Mastering Quantum Computing: A Comprehensive Guide to Learn Quantum Computing

Table of contents :
1. Preface
1.1 How to Use This Book
1.2 Required Background
2. Introduction to Quantum Computing
2.1 Historical Overview
2.2 Classical vs. Quantum Computing
2.3 Key Principles of Quantum Computing
2.4 Quantum Advantage
3. Quantum Mechanics for Computing
3.1 Quantum States
3.2 Superposition
3.3 Quantum Entanglement
4. Mathematical Foundations
4.1 Linear Algebra
4.2 Probability Theory
4.3: Complex Numbers
5. Introduction to Quantum Bits (Qubits)
5.1. State Vectors
5.2 Bloch Sphere Representation
6. Quantum Gates and Circuits
6.1 Pauli Gates: The Fundamental Building Blocks in Quantum Computing
6.2 Universal Quantum Gates
6.3 Quantum Circuit Model
7. Quantum Algorithms: Basics
7.1 Quantum Parallelism: A Revolution in Computational Efficiency
7.2 Grover's Algorithm: Revolutionizing Unstructured Search Problems
7.3 Quantum Fourier Transform: A Deep Dive
8. Quantum Search Algorithms
8.1 Variations of Grover's Algorithm
8.2 Quantum Walks: The Quantum Analogue of Classical Random Walks and Their Impact on Algorithmic Complexity
9. Quantum Factoring and Cryptography
9.1 Shor's Algorithm: Revolutionizing Cryptography and Computing
9.2 Post-Quantum Cryptography: An In-Depth Exploration
10. Error Correction and Fault Tolerance in Quantum Computing
10.2 Cat States and Steane Codes
11. Quantum Machine Learning
11.1. Quantum Support Vector Machines
11.2. Quantum Neural Networks
12. Quantum Simulation
12.1. Simulating Physical Systems
13. Quantum Optimization
13.1. Quantum Annealing
13.2. Variational Quantum Eigensolver (VQE)
14. Quantum Hardware Overview
14.1. Superconducting Qubits
14.2. Trapped Ions
14.3. Topological Qubits
15. Quantum Programming Languages
15.1 Qiskit: Unlocking the Potential of Quantum Computing
16. Quantum Computing Platforms
16.1 IBM Q Experience
16.2. Google Quantum AI Lab
16.3. Rigetti Quantum Computing: Pioneering the Quantum Cloud and Beyond
17. Applications in Finance and Economics: Unlocking Quantum Potential in Financial Markets and Economic Modeling
17.1 Portfolio Optimization: Quantum Computing’s Revolutionary Impact
17.2 Option Pricing: The Quantum Revolution
18. Applications in Medicine and Biology: A Quantum Leap Forward
18.1. Drug Discovery: A Quantum Paradigm Shift
18.2 Genetic Sequencing: Leveraging Quantum Algorithms
19. The Future of Quantum Computing—Unveiling the Realm of Infinite Possibilities
19.1 Quantum Supremacy: The Tipping Point of Quantum Computing
19.2 Milestones and Challenges: The Dichotomy Shaping the Quantum Future
20. Quantum Software and Libraries
20.1 Open Source Tools in Quantum Computing
20.2 Commercial Software in Quantum Computing
21. Further Reading and Resources
21.1 Books
22. Glossary of Terms
22.1 Alphabetical List of Terms
22.2 Notation Guide
22.3 About the author