Quantum Minds in Machine Learning

Chapter 1

Rise of the Quantum Machines: Fundamentals 1 The Essentials of Quantum Computing 2 The Qubit 5 State of a Qubit 5 The Bloch Sphere 6 Observables and Operators 8 The Hilbert Space 8 Measurements 9 Superposition 11 Entanglement 14 Quantum Operators and Gates 15 Identity Operators 16 Unitary Operators 16 The Pauli Group of Matrices and Gates 17 Phase Gates 18 Cartesian Rotation Gates 19 Hadamard Gate 19 CNOT Gate 20 SWAP Gate 21 Density Operator 22 Hamiltonian 22 Time Evolution of a System 23 No-Cloning Theorem 23 Fidelity 24 Complexity 25 Grover's Algorithm 25 Shor's Algorithm 28 Heisenberg's Uncertainty Principle 29 Learning from Data: AI, ML, and Deep Learning 30 Quantum Machine Learning 32 Setting up the Software Environment 33 Option 1: Native Python 36 Option 2: Anaconda Python 36 Installing the Required Packages and Libraries 37 Quantum Computing Cloud Access 38

Chapter 2

Machine Learning 41 Algorithms and Models 44 Bias 46 Variance 47 Overfitting of Data 52 Underfitting of Data 54 Ideal Fit of Data 54 Model Accuracy and Quality 57 Bayesian Learning 58 Applied ML Workflow 59 Validation of Models 61 The Hold-Out Method 61 The Cross-Validation Method 63 Linear Regression 68 Complexity 76 Supervised Learning 79 Unsupervised Learning 93 k-Means Clustering 96 Reinforcement Learning 97

Chapter 3

Neural Networks 99 Perceptron 100 Activation Functions 104 Hidden Layers 108 Backpropagation 109 Hands-on Lab: NN with TensorFlow Playground 109 Neural Network Architecture 115 Convolutional Neural Network (CNN) 116 Feedforward Neural Network 118 Hands-on Lab 1 120 Hands-on Lab 2 128

Chapter 4

Quantum Information Science 141 Quantum Information 143 Quantum Circuits and Bloch Sphere 145 Entropy: Classical vs. Quantum 165 Shannon Entropy 165 Von Neumann Entropy 169 Evolution of States 171 No-Cloning Theorem Revisited 180 Quantum Teleportation 181 Gate Scheduling 188 Quantum Parallelism and Function Evaluation 190 Deutsch's Algorithm 193 Deutsch's Algorithm with Cirq 196 Quantum Computing Systems 198

Chapter 5

QML Algorithms I 205 Quantum Complexity 209 Quantum Feature Maps 214 Quantum Embedding 215 Information Encoding 216 Basis Encoding 218 Amplitude Encoding 221 Tensor