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 MachโZehnder Interferometer
3.2.1 Particle Explanation
3.3 Big Ideas
3.4 Check Your Understanding
4 Creating Superposition: SternโGerlach
4.1 SternโGerlach 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 Schrรถdinger'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