**

3 Introduction to Quantum Physics

4 Quantum Physics Through Photon Polarization 1

5 Quantum Physics Through Photon Polarization 2

6 Quantum Physics Through Photon Polarization 3

7 Quantum Physics Through Photon Polarization 4

8 Quantum Physics Through Photon Polarization 5

9 Quantum Physics Through Photon Polarization 6

10 Quantum Physics Through Photon Polarization 7

11 Quantum Physics Through Photon Polarization 8

12 Quantum Physics Through Photon Polarization 9

13 Quantum Physics Through Photon Polarization 10

14 Quantum Physics Through Photon Polarization 11

15 Quantum Physics Through Photon Polarization 12

16 Quantum Physics Through Photon Polarization 13

17 Quantum Physics Through Photon Polarization 14

**Math Foundation Complex Numbers Probability Linear Algebra & Logic**

18 Quantum Computing Through Math

19 Boolean Algebra

20 Boolean Variables and Operators

21 Truth Tables

22 Logic Gates

23 Logic Circuits

24 AND Gate

25 OR Gate

26 NOT Gate

27 Multiple Input Gates

28 Equivalent Circuits 1

29 Equivalent Circuits 2

30 Universal Gate NAND

31 Exclusive OR

32 XOR for Assignment

33 XOR of Bit Sequences 1

34 XOR of Bit Sequences 2

35 Introduction to Cryptography

36 Cryptography with XOR

37 Shared Secret

38 Importance of Randomness

39 Breaking the Code

40 Introduction to Probability

41 Probability of a Boolean Expression

42 Mutually Exclusive Events

43 Independent Events

44 Manipulating Probabilities With Algebra

45 P Mutually Exclusive Events

46 P Independent Events

47 Complete Set of MutEx Events

48 P A OR B

49 Examples

50 Examples

51 P Bit Values

52 Analysis With Venn Diagrams

53 Venn Diagram P A AND B

54 Venn Diagram P A OR B

55 Venn Diagram P NOT A

56 Examples

57 Examples

58 Conditional Probability

59 Examples

60 Introduction to Statistics

61 Random Variables

62 Mapping Random Variables

63 Mean Average Expected Value

64 Example

65 Example

66 Beyond Mean

67 Standard Deviation

68 Examples

69 Combinations of Random Variables

70 Correlation

71 Analysis of Correlation

72 Introduction to Complex Numbers

73 Imaginary i

74 Addition

75 Subtraction

76 Multiplication by a Real

77 Division by a Real

78 Complex Multiplication

79 Examples

80 Complex Conjugates

81 Squared Magnitude

82 Complex Division

83 Examples

84 Eulers Formula

85 Polar Form

86 Examples

87 Fractional Powers

88 Complex Cube Roots of 1

89 Square Root of i

90 D Coordinates

91 Matrices

92 Matrix Dimensions

93 Matrix Addition

94 Matrix Subtraction

95 Scalar Multiplication

96 Matrix Multiplication

97 Examples

98 Examples

99 x3 Example

100 Exercises

101 More Multiplications

102 When is Multiplication Possible

103 Example

104 Not Commutative

105 Associative and Distributive

106 Dimension of Result

107 Odd Shaped Matrices

108 Examples

109 Outer Product

110 Exercise

111 Inner Product

112 Exercises

113 Identity Matrix

114 Matrix Inverse

115 Transpose

116 Transpose Examples

117 Transpose of Product

118 Complex Conjugate of Matrices

119 Adjoint

120 Unitary

121 Hermitian

122 Hermitian and Unitary

123 Why Hermitian or Unitary

124 Vectors and Transformations

125 Rotation in 2D

126 Special Directions

127 Eigen Vectors and Eigen Values

128 More Eigen Vectors

129 Computing Eigen Values

**Quantum Cryptography**

130 Photons

131 Photon Polarization

132 Experiments with Photon Polarization

133 NoCloning Theorem

134 Encoding with XOR

135 Encryption with SingleUse SharedSecrets

136 Encoding Data in Photon Polarization

137 Making the Protocol Secure

138 Exchanging Polarization Angles

139 Why is the BB84 protocol secure

140 Analysis

**Developing a Math Model for Quantum Physics**

141 Modeling Physics with Math

142 Subtractive Probabilities Through Complex Numbers

143 Modeling Superposition Through Matrices

144 Overview of Math Model

**Quantum Physics of Spin States**

145 Introduction to Spin States

146 Basis

147 Column Matrix Representation of Quantum State

148 State Vector

149 Experiments with Spin 1

150 Experiments with Spin 2

151 Experiments with Spin 3

