Table of contents

Grover's Algorithm from First Principles

A complete undergraduate path from quantum basics to designing and using quantum search algorithms

Read each section in order. Every title can be opened as a TheoryTrace document.

• Cover
• Copyright
• How to read this book
• Introduction
• Chapter 1: Why Quantum Search Matters
• Chapter 2: Complex Numbers, Vectors, and Inner Products
• Chapter 3: Qubits and Quantum States
• Chapter 4: Measurement and Probability
• Chapter 5: Quantum Gates and Circuits
• Chapter 6: Reversible Computation and Oracles
• Chapter 7: The Unstructured Search Problem
• Chapter 8: Phase Kickback and Phase Oracles
• Chapter 9: Creating the Uniform Superposition
• Chapter 10: The Diffusion Operator
• Chapter 11: One Full Grover Iteration
• Chapter 12: The Geometry of Amplitude Amplification
• Chapter 13: How Many Iterations Are Needed
• Chapter 14: Complexity and the Quadratic Speedup
• Chapter 15: Multiple Solutions and Unknown Solution Counts
• Chapter 16: Building Practical Grover Oracles
• Chapter 17: Worked Example: Searching a Small Space
• Chapter 18: Using Grover in Quantum Programming Frameworks
• Chapter 19: Noise, Hardware Limits, and Real Devices
• Chapter 20: Amplitude Amplification Beyond Search
• Chapter 21: Applications and Misapplications
• Chapter 22: From Grover to Future Quantum Algorithms
• Conclusion