Quantum Computing for the Quantum Curious
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Acknowledgments Contents Course Description About Prerequisites Fundamental Intermediate Advanced Learning Objectives Alternative Pathways 1 Introduction to Superposition 1.1 Classical Superposition 1.2 Quantum Superposition 1.3 Big Ideas 1.4 Activities 1.5 Check Your Understanding 2 What Is a Qubit? 2.1 Mathematical Representation of Qubits 2.1.1 Dirac Bra-Ket Notation 2.1.2 Examples 2.2 Matrix Representation 2.2.1 Examples 2.3 Bloch Sphere 2.4 Physical Realization of Qubits 2.5 Big Ideas 2.6 Check Your Understanding 3 Creating Superposition: The Beam Splitter 3.1 Beam Splitter 3.2 Mach–Zehnder Interferometer 3.2.1 Particle Explanation 3.3 Big Ideas 3.4 Check Your Understanding 4 Creating Superposition: Stern–Gerlach 4.1 Stern–Gerlach Apparatus 4.2 Measurement Basis 4.3 Geometric Representation of a Basis 4.4 Effect of Measurement 4.5 Big Ideas 4.6 Activities 4.7 Check Your Understanding 5 Quantum Cryptography 5.1 Cryptography Fundamentals 5.2 Classical Cryptography 5.3 BB84 Quantum Key Distribution 5.3.1 Before Sending the Message 5.3.2 Quantum Part 5.3.3 Example 5.3.4 Classical Post-processing 5.4 Detecting an Eavesdropper 5.4.1 Example 5.5 Big Ideas 5.6 Activities 5.7 Check Your Understanding 6 Quantum Gates 6.1 Single Qubit Gates 6.2 X (Also Called NOT) Gate 6.3 Hadamard Gate 6.4 Mathematics of the Hadamard Gate 6.4.1 Examples 6.5 Z Gate 6.6 Big Ideas 6.7 Activities 6.8 Check Your Understanding 7 Entanglement 7.1 Entanglement Fundamentals 7.2 Hidden Variable Theory 7.3 Multi-Qubit States 7.3.1 Example 7.4 Non-Entangled Systems 7.4.1 Example 7.5 Entangled Systems 7.5.1 Example 7.5.2 Example 7.6 Entangling Particles 7.7 CNOT Gate 7.8 Notation Convention 7.9 Examples 7.10 Big Ideas 7.11 Activities 7.12 Check Your Understanding 8 Quantum Teleportation 8.1 Scanning a Qubit 8.2 Teleportation Protocol 8.3 Big Ideas 8.4 Check Your Understanding 9 Quantum Algorithms 9.1 The Power of Quantum Computing 9.2 Limitations 9.3 Deutsch-Jozsa Algorithm 9.3.1 The Problem Statement 9.3.2 Conceptual Understanding 9.3.3 Quantum Algorithm 9.4 Quantum Computers Today 9.5 Big Ideas 9.6 Activities 9.7 Check Your Understanding 10 Worksheets 10.1 Correlation in Entangled States Lab 10.2 Polarizer Demo 10.3 Quantum Tic-Tac-Toe 10.3.1 The Rules 10.3.2 Connection to Quantum Physics 10.4 Schrödinger's Worm Using Five Qubits 10.5 Superposition vs. Mixed States Lab 10.6 Measurement Basis Lab 10.7 One-Time Pad 10.7.1 One-Time Pad: Alice 10.7.2 One-Time Pad (Bob) 10.8 BB84 Quantum Key Distribution 10.8.1 BB84 Quantum Key Distribution: Alice 10.8.2 BB84 Quantum Key Distribution: Bob 10.8.3 BB84 Quantum Key Distribution: Eve A Probability A.1 Introduction A.2 Combining Probabilities A.2.1 Key Words Review A.2.2 Key Ideas Review A.2.3 Check Your Understanding A.3 Histograms A.4 Mean, Median, and Mode A.4.1 Key Word Review A.4.2 Check Your Understanding A.5 Variance and Standard Deviation A.5.1 Key Word Review A.5.2 Check Your Understanding B Linear Algebra B.1 Introduction B.2 Scalars, Vectors, and Matrices B.2.1 Scalars B.2.2 Vectors Operations with Vectors B.2.3 Matrices Addition and Subtraction of Matrices Multiplication with Matrices Transposition B.3 Key Word Review B.4 Check Your Understanding Answers to Odds Answers to Odds Chapter 1 Solutions Chapter 2 Solutions Chapter 3 Solutions Chapter 4 Solutions Chapter 5 Solutions Chapter 6 Solutions Chapter 7 Solutions Chapter 8 Solutions Chapter 9 Solutions Chapter 10 Solutions 10.1 10.4 10.5 10.6 Appendix A Solutions A.2 A.4 A.5 Appendix B Solutions Index
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