**Modeling Quantum Spin States with Math**

152 Analysis of Experiments 1

153 Analysis of Experiments 2

154 Analysis of Experiments 3

155 Dirac BraKet Notation 1

156 Dirac BraKet Notation 2

157 More Experiment Analysis 1

158 More Experiment Analysis 2

159 On Random Behavior

**Reversible and Irreversible State Transformations**

160 Irreversible Transformations Measurement

161 Reversible State Transformations

**MultiQubit Systems**

162 Analyzing MultiQubit Systems

**Entanglement**

163 Entanglement

**Understanding Superposition and Entanglement With Quantum Simulators**

164 Download the Simulator Code

165 Installing Java and Running the Simulators

166 Launching the Superposition Simulator

167 Classical Photon

168 Quantum Photon

169 No Cloning

170 No Cloning

171 Measurement is Irreversible

172 Deterministic vs Probabilistic

173 Running the Simulator

174 Superposition 1

175 Superposition 2

176 Measurement and Superposition

177 Two Photon Systems

178 Entanglement

179 Simulating Entanglement 1

180 Simulating Entanglement 2

181 Simulating Entanglement 3

182 Simulating Entanglement 4

183 Independent Photons

184 Effect of Measurement

185 Summary

**Quantum Computing Model**

186 Quantum Circuits

187 Fanout

188 Uncomputing

189 Reversible Gates

190 Quantum NOT

191 Other Single Qubit Gates

192 CNOT Gate

193 CCNOT Toffoli Gate

194 Universal Gate

195 Fredkin Gate

196 Effects of Superposition and Entanglement on Quantum Gates

**Quantum Programming with Microsoft Q**

197 Q Qiskit or Cirq

198 Installing Q

199 Reminder

200 Q Simulation Architecture

201 Q Controller

202 Q Execution Model

203 Measuring Superposition States

204 Overview of 4Qubit Simulation Framework

205 Set Operation

206 Iterative Measurement

207 Verifying Output after Initialization 1

208 Verifying Output after Initialization 2

209 NOT Operation

210 Superposition

211 SWAP

212 CNOT

213 Significance of Superposition and Entanglement

214 Effect of Superposition on Quantum Gates

215 Toffoli Gate General Configuration

216 Verifying Results

217 Toffoli Configured as NOT

218 Toffoli Configured as AND

219 Toffoli Configured as Fanout

**IBM Quantum Experience**

220 IBM Quantum Note

221 IBM Quantum Experience

**Quantum Programming and Algorithms With IBM Qiskit**

222 Qiskit Code Resources

223 What is Qiskit

224 Installing Python and Qiskit

225 Interactive Python

226 Jupyter Notebooks

227 Spyder Python IDE

228 Variables and Assignment

229 Data Types

230 Operators

231 Type Conversion

232 Strings

233 Lists

234 Dictionaries

235 Loops

236 Decisions

237 Functions

238 Object Oriented Programming

239 Exceptions

240 Modules

241 Quantum Circuits 1

242 Quantum Circuits 2

243 Quantum Circuits 3

244 Quantum Circuits 4

245 Quantum Circuits 5

246 Running a Circuit

247 Circuit Matrix

248 Implementing BB84 Cryptography

249 Shors Algorithm

**Machine Learning Foundation**

250 Introduction to Machine Learning

251 What is AI

252 Structure of ML Systems

253 Learning With Models

254 Speed Up Learning

255 Underfit & Overfit

256 Classification

257 Sigmoid Models

258 Regularization 1

259 Regularization 2

260 Machine Learning Libraries

261 Machine Learning Coding

262 MultiLayer Network 1

263 MultiLayer Network 2

264 Convolution 1

265 Convolution 2

266 Convolution 3

267 Recurrent

**Quantum Machine Learning With Qiskit**

268 Quantum Machine Learning with KNN

269 KNN Problem Description

270 Code for Classical KNN

271 Code for Quantum KNN

272 Math for Classical KNN

273 Math Prerequisites for Quantum KNN

274 Math for Quantum KNN

275 Connecting Math and Code for Classical KNN

276 Connecting Math and Code for Quantum KNN

277 Introduction to Classification

278 Support Vector Machines Separation

279 Support Vector Machines Overfitting

280 Support Vector Machines Soft Margins

281 Support Vector Machines Higher Dimensions and Kernels

282 Support Vector Machines Multiple Classes

283 Quantum Support Vector Machines

284 Significance of Quantum Machine Learning

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